Chem Exp 1

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Pigments in Our Lives Whenever you paint a picture or a room, or use inks or cosmetics, you use pigments. A pigment is a substance that gives a color to another material. Most pigments are a mixture of a powder and a colorless solvent.

On the front cover of this book, you can see examples of inorganic pigments that are obtained from powdered minerals of different chemical elements. Cadmium in cadmium orange, chromium in chrome yellow, cobalt in cobalt violet, iron in red ocher, manganese in manganese purple. However, the elements chromium and cadmium are toxic and have been replaced by nontoxic pigments.

Organic pigments containing chains of the element carbon are obtained from plants and animals. Indigo dye from the plant Indigofera tinctoria is an organic compound with a deep, blue color used to color blue jeans and fabrics. Carbon black is a powdered form of the element carbon used to color plastics, tires, inks, and paints.

Color is seen when a pigment absorbs certain wavelengths of visible light and reflects the remaining wavelengths as a color. For example, a pigment that absorbs red and green light, and reflects the blue wavelengths, has a blue color. If a substance absorbs green light but relects red and blue wavelengths, it appears to have a violet color. A leaf with chlorophyll pigment is green because all wavelengths in sunlight are absorbed except green.

Mastering™ Chemistry is a learning platform designed with you in mind, offering:

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Sixth Edition

Timberlake &

Timberlake

Sixth Edition

ISBN-13: 978-0-13-487811-9 ISBN-10: 0-13-487811-6

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Atomic Masses of the Elements

aValues for atomic masses are given to four significant figures. bValues in parentheses are the mass number of an important radioactive isotope.

Name Symbol Atomic Number Atomic Massa

Actinium Ac 89 (227)b

Aluminum Al 13 26.98 Americium Am 95 (243) Antimony Sb 51 121.8 Argon Ar 18 39.95 Arsenic As 33 74.92 Astatine At 85 (210) Barium Ba 56 137.3 Berkelium Bk 97 (247) Beryllium Be 4 9.012 Bismuth Bi 83 209.0 Bohrium Bh 107 (264) Boron B 5 10.81 Bromine Br 35 79.90 Cadmium Cd 48 112.4 Calcium Ca 20 40.08 Californium Cf 98 (251) Carbon C 6 12.01 Cerium Ce 58 140.1 Cesium Cs 55 132.9 Chlorine Cl 17 35.45 Chromium Cr 24 52.00 Cobalt Co 27 58.93 Copernicium Cn 112 (285) Copper Cu 29 63.55 Curium Cm 96 (247) Darmstadtium Ds 110 (271) Dubnium Db 105 (262) Dysprosium Dy 66 162.5 Einsteinium Es 99 (252) Erbium Er 68 167.3 Europium Eu 63 152.0 Fermium Fm 100 (257) Flerovium Fl 114 (289) Fluorine F 9 19.00 Francium Fr 87 (223) Gadolinium Gd 64 157.3 Gallium Ga 31 69.72 Germanium Ge 32 72.64 Gold Au 79 197.0 Hafnium Hf 72 178.5 Hassium Hs 108 (265) Helium He 2 4.003 Holmium Ho 67 164.9 Hydrogen H 1 1.008 Indium In 49 114.8 Iodine I 53 126.9 Iridium Ir 77 192.2 Iron Fe 26 55.85 Krypton Kr 36 83.80 Lanthanum La 57 138.9 Lawrencium Lr 103 (262) Lead Pb 82 207.2 Lithium Li 3 6.941 Livermorium Lv 116 (293) Lutetium Lu 71 175.0 Magnesium Mg 12 24.31 Manganese Mn 25 54.94 Meitnerium Mt 109 (268)

Name Symbol Atomic Number Atomic Massa

Mendelevium Md 101 (258) Mercury Hg 80 200.6 Molybdenum Mo 42 95.94 Moscovium Mc 115 (289) Neodymium Nd 60 144.2 Neon Ne 10 20.18 Neptunium Np 93 (237) Nickel Ni 28 58.69 Nihonium Nh 113 (286) Niobium Nb 41 92.91 Nitrogen N 7 14.01 Nobelium No 102 (259) Oganesson Og 118 (294) Osmium Os 76 190.2 Oxygen O 8 16.00 Palladium Pd 46 106.4 Phosphorus P 15 30.97 Platinum Pt 78 195.1 Plutonium Pu 94 (244) Polonium Po 84 (209) Potassium K 19 39.10 Praseodymium Pr 59 140.9 Promethium Pm 61 (145) Protactinium Pa 91 231.0 Radium Ra 88 (226) Radon Rn 86 (222) Rhenium Re 75 186.2 Rhodium Rh 45 102.9 Roentgenium Rg 111 (272) Rubidium Rb 37 85.47 Ruthenium Ru 44 101.1 Rutherfordium Rf 104 (261) Samarium Sm 62 150.4 Scandium Sc 21 44.96 Seaborgium Sg 106 (266) Selenium Se 34 78.96 Silicon Si 14 28.09 Silver Ag 47 107.9 Sodium Na 11 22.99 Strontium Sr 38 87.62 Sulfur S 16 32.07 Tantalum Ta 73 180.9 Technetium Tc 43 (99) Tellurium Te 52 127.6 Tennessine Ts 117 (294) Terbium Tb 65 158.9 Thallium Tl 81 204.4 Thorium Th 90 232.0 Thulium Tm 69 168.9 Tin Sn 50 118.7 Titanium Ti 22 47.87 Tungsten W 74 183.8 Uranium U 92 238.0 Vanadium V 23 50.94 Xenon Xe 54 131.3 Ytterbium Yb 70 173.0 Yttrium Y 39 88.91 Zinc Zn 30 65.41 Zirconium Zr 40 91.22

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BASIC CHEMISTRY

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BASIC CHEMISTRY

Sixth Edition

Karen Timberlake William Timberlake

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Library of Congress Cataloging-in-Publication Data

Names: Timberlake, Karen, author. | Timberlake, William, author. Title: Basic chemistry / Karen Timberlake, William Timberlake. Description: Sixth edition. | New York, NY : Pearson, [2019] | Includes index. Identifiers: LCCN 2018048212 | ISBN 9780134878119 Subjects: LCSH: Chemistry--Textbooks. Classification: LCC QD31.3 .T54 2019 | DDC 540--dc23 LC record available at https://lccn.loc.gov/2018048212

ISBN 10: 0-134-87811-6; ISBN 13: 978-0-134-87811-9 (Student edition)

ISBN 10: 0-134-98699-7; ISBN 13: 978-0-13498699-9 (Looseleaf Edition)

ISBN 10: 0-135-24461-7; ISBN 13: 978-0-13524461-6 (NASTA)

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Brief Contents

1 Chemistry in Our Lives 1 2 Chemistry and Measurements 27 3 Matter and Energy 68 4 Atoms and Elements 100 5 Electronic Structure of Atoms and Periodic Trends 125 6 Ionic and Molecular Compounds 156 7 Chemical Quantities 183 8 Chemical Reactions 213 9 Chemical Quantities in Reactions 239 10 Bonding and Properties of Solids and Liquids 269 11 Gases 311 12 Solutions 350 13 Reaction Rates and Chemical Equilibrium 398 14 Acids and Bases 431 15 Oxidation and Reduction 476 16 Nuclear Chemistry 508 17 Organic Chemistry 540 18 Biochemistry 592

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vii

1 Chemistry in Our Lives 1

CAREER Forensic Scientist 1 1.1 Chemistry and Chemicals 2 1.2 Scientific Method: Thinking Like a Scientist 3

CHEMISTRY LINK TO HEALTH Early Chemist: Paracelsus 4

1.3 Studying and Learning Chemistry 6 1.4 Key Math Skills for Chemistry 9 1.5 Writing Numbers in Scientific Notation 17

UPDATE Forensic Evidence Helps Solve the Crime 21

Concept Map 21 Chapter Review 22 Key Terms 22 Key Math Skills 22 Understanding the Concepts 24 Additional Practice Problems 24 Challenge Problems 25 Answers to Engage Questions 25 Answers to Selected Problems 26

2 Chemistry and Measurements 27

CAREER Registered Nurse 27 2.1 Units of Measurement 28 2.2 Measured Numbers and Significant Figures 31 2.3 Significant Figures in Calculations 34 2.4 Prefixes and Equalities 39 2.5 Writing Conversion Factors 42 2.6 Problem Solving Using Unit Conversion 47

CHEMISTRY LINK TO HEALTH Toxicology and Risk–Benefit Assessment 52

Contents

2.7 Density 53 CHEMISTRY LINK TO HEALTH Bone Density 56

UPDATE Greg’s Visit with His Doctor 59

Concept Map 59 Chapter Review 60 Key Terms 61 Key Math Skills 61 Core Chemistry Skills 61 Understanding the Concepts 62 Additional Practice Problems 64 Challenge Problems 65 Answers to Engage Questions 65 Answers to Selected Problems 65

3 Matter and Energy 68

CAREER Dietitian 68 3.1 Classification of Matter 69

CHEMISTRY LINK TO HEALTH Breathing Mixtures 70

3.2 States and Properties of Matter 72 3.3 Temperature 75

CHEMISTRY LINK TO HEALTH Variation in Body Temperature 79

3.4 Energy 79 3.5 Specific Heat 82 3.6 Energy and Nutrition 87

CHEMISTRY LINK TO HEALTH Losing and Gaining Weight 89

UPDATE A Diet and Exercise Program 90

Concept Map 91 Chapter Review 91 Key Terms 92 Core Chemistry Skills 92 Understanding the Concepts 93 Additional Practice Problems 94 Challenge Problems 95 Answers to Engage Questions 96 Answers to Selected Problems 96 Combining Ideas from Chapters 1 to 3 98

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viii Contents

4 Atoms and Elements 100

CAREER Farmer 100 4.1 Elements and Symbols 101 4.2 The Periodic Table 103

CHEMISTRY LINK TO HEALTH Elements Essential to Health 106

4.3 The Atom 108 4.4 Atomic Number and Mass Number 111 4.5 Isotopes and Atomic Mass 113

UPDATE Improving Crop Production 117

Concept Map 118 Chapter Review 118 Key Terms 119 Core Chemistry Skills 119 Understanding the Concepts 120 Additional Practice Problems 121 Challenge Problems 122 Answers to Engage Questions 123 Answers to Selected Problems 123

5 Electronic Structure of Atoms and Periodic Trends 125

CAREER Materials Engineer 125 5.1 Electromagnetic Radiation 126

CHEMISTRY LINK TO HEALTH Biological Reactions to UV Light 128

5.2 Atomic Spectra and Energy Levels 129 5.3 Sublevels and Orbitals 131 5.4 Orbital Diagrams and Electron

Configurations 135 5.5 Electron Configurations and the Periodic

Table 139 5.6 Trends in Periodic Properties 143

UPDATE Developing New Materials for Computer Chips 148

Concept Map 149 Chapter Review 149 Key Terms 150 Core Chemistry Skills 151 Understanding The Concepts 151 Additional Practice Problems 152 Challenge Problems 153 Answers to Engage Questions 153 Answers to Selected Problems 154

6 Ionic and Molecular Compounds 156

CAREER Pharmacist 156 6.1 Ions: Transfer of Electrons 157

CHEMISTRY LINK TO HEALTH Some Important Ions in the Body 161

6.2 Ionic Compounds 161 6.3 Naming and Writing Ionic Formulas 164 6.4 Polyatomic Ions 168 6.5 Molecular Compounds: Sharing Electrons 172

UPDATE Compounds at the Pharmacy 176

Concept Map 177 Chapter Review 177 Key Terms 178 Core Chemistry Skills 178 Understanding the Concepts 179 Additional Practice Problems 179 Challenge Problems 180 Answers to Engage Questions 181 Answers to Selected Problems 181

7 Chemical Quantities 183

CAREER Veterinarian 183 7.1 The Mole 184 7.2 Molar Mass 188 7.3 Calculations Using Molar Mass 190 7.4 Mass Percent Composition 194

CHEMISTRY LINK TO THE ENVIRONMENT Fertilizers 196

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Contents ix

7.5 Empirical Formulas 197 7.6 Molecular Formulas 201

UPDATE Prescriptions for Max 204

Concept Map 204 Chapter Review 205 Key Terms 205 Core Chemistry Skills 205 Understanding the Concepts 207 Additional Practice Problems 207 Challenge Problems 208 Answers to Engage Questions 209 Answers to Selected Problems 209 Combining Ideas from Chapters 4 to 7 211

8 Chemical Reactions 213

CAREER Exercise Physiologist 213 8.1 Equations for Chemical Reactions 214 8.2 Balancing a Chemical Equation 217 8.3 Types of Chemical Reactions 223

CHEMISTRY LINK TO HEALTH Incomplete Combustion: Toxicity of Carbon Monoxide 227

8.4 Oxidation–Reduction Reactions 228 UPDATE Improving Natalie’s Overall Fitness 232

Concept Map 232 Chapter Review 233 Key Terms 233 Core Chemistry Skills 233 Understanding the Concepts 234 Additional Practice Problems 235 Challenge Problems 236 Answers to Engage Questions 237 Answers to Selected Problems 237

9 Chemical Quantities in Reactions 239

CAREER Environmental Scientist 239 9.1 Conservation of Mass 240 9.2 Mole Relationships in Chemical Equations 241 9.3 Mass Calculations for Chemical Reactions 245 9.4 Limiting Reactants 247

9.5 Percent Yield 252 9.6 Energy in Chemical Reactions 254

CHEMISTRY LINK TO HEALTH Cold Packs and Hot Packs 257

UPDATE Testing Water Samples for Insecticides 260

Concept Map 261 Chapter Review 261 Key Terms 262 Core Chemistry Skills 262 Understanding the Concepts 264 Additional Practice Problems 265 Challenge Problems 266 Answers to Engage Questions 267 Answers to Selected Problems 267

10 Bonding and Properties of Solids and Liquids 269

CAREER Histologist 269

10.1 Lewis Structures for Molecules and Polyatomic Ions 270

10.2 Resonance Structures 276 10.3 Shapes of Molecules and Polyatomic Ions

(VSEPR Theory) 279

10.4 Electronegativity and Bond Polarity 283 10.5 Polarity of Molecules 287 10.6 Intermolecular Forces Between Atoms

or Molecules 288

10.7 Changes of State 291 CHEMISTRY LINK TO HEALTH Steam Burns 297

UPDATE Histologist Stains Tissue with Dye 298

Concept Map 299 Chapter Review 299 Key Terms 300 Core Chemistry Skills 301 Understanding the Concepts 303 Additional Practice Problems 304 Challenge Problems 305 Answers to Engage Questions 306 Answers to Selected Problems 306 Combining Ideas from Chapters 8 to 10 309

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11 Gases 311

CAREER Respiratory Therapist 311 11.1 Properties of Gases 312

CHEMISTRY LINK TO HEALTH Measuring Blood Pressure 316

11.2 Pressure and Volume (Boyle’s Law) 317 CHEMISTRY LINK TO HEALTH Pressure–Volume Relationship in Breathing 318

11.3 Temperature and Volume (Charles’s Law) 320 11.4 Temperature and Pressure (Gay-Lussac’s

Law) 322 11.5 The Combined Gas Law 325 11.6 Volume and Moles (Avogadro’s Law) 327 11.7 The Ideal Gas Law 329 11.8 Gas Laws and Chemical Reactions 334 11.9 Partial Pressures (Dalton’s Law) 335

CHEMISTRY LINK TO HEALTH Blood Gases 337

CHEMISTRY LINK TO HEALTH Hyperbaric Chambers 340

UPDATE Exercise-Induced Asthma 341

Concept Map 342 Chapter Review 342 Key Terms 343 Core Chemistry Skills 344 Understanding the Concepts 345 Additional Practice Problems 346 Challenge Problems 347 Answers to Engage Questions 347 Answers to Selected Problems 348

12 Solutions 350

CAREER Dialysis Nurse 350 12.1 Solutions 351

CHEMISTRY LINK TO HEALTH Water in the Body 352

12.2 Electrolytes and Nonelectrolytes 355 CHEMISTRY LINK TO HEALTH Electrolytes in Body Fluids 356

12.3 Solubility 357 CHEMISTRY LINK TO HEALTH Gout and Kidney Stones: Saturation in Body Fluids 358

12.4 Solution Concentrations 363 12.5 Dilution of Solutions 371 12.6 Chemical Reactions in Solution 374 12.7 Molality and Freezing Point Lowering/Boiling

Point Elevation 378 12.8 Properties of Solutions: Osmosis 385

CHEMISTRY LINK TO HEALTH Hemodialysis and the Artificial Kidney 387

UPDATE Using Dialysis for Renal Failure 388

Concept Map 389 Chapter Review 389 Key Terms 390 Core Chemistry Skills 391 Understanding the Concepts 392 Additional Practice Problems 393 Challenge Problems 395 Answers to Engage Questions 396 Answers to Selected Problems 396

13 Reaction Rates and Chemical Equilibrium 398

CAREER Chemical Oceanographer 398 13.1 Rates of Reactions 399 13.2 Chemical Equilibrium 403 13.3 Equilibrium Constants 406 13.4 Using Equilibrium Constants 410 13.5 Changing Equilibrium Conditions:

Le Châtelier’s Principle 414 CHEMISTRY LINK TO HEALTH Oxygen– Hemoglobin Equilibrium and Hypoxia 417

CHEMISTRY LINK TO HEALTH Homeostasis: Regulation of Body Temperature 419

13.6 Equilibrium in Saturated Solutions 420 UPDATE Equilibrium of CO2 in the Ocean 424

Concept Map 424 Chapter Review 425 Key Terms 425 Core Chemistry Skills 426 Understanding the Concepts 427 Additional Practice Problems 428 Challenge Problems 429 Answers to Engage Questions 429 Answers to Selected Problems 430

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Contents xi

14 Acids and Bases 431

CAREER Medical Laboratory Technologist 431 14.1 Acids and Bases 432 14.2 Brønsted–Lowry Acids and Bases 434 14.3 Strengths of Acids and Bases 437 14.4 Dissociation of Weak Acids and Bases 442 14.5 Dissociation of Water 444 14.6 The pH Scale 447

CHEMISTRY LINK TO HEALTH Stomach Acid, HCl 453

14.7 Reactions of Acids and Bases 454 CHEMISTRY LINK TO HEALTH Antacids 456

14.8 Acid–Base Titration 457 14.9 Buffers 459

CHEMISTRY LINK TO HEALTH Buffers in the Blood Plasma 462

UPDATE Acid Reflux Disease 463

Concept Map 464 Chapter Review 465 Key Terms 466 Key Math Skills 466 Core Chemistry Skills 467 Understanding the Concepts 468 Additional Practice Problems 468 Challenge Problems 469 Answers to Engage Questions 470 Answers to Selected Problems 471 Combining Ideas from Chapters 11 to 14 473

15 Oxidation and Reduction 476

CAREER Dentist 476 15.1 Oxidation and Reduction 477 15.2 Balancing Oxidation–Reduction Equations

Using Half-Reactions 483 15.3 Electrical Energy from Oxidation– Reduction

Reactions 488 CHEMISTRY LINK TO THE ENVIRONMENT Corrosion: Oxidation of Metals 494

CHEMISTRY LINK TO THE ENVIRONMENT Fuel Cells: Clean Energy for the Future 496

15.4 Oxidation–Reduction Reactions That Require Electrical Energy 497 UPDATE Whitening Kimberly’s Teeth 499

Concept Map 500 Chapter Review 500 Key Terms 501 Core Chemistry Skills 501 Understanding the Concepts 502 Additional Practice Problems 503 Challenge Problems 504 Answers to Engage Questions 505 Answers to Selected Problems 505

16 Nuclear Chemistry 508

CAREER Radiation Technologist 508 16.1 Natural Radioactivity 509 16.2 Nuclear Reactions 512

CHEMISTRY LINK TO HEALTH Radon in Our Homes 514

16.3 Radiation Measurement 519 CHEMISTRY LINK TO HEALTH Radiation and Food 520

16.4 Half-Life of a Radioisotope 522 CHEMISTRY LINK TO THE ENVIRONMENT Dating Ancient Objects 524

16.5 Medical Applications Using Radioactivity 526 CHEMISTRY LINK TO HEALTH Brachytherapy 528

16.6 Nuclear Fission and Fusion 529 UPDATE Cardiac Imaging Using a Radioisotope 532

Concept Map 532 Chapter Review 533 Key Terms 533 Core Chemistry Skills 534 Understanding the Concepts 534 Additional Practice Problems 535 Challenge Problems 536 Answers to Engage Questions 536 Answers to Selected Problems 537 Combining Ideas from Chapters 15 and 16 538

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xii Contents

17 Organic Chemistry 540

CAREER Firefighter/Emergency Medical Technician 540

17.1 Alkanes 541 17.2 Alkenes, Alkynes, and Polymers 551

CHEMISTRY LINK TO HEALTH Hydrogenation of Unsaturated Fats 554

17.3 Aromatic Compounds 557 CHEMISTRY LINK TO HEALTH Some Common Aromatic Compounds 559

CHEMISTRY LINK TO HEALTH Polycyclic Aromatic Hydrocarbons (PAHs) 560

17.4 Alcohols and Ethers 560 CHEMISTRY LINK TO HEALTH Some Important Alcohols, Phenols, and Ethers 562

17.5 Aldehydes and Ketones 564 CHEMISTRY LINK TO HEALTH Some Important Aldehydes and Ketones 567

17.6 Carboxylic Acids and Esters 568 CHEMISTRY LINK TO HEALTH Carboxylic Acids in Metabolism 570

17.7 Amines and Amides 575 CHEMISTRY LINK TO THE ENVIRONMENT Alkaloids: Amines in Plants 576

UPDATE Diane’s Treatment in the Burn Unit 580

Concept Map 581 Chapter Review 581 Summary of Naming 582 Summary of Reactions 583 Key Terms 583 Core Chemistry Skills 584 Understanding the Concepts 585 Additional Practice Problems 585 Challenge Problems 587 Answers to Engage Questions 588 Answers to Selected Problems 588

18 Biochemistry 592

CAREER Diabetes Nurse 592 18.1 Carbohydrates 593

CHEMISTRY LINK TO HEALTH Hyperglycemia and Hypoglycemia 595

18.2 Disaccharides and Polysaccharides 598 CHEMISTRY LINK TO HEALTH How Sweet is My Sweetener? 600

18.3 Lipids 605 18.4 Amino Acids and Proteins 612

CHEMISTRY LINK TO HEALTH Essential Amino Acids and Complete Proteins 615

18.5 Protein Structure 617 18.6 Proteins as Enzymes 622 18.7 Nucleic Acids 624 18.8 Protein Synthesis 629

UPDATE Kate’s Program for Type 2 Diabetes 633

Concept Map 634 Chapter Review 635 Key Terms 636 Core Chemistry Skills 637 Understanding the Concepts 638 Additional Practice Problems 639 Challenge Problems 640 Answers to Engage Questions 641 Answers to Selected Problems 642 Combining Ideas from Chapters 17 and 18 645

Credits C-1

Glossary/Index I-1

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xiii

KEY MATH SKILLS Identifying Place Values 10 Using Positive and Negative Numbers in Calculations 11 Calculating Percentages 12 Solving Equations 13 Interpreting Graphs 14 Writing Numbers in Scientific Notation 17 Rounding Off 35 Calculating pH from [H3O

+] 449 Calculating [H3O

+] from pH 452

CORE CHEMISTRY SKILLS Counting Significant Figures 31 Using Significant Figures in Calculations 36 Using Prefixes 39 Writing Conversion Factors from Equalities 42 Using Conversion Factors 49 Using Density as a Conversion Factor 55 Identifying Physical and Chemical Changes 74 Converting Between Temperature Scales 76 Using Energy Units 80 Calculating Specific Heat 83 Using the Heat Equation 83 Counting Protons and Neutrons 111 Writing Atomic Symbols for Isotopes 113 Calculating Atomic Mass 115 Writing Electron Configurations 136 Using the Periodic Table to Write Electron

Configurations 140 Identifying Trends in Periodic Properties 144 Writing Positive and Negative Ions 158 Writing Ionic Formulas 163 Naming Ionic Compounds 164 Writing the Names and Formulas for Molecular

Compounds 173 Converting Particles to Moles 184 Calculating Molar Mass 188 Using Molar Mass as a Conversion Factor 190 Calculating Mass Percent Composition 195 Calculating an Empirical Formula 197 Calculating a Molecular Formula 202 Balancing a Chemical Equation 217 Classifying Types of Chemical Reactions 223 Identifying Oxidized and Reduced Substances 229 Using Mole–Mole Factors 242

Applications and Activities

Converting Grams to Grams 245 Calculating Quantity of Product from a Limiting

Reactant 248 Calculating Percent Yield 252 Using the Heat of Reaction 256 Drawing Lewis Symbols 270 Drawing Lewis Structures 271 Drawing Resonance Structures 276 Predicting Shape 279 Using Electronegativity 284 Identifying Polarity of Molecules 287 Identifying Intermolecular Forces 288 Calculating Heat for Change of State 292 Using the Gas Laws 317 Using the Ideal Gas Law 330 Calculating Mass or Volume of a Gas in a Chemical

Reaction 334 Calculating Partial Pressure 336 Using Solubility Rules 360 Calculating Concentration 363 Using Concentration as a Conversion Factor 365 Calculating the Quantity of a Reactant or Product

for a Chemical Reaction in Solution 375 Calculating the Freezing Point/Boiling Point of a

Solution 381 Writing the Equilibrium Expression 406 Calculating an Equilibrium Constant 407 Calculating Equilibrium Concentrations 412 Using Le Châtelier’s Principle 415 Writing the Solubility Product Expression 420 Calculating a Solubility Product Constant 421 Calculating the Molar Solubility 423 Identifying Conjugate Acid–Base Pairs 436 Calculating [H3O

+] and [OH-] in Solutions 446 Writing Equations for Reactions of Acids

and Bases 455 Calculating Molarity or Volume of an Acid or Base

in a Titration 457 Calculating the pH of a Buffer 460 Assigning Oxidation Numbers 478 Using Oxidation Numbers 480 Identifying Oxidizing and Reducing Agents 481 Using Half-Reactions to Balance Redox Equations 483 Identifying Spontaneous Reactions 488 Writing Nuclear Equations 512 Using Half-Lives 523 Naming and Drawing Alkanes 544

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xiv Applications and Activities

Writing Equations for Hydrogenation and Polymerization 553

Naming Aldehydes and Ketones 565 Naming Carboxylic Acids 569 Forming Esters 571 Forming Amides 577 Drawing Haworth Structures 595 Identifying Fatty Acids 605 Drawing Structures for Triacylglycerols 607 Drawing the Structure for an Amino Acid at

Physiological pH 613 Identifying the Primary, Secondary, Tertiary, and

Quaternary Structures of Proteins 620 Writing the Complementary DNA Strand 626 Writing the mRNA Segment for a DNA Template 630 Writing the Amino Acid for an mRNA Codon 631

Interactive Videos Solving Equations 14 Conversion Factors 48 Chemical vs. Physical Changes 75 Rutherford’s Gold-Foil Experiment 109 Isotopes and Atomic Mass 116 Naming and Writing Ionic Formulas 167 Drawing Lewis Structures with Multiple Bonds 275 Kinetic Molecular Theory 312 Solutions 374 Calculations Involving Solutions in Reactions 376 Acid–Base Titration 458 Calculation the pH of a Buffer 460 Writing Equations for an Isotope Produced by

Bombardment 519 Half-Lives 525 Naming Alkanes 547 Haworth Structures of Monosaccharides 596 Amino Acids at Physiological pH 613 Different Levels of Protein Structure 621 Protein Synthesis 630

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KAREN TIMBERLAKE is Professor Emerita of Chemistry at Los Angeles Valley College, where she taught chemistry for allied health and preparatory chemistry for 36 years. She received her bachelor’s degree in chemistry from the University of Washington and her master’s degree in biochemistry from the University of California at Los Angeles.

Professor Timberlake has been writing chemistry textbooks for more than 40 years. During that time, her name has become associated with the strategic use of pedagogical tools that promote student success in chemistry and the application of chemistry to real-life situations. More than one million students have learned chemistry using texts, laboratory manuals, and study guides written by Karen Timberlake. In addition to Basic Chemistry, sixth edition, she is also the author of General, Organic, and Biological Chemistry: Structures of Life, sixth edition, with the accompanying Study Guide and Selected Solutions Manual, and Chemistry: An Introduction to General, Organic, and Biological Chemistry, thirteenth edition, with the accompanying Study Guide and Selected Solutions Manual, Laboratory Manual, and Essential Laboratory Manual.

Professor Timberlake belongs to numerous scientific and educational organizations including the American Chemical

About the Authors

Society (ACS) and the National Science Te a c h e r s A s s o c i a t i o n ( N S TA ) . S h e has been the Western Regional Winner of Excellence in College Chemistry Teaching Award given by the Chemical Manufacturers Association. She received the McGuffey Award in Physical Sciences from the Textbook Authors Association for her textbook Chemistry: An Introduction to General, Organic, and Biological Chemistry, eighth edition. She received the “Texty” Textbook Excellence Award from the Textbook Authors Association for the first edition of Basic Chemistry. She has participated in education grants for science teaching including the Los Angeles Collaborative for Teaching Excellence (LACTE) and a Title III grant

at her college. She speaks at conferences and educational meetings on the use of student-centered teaching methods in chemistry to promote the learning success of students.

Her husband, William Timberlake, who is the coauthor of this text, is Professor Emeritus of Chemistry at Los Angeles Harbor College, where he taught preparatory and organic chemistry for 36 years. He received his bachelor’s degree in chemistry from Carnegie Mellon University and his master’s degree in organic chemistry from the University of California at Los Angeles.

When the Professors Timberlake are not writing textbooks, they relax by playing tennis, ballroom dancing, hiking, traveling, trying new restaurants, cooking, and enjoying care of their grandchildren, Daniel and Emily.

DEDICATION • Our son, John, daughter-in-law, Cindy, grandson, Daniel,

and granddaughter, Emily, for the precious things in life

• The wonderful students over many years whose hard work and commitment always motivated us and put purpose in our writing

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W elcome to the sixth edition of Basic Chemistry. This chemistry text was written and designed to prepare you for science-related professions, such as

engineering, nursing, medicine, environmental or agricultural science, or for careers such as laboratory technology. This text assumes no prior knowledge of chemistry. Our main objective in writing this text is to make the study of chemistry an engaging and positive experience for you by relating the structure and behavior of matter to real life. This new edition introduces more problem-solving strategies, Analyze the Problem with Connect features, Try It First and Engage features, and conceptual and challenge problems.

It is our goal to help you become a critical thinker by understanding scientific concepts that will form a basis for making important decisions about issues concerning health and the environment. Thus, we have utilized materials that

• help you to learn and enjoy chemistry • relate chemistry to careers that interest you • develop problem-solving skills • promote learning and success in chemistry

Active Reading Features for Successful Learning In this sixth edition of Basic Chemistry, we have increased our emphasis on providing features that promote student interaction with the textual content. We continue to develop features based on new research on learning theory and extend them throughout the text as a part of our study plan Strategies and Practices for Active Reading in Chemistry (SPARC).

With the success of students involved in active learning in the classroom, we see the opportunity to develop a parallel plan of reading and learning experiences using our textbook. As chemistry textbook authors we are interested in connecting cognitive science and learning research to improve student reading and learning. SPARC is the combination of utilizing reading strategies that increase learning and success in chemistry.

Strategies for Learning New Information

1. Combine graphics with words Students improve learning by receiving information in different ways. In this text, we combine text and ques- tions with illustrations using macro-to-micro art, tables, graphs, diagrams, videos, photos, and concept maps.

2. Connect abstract concepts with concrete representations New concepts are illustrated and explained with real-life examples, career stories and updates, Chemical Links to Health and the Environment, and Applications. Prompts of Key Math Skills and Core Chemistry Skills alert stu- dents to the fundamental ideas in each chapter.

Strategies for Connecting New Information

3. Ask inquiring questions Engage questions throughout each chapter ask students “why,” “how,” and “what if,” requiring them to link new information with prior knowledge.

4. Alternate problems containing solutions with similar problems that students must solve Many Sample Problems with Try It First reminders throughout each chapter contain step-by-step solutions that guide students through the process of problem-solving. An abundance of Practice Problems, Understanding the Concepts, Additional Problems, and Challenge Problems provide students with similar problem-solving experience. Answers are provided for immediate feedback.

Strategies for Recalling and Retrieving Information

5. Provide opportunities to practice recall and retrieval Throughout each chapter, students are encouraged to prac- tice the recall and retrieval of material by repeating practice every few days, weeks, and even months using Self Tests, Practice Problems, Understanding the Concepts, Additional Problems, and Challenge Problems. Review prompts remind students of key ideas in previous chapters.

6. Combine different but related topics and skills Better learning can be achieved by alternating different topics and types of content. In this text, problem sets including Understanding the Concepts, Additional Practice Problems, Challenge Problems, and Combining Ideas provide students practice of different topics or skills, rather than focusing on one topic or skill.

7. Assess to maintain and improve retention Every chapter provides many types of assessment such as Self Tests, Practice Problems, Understanding the Concepts, Additional Practice Problems, Challenge Problems, and Combining Ideas. By practicing informa- tion retrieval, checking progress, and reviewing, students improve their success on exams.

Preface

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xviii Preface

New and Updated for the Sixth Edition New and updated features have been added throughout this sixth edition, including the following:

• NEW! Chapter Openers provide timely examples and engaging, topical examples of the chemistry that is part of contemporary professions.

• NEW! Chapter Openers include references to new Update features at the end of the chapter that continue the story.

• NEW! Review heads are now listed at the beginning of each section to emphasize the Key Math Skills and Core Chemistry Skills from previous chapters required for learning new chemistry principles.

• NEW! Pictorial Representations using photos and graphs are added to increase the understanding of new topics.

• NEW! Sample Problems show Steps to guide the stu- dent through problem solving.

• NEW! Self Test icons in Sample Problems encourage students to use problem-solving strategies immediately as they review the content in a section.

• NEW! Expanded Self Test questions in Sample Problems provide students with additional self-testing practice.

• NEW! Margin icons Practice Problems encourage stu- dents to work related Practice Problems and self-assess as they study.

• NEW! Expanded Engage Questions and Answers are included in the chapter.

• NEW! Additional Practice Problems and Challenge Problems are added to help student practice testing and increase understanding of the concepts in the chapter.

• NEW! Three-Dimensional Representations, including ball-and-stick and space-filling models, are included to illustrate the shapes of molecules and polyatomic ions.

• NEW! Foreground colors in color palette are now ADA accessible.

• NEW! Multiple art pieces contain separate captions in boxes for each art.

• NEW! Concept Maps are tinted with color screens for emphasis of topics.

• NEW! Interactive Videos are added to illustrate more step-by-step problem-solving strategies.

Chapter Organization of the Sixth Edition In each textbook we write, we consider it essential to relate every chemical concept to real-life issues. Because a chemistry course may be taught in different time frames, it may be difficult to cover all the chapters in this text. However, each chapter is a complete package, which allows some chapters to be skipped or the order of presentation to be changed.

Chapter 1, Chemistry in Our Lives, discusses the Scientific Method in everyday terms and guides students in developing a study plan for learning chemistry, with a section of Key Math Skills that reviews the basic math, including scientific notation, needed in chemistry calculations.

• The Chapter Opener tells the story of a murder and features the work and career of forensic scientists.

• The Update feature describes the forensic evidence that helps to solve the murder and includes Applications.

• An updated Section 1.3, Studying and Learning Chemistry, expands the discussion of study strategies that improve learning and understanding of content.

• A new Decimal Place Value Chart is added in Section 1.4, Key Math Skills for Chemistry, to clarify decimal place values.

• In Section 1.4, Interpreting Graphs, the format for the x and y axes is standardized.

• Key Math Skills are: Identifying Place Values, Using Positive and Negative Numbers in Calculations, Calculating Percentages, Solving Equations, Interpreting Graphs, and Writing Numbers in Scientific Notation.

Chapter 2, Chemistry and Measurements, looks at measurement and emphasizes the need to understand numeri- cal relationships of the metric system. Significant figures are discussed in the determination of final answers. Prefixes from the metric system are used to write equalities and conversion factors for problem-solving strategies. Density is discussed and used as a conversion factor.

• The Chapter Opener tells the story of a patient with high blood pressure and features the work and career of a reg- istered nurse.

• The Update describes the patient’s status and follow-up visit with his doctor.

• In Section 2.5, conversion factors with multiple units are added in the Practice Problems.

• In Section 2.6, Steps as guides to problem solving are added to Sample Problems 2.3, 2.4, and 2.5.

• In Section 2.6, a new type of Sample Problem and new Practice Problems for the conversion of units in a frac- tion are added.

• Sample Problems relate problem solving to health- related topics such as the measurements of blood volume, omega-3 fatty acids, radiological imaging, body fat, cholesterol, and medication orders.

• Applications feature questions about measurements, daily values for minerals and vitamins, and equalities and conversion factors for medications.

• Key Math Skill is: Rounding Off. • Core Chemistry Skills are: Counting Significant Figures,

Using Significant Figures in Calculations, Using Prefixes, Writing Conversion Factors from Equalities, Using Con- version Factors, and Using Density as a Conversion Factor.

Chapter 3, Matter and Energy, classifies matter and states of matter, describes temperature measurement, and discusses energy, specific heat, and energy in nutrition. Physical and

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Preface xix

chemical properties and physical and chemical changes are discussed.

• The Chapter Opener describes diet and exercise for an overweight adolescent at risk for type 2 diabetes and fea- tures the work and career of a dietitian.

• The Update describes the diet prepared with a dietitian for weight loss.

• Figures of Decomposition of Salt, and Separation of Mixtures by Filtration are moved to Section 3.2 for clarity of content.

• In Section 3.5, Specific Heat, a new Sample Problem using heat exchange data is added along with new Practice Problems.

• Practice Problems and Sample Problems include high temperatures used in cancer treatment, the energy pro- duced by a high-energy shock output of a defibrillator, body temperature lowering using a cooling cap, ice bag therapy for muscle injury, dental implants, and energy values for food.

• Core Chemistry Skills are: Identifying Physical and Chemical Changes, Converting Between Temperature Scales, Using Energy Units, Calculating Specific Heat, and Using the Heat Equation.

• The interchapter problem set, Combining Ideas from Chapters 1 to 3, completes the chapter.

Chapter 4, Atoms and Elements, introduces elements and atoms and the periodic table. The names and symbols for the newest elements 113, Nihonium, Nh, 115, Moscovium, Mc, 117, Tennessine, Ts, and 118, Oganesson, Og, are included on the periodic table. Atomic numbers and mass numbers are deter- mined for isotopes. Atomic mass is calculated using the masses of the naturally occurring isotopes and their abundances.

• The Chapter Opener and Update discuss the improve- ment in crop production and feature the work and career of a farmer.

• Atomic number and mass number are used to calculate the number of protons and neutrons in an atom.

• The number of protons and neutrons are used to calculate the mass number and to write the atomic symbol for an isotope.

• Figure 4.3 now includes Francium (Fr) in Group 1A (1), and Figure 4.4 now includes Tennessine (Ts).

• Core Chemistry Skills are: Counting Protons and Neutrons, Writing Atomic Symbols for Isotopes, and Calculating Atomic Mass.

Chapter 5, Electronic Structure of Atoms and Periodic Trends, uses the electromagnetic spectrum to explain atomic spectra and develop the concept of energy levels and sublevels. Electrons in sublevels and orbitals are represented using orbital diagrams and electron configurations. Periodic properties of elements, including atomic size, ionization energy and metallic character, are related to their valence electrons. Small periodic tables illustrate the trends of periodic properties.

• The Chapter Opener and Update discuss the development of new products of metals, plastics, and semiconductors, and career of a materials engineer.

• The electromagnetic spectrum is described with everyday examples and a diagram.

• The three-dimensional representations of the s, p, and d orbitals are drawn.

• The trends in periodic properties are described for valence electrons, atomic size, ionization energy, and metallic character.

• A photo of infrared radiation used to keep food warm, and a photo of gamma knife radiation used to kill cancer cells are added.

• Table 5.2 for electron capacity in sublevels is reordered with Energy Level n = 1 at the top and Energy Level n = 4 at the bottom.

• Core Chemistry Skills are: Writing Electron Configurations, Using the Periodic Table to Write Electron Configurations, and Identifying Trends in Periodic Properties.

Chapter 6, Ionic and Molecular Compounds, describes the formation of ionic and covalent bonds. Chemical formulas are written, and ionic compounds—including those with poly- atomic ions—and molecular compounds are named.

• The Chapter Opener describes the chemistry of aspirin and features the work and career of a pharmacist.

• The Update describes several types of compounds at a pharmacy and includes Applications.

• New art is added or updated to provide everyday exam- ples of the content.

• New material on polyatomic ions compares the names of ate ions and ite ions, the charge of sulfate and sulfite, phosphate and phosphite, carbonate and hydrogen carbonate, and the formulas and charges of halogen polyatomic ions with oxygen.

• Core Chemistry Skills are: Writing Positive and Negative Ions, Writing Ionic Formulas, Naming Ionic Compounds, and Writing the Names and Formulas for Molecular Compounds.

Chapter 7, Chemical Quantities, discusses Avogadro’s number, the mole, and molar masses of compounds, which are used in calculations to determine the mass or number of parti- cles in a quantity of a substance. The mass percent composition of a compound is calculated and used to determine its empiri- cal and molecular formula.

• The Chapter Opener and Update describe the diagno- sis and treatment of a pet and the work and career of a veterinarian.

• Core Chemistry Skills are: Converting Particles to Moles, Calculating Molar Mass, Using Molar Mass as a Conversion Factor, Calculating Mass Percent Composi- tion, Calculating an Empirical Formula, and Calculating a Molecular Formula.

• The interchapter problem set, Combining Ideas from Chapters 4 to 7, completes the chapter.

Chapter 8, Chemical Reactions, shows students how to balance chemical equations, and discusses how to classify chemical reactions into types: combination, decomposition, single replacement, double replacement, combustion, and oxidation–reduction.

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xx Preface

• The Chapter Opener and Update discuss tests and treatment for emphysema and the work and career of an exercise physiologist.

• Core Chemistry Skills are: Balancing a Chemical Equation, Classifying Types of Chemical Reactions, and Identifying Oxidized and Reduced Substances.

Chapter 9, Chemical Quantities in Reactions, describes the mole and mass relationships among the reactants and prod- ucts and provides calculations of limiting reactants and percent yields. The chapter concludes with a discussion of energy in reactions.

• The Chapter Opener describes insecticides and pharma- ceuticals used on a ranch and discusses the career of an environmental scientist.

• The Update describes the collection of soil and water samples for testing for insecticides.

• Mole and mass relationships among the reactants and products are examined along with calculations of percent yield and limiting reactants.

• Material including new problems with three equations and calculations using Hess’s Law is rewritten for clarity.

• Core Chemistry Skills are: Using Mole–Mole Factors, Converting Grams to Grams, Calculating Quantity of Product from a Limiting Reactant, Calculating Percent Yield, and Using the Heat of Reaction.

Chapter 10, Bonding and Properties of Solids and Liquids, introduces Lewis structures for molecules and ions with single and multiple bonds as well as resonance structures. Electronegativity leads to a discussion of the polarity of bonds and molecules. Lewis structures and VSEPR theory illustrate covalent bonding and the three-dimensional shapes of molecules and ions. The intermolecular forces between particles and their impact on states of matter and changes of state are described. The energy involved with changes of state is calculated.

• The Chapter Opener and Update describe the process- ing of a tissue sample and the work and career of a histologist.

• New three-dimensional representations of ball-and-stick models and space-filling models are added to illustrate shapes of molecules and polyatomic ions.

• Lewis structures are drawn for molecules and ions with single, double, and triple bonds. Resonance structures are drawn if two or more Lewis structures are possible.

• Shapes and polarity of bonds and molecules are predicted using VSEPR theory.

• Intermolecular forces in compounds are discussed including ionic bonds, hydrogen bonds, dipole–dipole attractions, and dispersion forces.

• Core Chemistry Skills are: Drawing Lewis Symbols, Drawing Lewis Structures, Drawing Resonance Structures, Predicting Shape, Using Electronegativity, Identifying Polarity of Molecules, Identifying Intermolecular Forces, and Calculating Heat for Change of State.

• The interchapter problem set, Combining Ideas from Chapters 8 to 10, completes the chapter.

Chapter 11, Gases, discusses the properties of gases and calculates changes in gases using the gas laws: Boyle’s, Charles’s, Gay-Lussac’s, Avogadro’s, Dalton’s, and the Ideal Gas Law. Problem-solving strategies enhance the discussion and calculations with gas laws including chemical reactions using the ideal gas law.

• The Chapter Opener and Update feature the work and career of a respiratory therapist, who uses oxygen to treat a child with asthma.

• Applications include calculations of mass or pressure of oxygen in uses of hyperbaric chambers.

• Core Chemistry Skills are: Using the Gas Laws, Using the Ideal Gas Law, Calculating Mass or Volume of a Gas in a Chemical Reaction, and Calculating Partial Pressure.

Chapter 12, Solutions, describes solutions, electrolytes, saturation and solubility, insoluble salts, concentrations, and osmosis. The concentrations of solutions are used to determine volume or mass of solute. The volumes and molarities of solutions are used in calculations for dilutions and titration. Properties of solutions, freezing and boiling points, osmosis, and dialysis are discussed.

• The Chapter Opener describes a patient with kidney failure and dialysis treatment and features the work and career of a dialysis nurse.

• The Update discusses dialysis treatment and electrolyte levels in the dialysate fluid.

• A new example of suspensions used to purify water in treatment plants is added.

• New art illustrates the freezing point decrease and boil- ing point increase for aqueous solutions with increasing number of moles of solute in one kilogram of water.

• Core Chemistry Skills are: Using Solubility Rules, Calcu- lating Concentration, Using Concentration as a Conversion Factor, Calculating the Quantity of a Reactant or Product for a Chemical Reaction in Solution, and Calculating the Freezing Point/Boiling Point of a Solution.

Chapter 13, Reaction Rates and Chemical Equilibrium, looks at the rates of reactions and the equilibrium condition when forward and reverse rates for a reaction become equal. Equilibrium expressions for reactions are written and equilib- rium constants are calculated. The equilibrium constant is used to calculate the concentration of a reactant or product at equi- librium. Le Châtelier’s principle is used to evaluate the impact on concentrations when stress is placed on a system at equi- librium. The concentrations of solutes in a solution is used to calculate the solubility product constant (Ksp).

• The Chapter Opener and Update discuss the equilibrium of CO2 in the ocean and feature the work and career of a chemical oceanographer.

• Core Chemistry Skills are: Writing the Equilibrium Expression, Calculating an Equilibrium Constant, Calculating Equilibrium Concentrations, Using Le Châtelier’s Principle, Writing the Solubility Product Expression, Calculating a Solubility Product Constant, and Calculating the Molar Solubility.

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Chapter 14, Acids and Bases, discusses acids and bases and their strengths, and conjugate acid–base pairs. The dissociation of strong and weak acids and bases is related to their strengths as acids or bases. The dissociation of water leads to the water dissociation expression, Kw, the pH scale, and the calculation of pH. Chemical equations for acids in reactions are balanced and titration of an acid is illustrated. Buffers are discussed along with their role in the blood. The pH of a buffer is calculated.

• The Chapter Opener describes a blood sample for an emergency room patient sent to the clinical laboratory for analysis of blood pH and CO2 gas and describes the work and career of a medical laboratory technologist.

• The Update describes the symptoms and treatment for acid reflux disease (GERD).

• Key Math Skills are: Calculating pH from [H3O +], and

Calculating [H3O +] from pH.

• Core Chemistry Skills are: Identifying Conjugate Acid– Base Pairs, Calculating [H3O

+] and [OH-] in Solutions, Writing Equations for Reactions of Acids and Bases, Calculating Molarity or Volume of an Acid or Base in a Titration, and Calculating the pH of a Buffer.

• The interchapter problem set, Combining Ideas from Chapters 11 to 14, completes the chapter.

Chapter 15, Oxidation and Reduction, looks at the characteristics of oxidation and reduction reactions. Oxidation numbers are assigned to the atoms in elements, molecules, and ions to determine the components that lose electrons during oxidation and gain electrons during reduction. The half-reaction method is utilized to balance oxidation–reduction reactions. The production of electrical energy in voltaic cells and the requirement of electrical energy in electrolytic cells are diagrammed using half-cells. The activity series is used to determine the spotaneous direction of an oxidation–reduction reaction.

• The Chapter Opener and Update discuss the reactions involved in teeth whitening and the work and career of a dentist.

• New material and art on lithium-ion batteries is added. • Core Chemistry Skills are: Assigning Oxidation Numbers,

Using Oxidation Numbers, Identifying Oxidizing and Reducing Agents, Using Half-Reactions to Balance Redox Equations, and Identifying Spontaneous Reactions.

Chapter 16, Nuclear Chemistry, looks at the types of radiation emitted from the nuclei of radioactive atoms. Nuclear equations are written and balanced for both naturally occurring radioactivity and artificially produced radioactivity. The half- lives of radioisotopes are discussed, and the amount of time for a sample to decay is calculated. Radioisotopes important in the field of nuclear medicine are described. Fission and fusion and their role in energy production are discussed.

• The Chapter Opener and Update describe a stress test using a radioactive isotope and feature the work and career of a radiation technologist.

• Core Chemistry Skills are: Writing Nuclear Equations, and Using Half-Lives.

• The interchapter problem set, Combining Ideas from Chapters 15 and 16, completes the chapter.

Chapter 17, Organic Chemistry, compares inorganic and organic compounds, and describes the condensed structural and line-angle formulas of alkanes, alkenes, alcohols, ethers, aldehydes, ketones, carboxylic acids, esters, amines, and amides.

• The Chapter Opener and Update describe emergency treatment for burns and feature the work and career of a firefighter/emergency medical technician.

• The properties of organic and inorganic compounds are compared in Table 17.1.

• Line-angle formulas are added to Table 17.2 IUPAC Names and Formulas of the First 10 Alkanes.

• More line-angle structures are included in text examples, sample problems, questions, and problems.

• The two-dimensional and three-dimensional repre- sentations of methane and ethane are illustrated using condensed structural formulas, expanded structural for- mulas, ball-and-stick models, space-filling models, and wedge–dash models.

• Core Chemistry Skills are: Naming and Drawing Alkanes, Writing Equations for Hydrogenation and Polymeriza- tion, Naming Aldehydes and Ketones, Naming Carboxylic Acids, Forming Esters, and Forming Amides.

Chapter 18, Biochemistry, looks at the chemical structures and reactions of chemicals that occur in living systems. We focus on four types of biomolecules—carbohydrates, lipids, proteins, and nucleic acids—as well as their biochemical reactions.

• The Chapter Opener and Update describe diagnosis and treatment of diabetes and feature the work and career of a diabetes nurse.

• Monosaccharides are classified as aldo or keto pentoses or hexoses.

• Haworth structures are drawn for monosaccharides, disaccharides, and polysaccharides.

• The shapes of proteins are related to the activity and regulation of enzyme activity.

• The genetic code is described and utilized in the process of protein synthesis.

• Core Chemistry Skills are: Drawing Haworth Structures, Identifying Fatty Acids, Drawing Structures for Triacyl- glycerols, Drawing the Structure for an Amino Acid at Physiological pH, Identifying the Primary, Secondary, Tertiary, and Quaternary Structures of Proteins, Writing the Complementary DNA Strand, Writing the mRNA Segment for a DNA Template, and Writing the Amino Acid for an mRNA Codon.

• The interchapter problem set, Combining Ideas from Chapters 17 and 18, completes the chapter.

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xxii Preface

Acknowledgments The preparation of a new text is a continuous effort of many people. We are thankful for the support, encouragement, and dedication of many people who put in hours of tireless effort to produce a high-quality book that provides an outstanding learning package. The editorial team at Pearson has done an exceptional job. We want to thank Jeanne Zalesky, Director, Courseware Portfolio Management, and Editor Jessica Moro, who supported our vision of this sixth edition and the development of strategies based on learning theory research.

We appreciate all the wonderful work of Melanie Field, Content Producer, who skillfully brought together files, art, web site materials, and all the things it takes to prepare a book for production. We appreciate the work of Rose Kernan at SPi Global, who brilliantly coordinated all phases of the manuscript to the final pages of a beautiful book. Thanks to Mark Quirie, manuscript and accuracy reviewer, and Karen Slaght, who analyzed and edited the manuscripts and pages to make sure the words and problems were correct to help students learn chemistry. Their keen eyes and thoughtful comments were extremely helpful in the development of this text.

We appreciate the contributions from Dr. John Timberlake that connected recent learning theory research with our effort to encourage students to incorporate active reading in their study plan.

Thanks to Kristen Flathman, Managing Producer, Coleen Morrison, Courseware Analyst, and Barbara Yien, Course- ware Director, for their excellent review of pages and helpful suggestions.

We am especially proud of the art program in this text, which lends beauty and understanding to chemistry. We would like to thank Jay McElroy, Art Courseware Analyst, and Stephanie Marquez and Alicia Elliott, Photo and Illustration Project Managers, Mark Ong, Design Manager, and Tamara

Newnam, Cover and Interior Designer, whose creative ideas provided the outstanding design for the cover and pages of the book. We appreciate the tireless efforts of Namrata Aggarwal, Photo Researcher, and Matt Perry, Rights and Permissions Project Manager, in researching and selecting vivid photos for the text so that students can see the beauty of chemistry. Thanks also to Bio-Rad Laboratories for their courtesy and use of KnowItAll ChemWindows, drawing software that helped us produce chemical structures for the manuscript. The macro-to- micro illustrations designed by Jay McElroy and Imagineering Art give students visual impressions of the atomic and molecular organization of everyday things and are a fantastic learning tool. We also appreciate all the hard work in the field put in by the marketing team and Allison Rona, Marketing Manager.

We am extremely grateful to an incredible group of peers for their careful assessment of all the new ideas for the text; for their suggested additions, corrections, changes, and deletions; and for providing an incredible amount of feedback about improvements for the book. We admire and appreciate every one of you.

If you would like to share your experience with chemistry, or have questions and comments about this text, We would appreciate hearing from you.

Karen Timberlake William Timberlake

Email: [email protected]

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xxiii

Sixth Edition Reviewers Jennifer Bell Daytona State College, Main

Karen Endebrock Daytona State College, Deland

Paul Forster University of Nevada, Las Vegas

Ann Mills Minnesota West Community and Technical College, Worthington

Phil Nubel Waubonsee Community College

Amy Whiting North Central Texas College

Accuracy Reviewer Mark Quirie Algonquin College

Reviewers

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BASIC CHEMISTRY

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Help students master the math and problem solving they will use in their future careers

Basic Chemistry introduces students to the essential scientific and mathematical concepts of chemistry while providing the scaffolded support they need. With accessible language and a moderate pace, the text is easy- to-follow for first-time chemistry students. The 6th Edition incorporates sound pedagogy and the best principles from learning design theory to create an updated learning program designed for today’s students. The applied focus helps students connect chemistry with their interests and potential careers. Enhanced digital tools and additional practice problems in Mastering Chemistry ensure students master the basic quantitative and science skills needed to succeed in this course and beyond.

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Art and Videos that are more understandable than ever before

P. 74

Updated! Art program incorporates sound pedagogy and the best learning design principles based on the way today’s students learn.

74 CHAPTER 3 Matter and Energy

TABLE 3.3 Summary of Physical and Chemical Properties and Changes Physical Chemical

Property A characteristic of a substance: color, shape, odor, luster, size, melting point, or density.

A characteristic that indicates the ability of a substance to form another substance: paper can burn, iron can rust, silver can tarnish.

Change A change in a physical property that retains the identity of the substance: a change of state, a change in size, or a change in shape.

A change in which the original substance is converted to one or more new substances: paper burns, iron rusts, silver tarnishes.

TABLE 3.4 Examples of Some Physical and Chemical Changes Physical Changes Chemical Changes

Water boils to form water vapor. Water and cesium combine explosively.

Paper is cut into tiny pieces of confetti. Paper burns with a bright flame and produces heat, ashes, carbon dioxide, and water vapor.

Sugar dissolves in water to form a sugar solution.

Heating sugar forms a smooth, caramel- colored substance.

Iron has a melting point of 1538 °C. Iron, which is gray and shiny, combines with oxygen to form orange-red iron oxide (rust).

A chemical change occurs when sugar is heated, forming a caramelized topping for flan.

CORE CHEMISTRY SKILL Identifying Physical and Chemical

Changes

ENGAGE 3.5 Why is the melting point of iron, 1538 °C, a physical property, whereas the heating of iron with oxygen to form rust, Fe2O3, is a chemical property?

FIGURE 3.3 The decomposition of salt, NaCl, produces the elements sodium and chlorine.

Sodium metal

Sodium chloride

Chemical change

Chlorine gasand

ENGAGE 3.4 Why is the decomposition of salt a chemical change?

SAMPLE PROBLEM 3.2 Physical and Chemical Changes

TRY IT FIRST

Classify each of the following as a physical or chemical change:

a. A gold ingot is hammered to form gold leaf. b. Gasoline burns in air. c. Garlic is chopped into small pieces. d. Milk left in a warm room turns sour. e. A mixture of oil and water is separated.

A gold ingot is hammered to form gold leaf.

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In-art captions replace long legends, and the flow and size of the art is updated to help increase student understanding.

3.1 Classification of Matter 69

3.1 Classification of Matter LEARNING GOAL Classify examples of matter as pure substances or mixtures.

Matter is anything that has mass and occupies space. Matter is everywhere around us: the orange juice we had for breakfast, the water we put in the coffee maker, the plastic bag we put our sandwich in, our toothbrush and toothpaste, the oxygen we inhale, and the carbon dioxide we exhale. All of this material is matter. The different types of matter are classified by their composition.

Pure Substances: Elements and Compounds All matter is made of extremely small particles called atoms. Much of matter is made of atoms bonded together in definite arrangements called molecules. A pure substance is matter that consists of just one type of atom or one type of molecule. An element, the simplest type of a pure substance, is composed of only one type of atom such as silver, iron, or aluminum. Silver is composed of silver atoms, iron of iron atoms, and aluminum of aluminum atoms. A full list of the elements is found on the inside front cover of this text.

A compound is also a pure substance, but it consists of atoms of two or more elements always chemically combined in the same proportion. For example, in the compound water, there are two hydrogen atoms for every one oxygen atom, which is represented by the formula H2O. This means that water always has the same composi- tion of H2O. Another compound that consists of a chemical combination of hydrogen and oxygen is hydrogen peroxide. It has two hydrogen atoms for every two oxygen atoms and is represented by the formula H2O2. Thus, water (H2O) and hydrogen peroxide (H2O2) are different compounds even though they contain the same elements, hydrogen and oxygen.

ENGAGE 3.1 Why are elements and compounds both pure substances?

PRACTICE PROBLEMS Try Practice Problems 3.1 and 3.2

LOOKING AHEAD

3.1 Classification of Matter 69

3.2 States and Properties of Matter 72

3.3 Temperature 75 3.4 Energy 79 3.5 Specific Heat 82 3.6 Energy and Nutrition 87

Aluminum atom

An aluminum can consists of many atoms of aluminum.

H H O

Water molecule

A water molecule, H2O, consists of two atoms of hydrogen (white) for one atom of oxygen (red).

H O

O Hydroxide peroxide molecule

A hydroxide peroxide molecule, H2O2, consists of two atoms of hydrogen (white) for every two atoms of oxygen (red).

Mixtures In a mixture, two or more different substances are physically mixed. Much of the matter in our everyday lives consists of mixtures. The air we breathe is a mixture of mostly oxygen and nitrogen gases. The steel in buildings and railroad tracks is a mixture of iron, nickel, carbon, and chromium. The brass in doorknobs and musical instruments is a mixture of

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3.1 Classification of Matter 69

3.1 Classification of Matter LEARNING GOAL Classify examples of matter as pure substances or mixtures.

ENGAGE 3.1 Why are elements and compounds both pure substances?

PRACTICE PROBLEMS Try Practice Problems 3.1 and 3.2

LOOKING AHEAD

3.1 Classification of Matter 69

3.2 States and Properties of Matter 72

3.3 Temperature 75 3.4 Energy 79 3.5 Specific Heat 82 3.6 Energy and Nutrition 87

Aluminum atom

An aluminum can consists of many atoms of aluminum.

H H O

Water molecule

A water molecule, H2O, consists of two atoms of hydrogen (white) for one atom of oxygen (red).

H O

O Hydroxide peroxide molecule

A hydroxide peroxide molecule, H2O2, consists of two atoms of hydrogen (white) for every two atoms of oxygen (red).

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Engage students in learning chemistry

Updated! Chemistry Links to Health and Chemistry Links to the Environment appear throughout the text and relate chemistry concepts to real-life topics in health, the environment, and medicine. High-interest topics include weight loss and weight gain, hyperglycemia and hypoglycemia, antacids, gout and kidney stones, sweeteners, and essential amino acids. Follow-up questions also appear throughout the text.

Updated! Interactive Videos give students an opportunity to reinforce what they just learned by showing how chemistry works in real life and introducing a bit of humor into chemical problem solving and demonstrations. Topics include Using Conversion Factors, Mass Calculations for Reactions, Concentration of Solutions, Balancing Nuclear Equations, and Chemical v. Physical Change.

52 CHAPTER 2 Chemistry and Measurements

Chemistry Link to Health Toxicology and Risk–Benefit Assessment

Each day, we make choices about what we do or what we eat, often without thinking about the risks associated with these choices. We are aware of the risks of cancer from smoking or the risks of lead poisoning, and we know there is a greater risk of having an accident if we cross a street where there is no light or crosswalk.

A basic concept of toxicology is the statement of Paracelsus that the dose is the difference between a poison and a cure. To evaluate the level of danger from various substances, natural or synthetic, a risk assessment is made by exposing laboratory animals to the sub- stances and monitoring the health effects. Often, doses very much greater than humans might ordinarily encounter are given to the test animals.

Many hazardous chemicals or substances have been identified by these tests. One measure of toxicity is the LD50, or lethal dose, which is the con- centration of the substance that causes death in 50% of the test animals. A dosage is typically measured in milligrams per kilogram (mg/kg) of body mass or micrograms per kilogram (mcg/kg) of body mass.

Other evaluations need to be made, but it is easy to compare LD50 values. Parathion, a pesticide, with an LD50 of 3 mg/kg, would be highly toxic. This means that 3 mg of parathion per kg of body mass would be fatal to half the test animals. Table salt (sodium chloride) with an LD50 of 3300 mg/kg would have a much lower toxicity. You would need to ingest a huge amount of salt before any toxic effect

would be observed. Although the risk to animals can be evaluated in the laboratory, it is more difficult to determine the impact in the envi- ronment since there is also a difference between continued exposure and a single, large dose of the substance.

TABLE 2.9 lists some LD50 values and compares substances in order of increasing toxicity.

Substance LD50 (mg/kg)

Table sugar 29 700

Boric acid 5140

Baking soda 4220

Table salt 3300

Ethanol 2080

Aspirin 1100

Codeine 800

Oxycodone 480

Caffeine 192

DDT 113

Cocaine (injected) 95

Dichlorvos (pesticide strips) 56

Ricin 30

Sodium cyanide 6

Parathion 3

TABLE 2.9 Some LD50 Values for Substances Tested in Rats

The LD50 of caffeine is 192 mg/kg.

PRACTICE PROBLEMS

2.6 Problem Solving Using Unit Conversion

2.57 Perform each of the following conversions using metric conversion factors:

a. 44.2 mL to liters b. 8.65 m to nanometers c. 5.2 * 108 g to megagrams d. 0.72 ks to milliseconds

2.58 Perform each of the following conversions using metric conversion factors:

a. 4.82 * 10-5 L to picoliters b. 575.2 dm to kilometers c. 5 * 10-4 kg to micrograms d. 6.4 * 1010 ps to seconds

2.59 Perform each of the following conversions using metric and U.S. conversion factors:

a. 3.428 lb to kilograms b. 1.6 m to inches c. 4.2 L to quarts d. 0.672 ft to millimeters

2.60 Perform each of the following conversions using metric and U.S. conversion factors:

a. 0.21 lb to grams b. 11.6 in. to centimeters c. 0.15 qt to milliliters d. 35.41 kg to pounds

2.61 Use metric conversion factors to solve each of the following problems: a. If a student is 175 cm tall, how tall is the student in

meters? b. A cooler has a volume of 5000 mL. What is the capacity of

the cooler in liters? c. A hummingbird has a mass of 0.0055 kg. What is the mass,

in grams, of the hummingbird? d. A balloon has a volume of 3500 cm3. What is the volume in

liters?

2.62 Use metric conversion factors to solve each of the following problems: a. The Daily Value (DV) for phosphorus is 800 mg. How many

grams of phosphorus are recommended? b. A glass of orange juice contains 3.2 dL of juice. How many

milliliters of orange juice are in the glass? c. A package of chocolate instant pudding contains 2840 mg of

sodium. How many grams of sodium are in the pudding? d. A jar contains 0.29 kg of olives. How many grams of olives

are in the jar?

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Tools to help students succeed

Marginal notes and end-of-chapter problems deepen the connection between key math skills, core chemistry skills, textual content, practice problems, and why they are so important to success in the course.

The Chemistry Primer in Mastering Chemistry helps students remediate their chemistry math skills and prepare for their first college chemistry course. Scaled to students’ needs, remediation is only suggested to students that perform poorly on an initial assessment. Remediation includes tutorials, wrong-answer specific feedback, video instruction, and stepwise scaffolding to build students’ abilities.

1.3 Studying and Learning Chemistry 7

5. Study different topics in a chapter, and relate the new concepts to concepts you know. We learn material more efficiently by relating it to information we already know. By increasing connections between concepts, we can retrieve information when we need it.

Helpful Not helpful

Testing practice Highlighting

Studying different ideas at the same time

Underlining Reading the chapter many times

Retesting a few days later Memorizing the key words

Cramming

ENGAGE 1.3 Why is self-testing helpful for learning new concepts?

SAMPLE PROBLEM 1.2 Strategies for Learning Chemistry

TRY IT FIRST

Predict which student, a, b, or c, will be most successful on the exam.

a. Bill, who reads the chapter four times b. Jennifer, who reads the chapter two times and works all the problems at the end of each

section c. Mark, who reads the chapter the night before the exam

SOLUTION

b. Jennifer, who reads the chapter two times and works all the problems at the end of each section, interacts with the content in the chapter using self-testing to make connections between concepts and practicing retrieving information learned previously.

SELF TEST 1.2

What are two more ways that Jennifer could improve her retrieval of information?

ANSWER

1. Jennifer could wait two or three days and practice working the problems in each section again to determine how much she has learned. Retesting strengthens connections between new and previously learned information for longer lasting memory and more efficient retrieval.

2. Jennifer could also ask questions as she reads and try to study at a regular pace to avoid cramming.

Features in This Text That Help You Study and Learn Chemistry This text has been designed with study features to support your learning. On the inside of the front cover is a periodic table of the elements. On the inside of the back cover are tables that summarize useful information needed throughout your study of chemistry. Each chapter begins with Looking Ahead, which outlines the topics in the chapter. At the beginning of each section, a Learning Goal describes the topics to learn. Review icons in the margins refer to Key Math Skills or Core Chemistry Skills from previous chapters that relate to new material in the chapter. Key Terms are bolded when they first appear in the text and are summarized at the end of each chapter. They are also listed and defined in the comprehensive Glossary and Index, which appears at the end of the text. Key Math Skills and Core Chemistry Skills that are critical to learning chemistry are indicated by icons in the margin and summarized at the end of each chapter.

Before you begin reading, obtain an overview of a chapter by reviewing the topics in Looking Ahead. As you prepare to read a section of the chapter, look at the section title, and turn it into a question. Asking yourself questions about new topics builds new connections to material you have already learned. For example, for Section 1.1, “Chemistry and Chemi- cals,” you could ask, “What is chemistry?” or “What are chemicals?” At the beginning of

REVIEW

KEY MATH SKILL

CORE CHEMISTRY SKILL

ENGAGE

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P. 7

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Build students’ problem-solving skills

Core Chemistry Skills and Key Math Skills Tutorials in Mastering Chemistry provide assignable practice problems related to the in-text feature boxes, ensuring that students master the basic quantitative and science skills they need to succeed in the course.

NEW! Pedagogical features in worked Sample Problems throughout the text help students build stronger problem-solving skills, setting them up for success in this and future courses. TRY IT FIRST! Feature encourages students to solve the problem before looking at the solution.

UPDATED! Connect feature added to Analyze the Problem boxes specify information that relates the Given and Need boxes to help students identify and connect the components within a word problem and show STEPs as guides that set up a solution strategy.

NEW! Engage questions remind students to pause and answer a question related to the material.

UPDATED! Self Tests provide students with immediate problem solving and feedback with answers.

NEW! Practice Problems suggest problems to work as students study the section.

446 CHAPTER 14 Acids and Bases

in [H3O +] and a decrease in [OH-], which makes an acidic solution. If base is added, [OH-]

increases and [H3O +] decreases, which gives a basic solution. However, for any aqueous

solution, whether it is neutral, acidic, or basic, the product [H3O +][OH-] is equal to Kw

(1.0 * 10-14 at 25 °C) (see TABLE 14.6).

ENGAGE 14.7 Is a solution that has a [H3O

+] of 1.0 * 10-3 M acidic, basic, or neutral?

PRACTICE PROBLEMS Try Practice Problems 14.35 and 14.36

Type of Solution [H3O +] [OH−] Kw (25 °C)

Neutral 1.0 * 10-7 M 1.0 * 10-7 M 1.0 * 10-14

Acidic 1.0 * 10-2 M 1.0 * 10-12 M 1.0 * 10-14

Acidic 2.5 * 10-5 M 4.0 * 10-10 M 1.0 * 10-14

Basic 1.0 * 10-8 M 1.0 * 10-6 M 1.0 * 10-14

Basic 5.0 * 10-11 M 2.0 * 10-4 M 1.0 * 10-14

TABLE 14.6 Examples of [H3O +] and [OH−] in Neutral, Acidic, and Basic

Solutions

Using the Kw to Calculate [H3O +] and [OH−] in a Solution

If we know the [H3O +] of a solution, we can use the Kw to calculate [OH

-]. If we know the [OH-] of a solution, we can calculate [H3O

+] from their relationship in the Kw, as shown in Sample Problem 14.6.

Kw = [H3O +][OH-]

[OH-] = Kw

[H3O +] [H3O

+] = Kw

[OH-]

ENGAGE 14.9 Why does the [H3O

+] of an aqueous solution increase if the [OH-] decreases?

SAMPLE PROBLEM 14.6 Calculating the [H3O +] of a Solution

TRY IT FIRST

A vinegar solution has a [OH-] = 5.0 * 10-12 M at 25 °C. What is the [H3O+] of the vinegar solution? Is the solution acidic, basic, or neutral?

SOLUTION

STEP 1 State the given and needed quantities.

ANALYZE THE PROBLEM

Given Need Connect

[OH-] = 5.0 * 10-12 M [H3O+] Kw = [H3O+][OH-]

STEP 2 Write the Kw for water and solve for the unknown [H3O +].

Kw = [H3O +][OH-] = 1.0 * 10-14

Solve for [H3O +] by dividing both sides by [OH-].

[OH-] =

[H3O +][OH-]

[OH-]

[H3O +] =

1.0 * 10-14

[OH-]

STEP 3 Substitute the known [OH−] into the equation and calculate.

[H3O +] =

1.0 * 10-14

[5.0 * 10-12] = 2.0 * 10-3 M

Because the [H3O +] of 2.0 * 10-3 M is larger than the [OH-] of 5.0 * 10-12 M,

the solution is acidic.

ENGAGE 14.8 If you know the [H3O

+] of a solution, how do you use the Kw to calculate the [OH-]?

CORE CHEMISTRY SKILL Calculating [H3O

+] and [OH-] in Solutions

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14.6 The pH Scale 447

SELF TEST 14.6

a. What is the [H3O +] of an ammonia cleaning solution with [OH-] = 4.0 * 10-4 M? Is

the solution acidic, basic, or neutral? b. The [H3O

+] of tomato juice is 6.3 * 10-5 M. What is the [OH-] of the juice? Is the tomato juice acidic, basic, or neutral?

ANSWER

a. [H3O +] = 2.5 * 10-11 M, basic b. [OH-] = 1.6 * 10-10 M, acidic

PRACTICE PROBLEMS

14.5 Dissociation of Water

14.33 Why are the concentrations of H3O + and OH- equal in pure water?

14.34 What is the meaning and value of Kw at 25 °C?

14.35 In an acidic solution, how does the concentration of H3O +

compare to the concentration of OH-?

14.36 If a base is added to pure water, why does the [H3O +] decrease?

14.37 Indicate whether each of the following solutions is acidic, basic, or neutral:

a. [H3O +] = 2.0 * 10-5 M

b. [H3O +] = 1.4 * 10-9 M

c. [OH-] = 8.0 * 10-3 M d. [OH-] = 3.5 * 10-10 M 14.38 Indicate whether each of the following solutions is acidic, basic,

or neutral: a. [H3O

+] = 6.0 * 10-12 M b. [H3O

+] = 1.4 * 10-4 M c. [OH-] = 5.0 * 10-12 M d. [OH-] = 4.5 * 10-2 M 14.39 Calculate the [H3O

+] of each aqueous solution with the following [OH-]:

a. coffee, 1.0 * 10-9 M b. soap, 1.0 * 10-6 M c. cleanser, 2.0 * 10-5 M d. lemon juice, 4.0 * 10-13 M

14.40 Calculate the [H3O +] of each aqueous solution with the

following [OH-]: a. NaOH solution, 1.0 * 10-2 M b. milk of magnesia, 1.0 * 10-5 M c. aspirin, 1.8 * 10-11 M d. seawater, 2.5 * 10-6 M

Applications

14.41 Calculate the [OH-] of each aqueous solution with the following [H3O

+]: a. stomach acid, 4.0 * 10-2 M b. urine, 5.0 * 10-6 M c. orange juice, 2.0 * 10-4 M d. bile, 7.9 * 10-9 M 14.42 Calculate the [OH-] of each aqueous solution with the

following [H3O +]:

a. baking soda, 1.0 * 10-8 M b. blood, 4.2 * 10-8 M c. milk, 5.0 * 10-7 M d. pancreatic juice, 4.0 * 10-9 M

14.6 The pH Scale LEARNING GOAL Calculate pH from [H3O

+]; given the pH, calculate the [H3O +] and

[OH-] of a solution.

In the environment, the acidity, or pH, of rain can have significant effects. When rain becomes too acidic, it can dissolve marble statues and accelerate the corrosion of metals. In lakes and ponds, the acidity of water can affect the ability of plants and fish to survive. The acidity of soil around plants affects their growth. If the soil pH is too acidic or too basic, the roots of the plant cannot take up some nutrients. Most plants thrive in soil with a nearly neutral pH, although certain plants, such as orchids, camellias, and blueberries, require a more acidic soil.

Although we have expressed H3O + and OH- as molar concentrations, it is more conve-

nient to describe the acidity of solutions using the pH scale. On this scale, a number between 0 and 14 represents the H3O

+ concentration for common solutions. A neutral solution has a pH of 7.0 at 25 °C. An acidic solution has a pH less than 7.0; a basic solution has a pH greater than 7.0 (see FIGURE 14.4).

When we relate acidity and pH, we are using an inverse relationship, which is when one component increases while the other component decreases. When an acid is added to pure water, the [H3O

+] (acidity) of the solution increases but its pH decreases. When a base is added to pure water, it becomes more basic, which means its acidity decreases and the pH increases.

PRACTICE PROBLEMS Try Practice Problems 14.37 to 14.42

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Give students anytime, anywhere access with Pearson eText

Pearson eText is a simple-to-use, mobile-optimized, personalized reading experience available within Mastering. It allows students to easily highlight, take notes, and review key vocabulary all in one place—even when offline. Seamlessly integrated videos, rich media, and interactive self-assessment questions engage students and give them access to the help they need, when they need it. Pearson eText is available within Mastering when packaged with a new book; students can also purchase Mastering with Pearson eText online.

For instructors not using Mastering, Pearson eText can also be adopted on its own as the main course material.

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Improve learning with Dynamic Study Modules

Dynamic Study Modules in Mastering Chemistry help students study effectively— and at their own pace—by keeping them motivated and engaged. The assignable modules rely on the latest research in cognitive science, using methods—such as adaptivity, gamification, and intermittent rewards—to stimulate learning and improve retention.

Each module poses a series of questions about a course topic. These question sets adapt to each student’s performance and offer personalized, targeted feedback to help them master key concepts. With Dynamic Study Modules, students build the confidence they need to deepen their understanding, participate meaningfully, and perform better—in and out of class.

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Instructor support you can rely on

Basic Chemistry includes a full suite of instructor support materials in the Instructor Resources area in Mastering Chemistry.

Resources include customizable PowerPoint lecture and image presentations; all images and worked examples from the text; and a test bank.

A01_TIMB8119_06_SE_VWT.indd 34 11/29/18 1:24 PM

In the forensic laboratory, Sarah analyzes Gloria’s stomach contents and blood for toxic compounds. You can view the results of the tests on the forensic evidence in the UPDATE Forensic Evidence Helps Solve the Crime, page 21, and determine if Gloria ingested a toxic level of ethylene glycol (antifreeze).

UPDATE Forensic Evidence Helps Solve the Crime

A call came in to 911 from a man who arrived home from work to find his wife, Gloria, lying on their living room floor. When the police arrive, they pronounce the woman dead. There is no blood at the scene, but the police do find a glass on the side table that contains a small amount of liquid. In an adjacent laundry room, the police find a half-empty bottle of antifreeze, which contains the toxic compound ethylene glycol. The bottle, glass, and liquid are bagged and sent to the forensic laboratory. At the morgue, Gloria’s height is measured as 1.673 m, and her mass is 60.5 kg.

Sarah, a forensic scientist, uses scientific procedures and chemical tests to examine the evidence from law enforcement agencies. She analyzes blood, stomach contents, and the unknown liquid from Gloria’s home, as well as the fingerprints on the glass. She also looks for the presence of drugs, poisons, and alcohol.

CAREER

Forensic Scientist Most forensic scientists work in crime laboratories that are part of city or county legal systems. They analyze bodily fluids and tissue samples collected by crime scene investigators. In analyzing these samples, forensic scientists identify the presence or absence of specific chemicals within the body to help solve criminal cases. Some of the chemicals they look for include alcohol, illegal or prescription drugs, poisons, arson debris, metals, and various gases such as carbon monoxide. To identify these substances, they use a variety of instruments and highly specific methodologies. Forensic scientists analyze samples from criminal suspects, athletes, and potential employees. They also work on cases involving environmental contamination and animal samples for wildlife crimes. Forensic scientists usually have a bachelor’s degree that includes courses in math, chemistry, and biology.

Chemistry in Our Lives 1

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2 CHAPTER 1 Chemistry in Our Lives

1.1 Chemistry and Chemicals LEARNING GOAL Define the term chemistry, and identify chemicals.

Now that you are in a chemistry class, you may be wondering what you will be learning. What questions in science have you been curious about? Perhaps you are interested in what smog is or how aspirin relieves a headache. Just like you, chemists are curious about the world we live in.

How does car exhaust produce the smog that hangs over our cities? One component of car exhaust is nitrogen oxide (NO), which forms in car engines where high temperatures convert nitrogen gas (N2) and oxygen gas (O2) to NO. In the atmosphere, the NO(g) reacts with O2(g) to form NO2(g), which has a reddish brown color of smog. In chemistry, reactions are written in the form of equations:

N2(g) + O2(g) h 2NO(g) 2NO(g) + O2(g) h 2NO2(g)

Smog

Why does aspirin relieve a headache? When a part of the body is injured, substances called prostaglandins are produced, which cause inflammation and pain. Aspirin acts to block the production of prostaglandins, reducing inflammation and pain. Chemists in the medical field develop new treatments for diabetes, genetic defects, cancer, AIDS, and other diseases. For the forensic scientist, the nurse, the dietitian, the chemical engineer, or the agricultural scientist, chemistry plays a central role in understanding problems and assessing possible solutions.

Chemistry Chemistry is the study of the composition, structure, properties, and reactions of matter. Matter is another word for all the substances that make up our world. Perhaps you imagine that chemistry takes place only in a laboratory where a chemist is working in a white coat and goggles. Actually, chemistry happens all around you every day and has an impact on everything you use and do. You are doing chemistry when you cook food, add bleach to your laundry, or start your car. A chemical reaction has taken place when silver tarnishes or an antacid tablet fizzes when dropped into water. Plants grow because chemical reactions convert carbon dioxide, water, and energy to carbohydrates. Chemical reactions take place when you digest food and break it down into substances that you need for energy and health.

Chemicals A chemical is a substance that always has the same composition and properties wherever it is found. All the things you see around you are composed of one or more chemicals. Often the terms chemical and substance are used interchangeably to describe a specific type of matter.

Every day, you use products containing substances that were developed and prepared by chemists. Soaps and shampoos contain chemicals that remove oils on your skin and scalp. In cosmetics and lotions, chemicals are used to moisturize, prevent deterioration of the product, fight bacteria, and thicken the product. Perhaps you wear a ring or watch made of gold, silver, or platinum. Your breakfast cereal is probably fortified with iron, calcium, and phosphorus, whereas the milk you drink is enriched with vitamins A and D. When you brush your teeth, the substances in toothpaste clean your teeth, prevent plaque formation, and stop tooth decay. Some of the chemicals used to make toothpaste are listed in TABLE 1.1.

ENGAGE 1.1 Why is water a chemical?

PRACTICE PROBLEMS Try Practice Problems 1.1 to 1.6

Molecules of NO2

The chemical reaction of NO with oxygen in the air forms NO2, which produces the reddish brown color of smog.

LOOKING AHEAD

1.1 Chemistry and Chemicals 2

1.2 Scientific Method: Thinking Like a Scientist 3

1.3 Studying and Learning Chemistry 6

1.4 Key Math Skills for Chemistry 9

1.5 Writing Numbers in Scientific Notation 17

Antacid tablets undergo a chemical reaction when dropped into water.

Toothpaste is a combination of many chemicals.

Chemical Function

Calcium carbonate Used as an abrasive to remove plaque

Sorbitol Prevents loss of water and hardening of toothpaste

Sodium lauryl sulfate Used to loosen plaque

Titanium dioxide Makes toothpaste white and opaque

Sodium fluorophosphate Prevents formation of cavities by strengthening tooth enamel

Methyl salicylate Gives toothpaste a pleasant wintergreen flavor

TABLE 1.1 Chemicals Commonly Used in Toothpaste

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1.2 Scientific Method: Thinking Like a Scientist 3

Branches of Chemistry The field of chemistry is divided into several branches. General chemistry is the study of the composition, properties, and reactions of matter. Organic chemistry is the study of substances that contain the element carbon. Biological chemistry is the study of the chemical reactions that take place in biological systems. Today chemistry is often combined with other sciences, such as geology and physics, to form cross-disciplines such as geochemistry and physical chemistry. Geochemistry is the study of the chemical composition of ores, soils, and minerals of the surface of the Earth and other planets. Physical chemistry is the study of the physical nature of chemical systems, including energy changes. A geochemist collects newly

erupted lava samples from Kilauea Volcano, Hawaii.

PRACTICE PROBLEMS

1.1 Chemistry and Chemicals

In every chapter, odd-numbered exercises in the Practice Problems are paired with even-numbered exercises. The answers for the orange- shaded, odd-numbered Practice Problems are given at the end of each chapter. The complete solutions to the odd-numbered Practice Problems are in the Study Guide and Student Solutions Manual.

1.1 Write a one-sentence definition for each of the following: a. chemistry b. chemical

1.2 Ask two of your friends (not in this class) to define the terms in problem 1.1. Do their answers agree with the definitions you provided?

Applications

1.3 Obtain a bottle of multivitamins, and read the list of ingredients. What are four chemicals from the list?

1.4 Obtain a box of breakfast cereal, and read the list of ingredients. What are four chemicals from the list?

1.5 Read the labels on some items found in a drugstore. What are the names of some chemicals contained in those items?

1.6 Read the labels on products used to wash your dishes. What are the names of some chemicals contained in those products?

1.2 Scientific Method: Thinking Like a Scientist LEARNING GOAL Describe the scientific method.

When you were very young, you explored the things around you by touching and tasting. As you grew, you asked questions about the world in which you live. What is lightning? Where does a rainbow come from? Why is the sky blue? As an adult, you may have wondered how antibiotics work or why vitamins are important to your health. Every day, you ask questions and seek answers to organize and make sense of the world around you.

When the late Nobel Laureate Linus Pauling (1901–1994) described his student life in Oregon, he recalled that he read many books on chemistry, mineralogy, and physics. “I mulled over the properties of materials: why are some substances colored and others not, why are some minerals or inorganic compounds hard and others soft?” He said, “I was building up this tremendous background of empirical knowledge and at the same time asking a great number of questions.” Linus Pauling won two Nobel Prizes: the first, in 1954, was in chemistry for his work on the nature of chemical bonds and the determination of the structures of complex substances; the second, in 1962, was the Peace Prize, for his opposition to the spread of nuclear weapons.

The Scientific Method The process of trying to understand nature is unique to each scientist. However, the scientific method is a process that scientists use to make observations in nature, gather data, and explain natural phenomena (see the figure on the next page).

1. Make Observations The first step in the scientific method is to make observations about nature and ask questions about what you observe. When an observation always seems to be true, it may be stated as a law that predicts that behavior and is often

Linus Pauling won the Nobel Prize in Chemistry in 1954.

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4 CHAPTER 1 Chemistry in Our Lives

measurable. However, a law does not explain that observation. For example, we can use the Law of Gravity to predict that if we drop our chemistry book, it would fall on the floor, but this law does not explain why our book falls.

2. Form a Hypothesis A scientist forms a hypothesis, which gives a possible explanation of an observation or a law. The hypothesis must be stated in such a way that it can be tested by experiments.

3. Design Experiments To determine if a hypothesis is valid, experiments are done to find a relationship between the hypothesis and the observations. The results of the experiments may confirm the validity of the hypothesis. However, experiments may also show that the hypothesis is invalid, which means that it is modified or discarded. Then new experiments will be designed to test the new hypothesis.

4. Draw a Conclusion When many experiments give consistent results, we may draw the conclusion that the hypothesis is valid. Even then, more experiments are done to test the hypothesis. If new experimental results indicate the hypothesis is not valid, it is modified or replaced.

Law

Form a Hypothesis

The hypothesis is modified if the results of the experiments do not support it.

Design Experiments

Draw a Conclusion

Make Observations

Scientific Method

The scientific method develops a conclusion about nature using observations, hypotheses, and experiments.

Chemistry Link to Health Early Chemist: Paracelsus

For many centuries, chemistry has been the study of changes in matter. From the time of the ancient Greeks to the sixteenth century, alchemists described matter in terms of four components of nature: earth, air, fire, and water. By the eighth century, alchemists believed that they could change metals such as copper and lead into gold and silver. Although these efforts failed, the alchemists provided informa- tion on the chemical reactions involved in the extraction of metals from ores. The alchemists also designed some of the first laboratory equipments and developed early laboratory procedures. These early efforts were some of the first observations and experiments using the scientific method.

Paracelsus (1493–1541) was a physician and an alchemist who thought that alchemy should be about preparing new medicines. Using observation and experimentation, he proposed that a healthy body was regulated by a series of chemical processes that could be unbalanced by certain chemical compounds and rebalanced by using minerals and medicines. For example, he determined that inhaled

dust caused lung disease in miners. He also thought that goiter was a problem caused by contaminated water, and he treated syphilis

with compounds of mercury. His opinion of medicines was that the right dose makes the difference between a poison and a cure. Paracelsus changed alchemy in ways that helped establish mod- ern medicine and chemistry.

Swiss physician and alchemist Paracelsus (1493–1541) believed that chemicals and minerals could be used as medicines.

Using the Scientific Method in Everyday Life You may be surprised to realize that you use the scientific method in your everyday life. Suppose you visit a friend in her home. Soon after you arrive, your eyes start to itch and you begin to sneeze. Then you observe that your friend has a new cat. Perhaps you form the hypothesis that you are allergic to cats. To test your hypothesis, you leave your friend’s home. If the sneezing stops, perhaps your hypothesis is correct. You test your hypothesis further by visiting another friend who also has a cat. If you start to sneeze again, your experimental results support your hypothesis, and you come to the conclusion that you are allergic to cats. However, if you continue sneezing after you leave your friend’s home, your hypothesis is not supported. Now you need to form a new hypothesis, which could be that you have a cold.

ENGAGE 1.2 Why would the following statement, “Today I placed two tomato seedlings in the garden, and two more in a closet. I will give all the plants the same amount of water and fertilizer,” be considered an experiment?

SAMPLE PROBLEM 1.1 Scientific Method

TRY IT FIRST

Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion:

a. During an assessment in the emergency room, a nurse writes that the patient has a resting pulse of 30 beats/min.

Through observation you may think that you are allergic to cats.

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1.2 Scientific Method: Thinking Like a Scientist 5

b. Repeated studies show that lowering sodium in the diet leads to a decrease in blood pressure.

c. A nurse thinks that an incision from a recent surgery that is red and swollen is infected.

SOLUTION

a. observation b. conclusion c. hypothesis

SELF TEST 1.1

Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion:

a. Drinking coffee at night keeps me awake. b. I will try drinking coffee only in the morning. c. If I stop drinking coffee in the afternoon, I will be able to sleep at night. d. When I drink decaffeinated coffee, I sleep better at night. e. I am going to drink only decaffeinated coffee. f. I sleep better at night because I stopped drinking caffeinated drinks.

PRACTICE PROBLEMS Try Practice Problems 1.7 to 1.10

ANSWER

a. observation b. experiment c. hypothesis d. observation e. experiment f. conclusion

Nurses make observations in the hospital.

PRACTICE PROBLEMS

1.2 Scientific Method: Thinking Like a Scientist

1.7 Identify each activity, a to f, as an observation, a hypothesis, an experiment, or a conclusion. At a popular restaurant, where Chang is the head chef, the fol- lowing occurred: a. Chang determined that sales of the house salad had dropped. b. Chang decided that the house salad needed a new dressing. c. In a taste test, Chang prepared four bowls of sliced

cucumber, each with a new dressing: sesame seed, olive oil and balsamic vinegar, creamy Italian, and blue cheese.

d. Tasters rated the sesame seed salad dressing as the favorite. e. After two weeks, Chang noted that the orders for the house

salad with the new sesame seed dressing had doubled. f. Chang decided that the sesame seed dressing improved the

sales of the house salad because the sesame seed dressing enhanced the taste.

1.8 Identify each activity, a to f, as an observation, a hypothesis, an experiment, or a conclusion. Lucia wants to develop a process for dyeing shirts so that the color will not fade when the shirt is washed. She proceeds with the following activities: a. Lucia notices that the dye in a design fades when the shirt is

washed. b. Lucia decides that the dye needs something to help it

combine with the fabric.

c. She places a spot of dye on each of four shirts and then places each one separately in water, salt water, vinegar, and baking soda and water.

d. After one hour, all the shirts are removed and washed with a detergent.

e. Lucia notices that the dye has faded on the shirts in water, salt water, and baking soda, whereas the dye did not fade on the shirt soaked in vinegar.

f. Lucia thinks that the vinegar binds with the dye so it does not fade when the shirt is washed.

Applications

1.9 Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion: a. One hour after drinking a glass of regular milk, Jim

experienced stomach cramps. b. Jim thinks he may be lactose intolerant. c. Jim drinks a glass of lactose-free milk and does not have any

stomach cramps. d. Jim drinks a glass of regular milk to which he has added

lactase, an enzyme that breaks down lactose, and has no stomach cramps.

1.10 Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion: a. Sally thinks she may be allergic to shrimp. b. Yesterday, one hour after Sally ate a shrimp salad, she broke

out in hives. c. Today, Sally had some soup that contained shrimp, but she

did not break out in hives. d. Sally realizes that she does not have an allergy to

shrimp.

Customers rated the sesame seed dressing as the best.

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6 CHAPTER 1 Chemistry in Our Lives

1.3 Studying and Learning Chemistry LEARNING GOAL Identify strategies that are effective for learning. Develop a study plan for learning chemistry.

Here you are taking chemistry, perhaps for the first time. Whatever your reasons for choosing to study chemistry, you can look forward to learning many new and exciting ideas.

Strategies to Improve Learning and Understanding Success in chemistry utilizes good study habits, connecting new information with your knowledge base, rechecking what you have learned and what you have forgotten, and retrieving what you have learned for an exam. Let’s take a look at ways that can help you study and learn chemistry. Suppose you were asked to indicate if you think each of the following common study habits is helpful or not helpful:

Helpful Not helpful

Highlighting

Underlining

Reading the chapter many times

Memorizing the key words

Testing practice

Cramming

Studying different ideas at the same time

Retesting a few days later

Learning chemistry requires us to place new information in our long-term memory, which allows us to remember those ideas for an exam, a process called retrieval. Thus, our study habits need to help us to recall knowledge. The study habits that are not very helpful in retrieval include highlighting, underlining, reading the chapter many times, memorizing key words, and cramming. If we want to recall new information, we need to connect it with prior knowledge. By doing practice tests, you develop the skills needed to retrieve new information. We can determine how much we have learned by going back a few days later and retesting. Another useful learning strategy is to study different ideas at the same time, which allows us to connect those ideas and to differentiate between them. Although these study habits may take more time and seem more difficult, they help us find the gaps in our knowledge and connect new information with what we already know.

Tips for Using New Study Habits for Successful Learning

1. Do not keep rereading text or notes. Reading the same material over and over will make that material seem familiar but does not mean that you have learned it. You need to test yourself to find out what you do and do not know.

2. Ask yourself questions as you read. Asking yourself questions as you read requires you to interact continually with new material. The Engage features in the margin of this text are helpful in asking you to think about new material. By linking new material with long-term knowledge, you make pathways for retrieving new material.

3. Self-test by giving yourself quizzes. Using problems in the text or sample exams, practice taking tests frequently.

4. Study at a regular pace rather than cramming. Once you have tested your- self, go back in a few days and practice testing and retrieving information again. We do not recall all the information when we first read it. By frequent quizzing and retesting, we identify what we still need to learn. Sleep is also important for strengthening the associations between newly learned information. Lack of sleep may interfere with retrieval of information as well. So staying up all night to cram for your chemistry exam is not a good idea. Success in chemistry is a combined effort to learn new information and then to retrieve that information when you need it for an exam.

Students learn by continuously asking and answering questions as they study new material.

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1.3 Studying and Learning Chemistry 7

Helpful Not helpful

Testing practice Highlighting

Studying different ideas at the same time

Underlining Reading the chapter many times

Retesting a few days later Memorizing the key words

Cramming

ENGAGE 1.3 Why is self-testing helpful for learning new concepts?

SAMPLE PROBLEM 1.2 Strategies for Learning Chemistry

TRY IT FIRST

Predict which student, a, b, or c, will be most successful on the exam.

a. Bill, who reads the chapter four times b. Jennifer, who reads the chapter two times and works all the problems at the end of each

section c. Mark, who reads the chapter the night before the exam

SOLUTION

SELF TEST 1.2

What are two more ways that Jennifer could improve her retrieval of information?

ANSWER

2. Jennifer could also ask questions as she reads and try to study at a regular pace to avoid cramming.

REVIEW

KEY MATH SKILL

CORE CHEMISTRY SKILL

ENGAGE

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8 CHAPTER 1 Chemistry in Our Lives

each section, a Learning Goal states what you need to understand. As you read the text, you will see Engage questions in the margin, which remind you to pause your reading and test yourself with a question related to the material. The Answers to Engage Questions are at the end of each chapter.

Several Sample Problems are included in each chapter. The Try It First feature reminds you to work the problem before you look at the Solution. It is helpful to try to work a problem first because it helps you link what you know to what you need to learn. The Analyze the Problem feature includes Given, the information you have; Need, what you have to accomplish; and Connect, how you proceed. Sample Problems include a Solution that shows the steps you can use for problem solving. Work the associated Self Test problems, and compare your answer to the one provided.

TRY IT FIRST

ANALYZE THE PROBLEM

Given Need Connect

At the end of each chapter section, you will find a set of Practice Problems that allows you to apply problem solving immediately to the new concepts. Throughout each section, Practice Problem icons remind you to try the indicated Practice Problems as you study. The Applications in the Practice Problems relate the content to health, careers, and real-life examples. The problems are paired, which means that each of the odd-numbered problems is matched to the following even-numbered problem. At the end of each chapter, the Answers to all the odd-numbered problems are provided. If the answers match yours, you most likely understand the topic; if not, you need to study the section again.

Throughout each chapter, boxes titled Chemistry Link to Health and Chemistry Link to the Environment help you relate the chemical concepts you are learning to real-life situ- ations. Many of the figures and diagrams use macro-to-micro illustrations to depict the atomic level of organization of ordinary objects, such as the atoms in aluminum foil. These visual models illustrate the concepts described in the text and allow you to “see” the world in a microscopic way. Interactive Video suggestions illustrate content as well as problem solving.

At the end of each chapter, you will find several study aids that complete the chapter. Chapter Reviews provide a summary in easy-to-read bullet points, and Concept Maps visually show the connections between important topics. Understanding the Concepts are problems that use art and models to help you visualize concepts and connect them to your background knowledge. Additional Practice Problems and Challenge Problems provide additional exercises to test your understanding of the topics in the chapter.

After some chapters, problem sets called Combining Ideas test your ability to solve problems containing material from more than one chapter.

Many students find that studying with a group can be beneficial to learning. In a group, students motivate each other to study, fill in gaps, and correct misunderstandings by teaching and learning together. Studying alone does not allow the process of peer correction. In a group, you can cover the ideas more thoroughly as you discuss the reading and problem solve with other students.

Making a Study Plan As you embark on your journey into the world of chemistry, think about your approach to studying and learning chemistry. You might consider some of the ideas in the following list. Check those ideas that will help you successfully learn chemistry. Commit to them now. Your success depends on you.

My study plan for learning chemistry will include the following:

reading the chapter before class going to class reviewing the Learning Goals keeping a problem notebook reading the text working the Practice Problems as I read each section answering the Engage questions trying to work the Sample Problem before looking at the Solution studying different topics at the same time organizing a study group

PRACTICE PROBLEMS

INTERACTIVE VIDEO

Illustrating the atoms of aluminum in aluminum foil is an example of macro-to-micro art.

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1.4 Key Math Skills for Chemistry 9

seeing the professor during office hours reviewing Key Math Skills and Core Chemistry Skills attending review sessions studying as often as I can

PRACTICE PROBLEMS Try Practice Problems 1.11 to 1.14

SAMPLE PROBLEM 1.3 A Study Plan for Learning Chemistry

TRY IT FIRST

Which of the following activities should you include in your study plan for learning chemistry successfully?

a. reading the chapter over and over until you think you understand it b. going to the professor’s office hours c. doing the Self Test associated with each Sample Problem d. waiting to study until the night before the exam e. trying to work the Sample Problem before looking at the Solution f. retesting on new information a few days later

SOLUTION

b, c, e, and f

SELF TEST 1.3

Which of the following will help you learn chemistry?

a. skipping review sessions b. working Practice Problems as you read each section c. staying up all night before an exam d. reading the assignment before class e. highlighting the key ideas in the text

ANSWER

b and d

PRACTICE PROBLEMS

1.3 Studying and Learning Chemistry

1.11 What are four things you can do to help yourself to succeed in chemistry?

1.12 What are four things that would make it difficult for you to learn chemistry?

1.13 A student in your class asks you for advice on learning chemistry. Which of the following might you suggest? a. forming a study group b. skipping class c. asking yourself questions while reading the text

d. waiting until the night before an exam to study e. answering the Engage questions

1.14 A student in your class asks you for advice on learning chemistry. Which of the following might you suggest?

a. studying different topics at the same time b. not reading the text; it’s never on the test c. attending review sessions d. working the problems again after a few days e. keeping a problem notebook

1.4 Key Math Skills for Chemistry LEARNING GOAL Review math concepts used in chemistry: place values, positive and negative numbers, percentages, solving equations, and interpreting graphs.

During your study of chemistry, you will work many problems that involve numbers. You will need various math skills and operations. We will review some of the key math skills that are particularly important for chemistry. As we move through the chapters, we will also reference the key math skills as they apply.

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10 CHAPTER 1 Chemistry in Our Lives

Identifying Place Values The name of each place value depends on its position relative to the decimal point. For the number 482.57 in the Decimal Place Value Chart, the place values increase 10 times moving to the left and decrease 10 times by moving to the right. The digits on the left of the decimal point on the place value chart are 4 hundreds (400), 8 tens (80), and 2 ones (2), or four hundred eighty-two (482). The digits on the right of the decimal point are 5 tenths (.5), and 7 hundredths (.07), or fifty-seven hundredths (.57).

A premature baby has a mass of 2518 g. We can assign the place values for the number 2518 as follows:

Digit Place Value

2 thousands

5 hundreds

1 tens

8 ones

A silver coin has a mass of 6.407 g. We can assign the place values for the number 6.407 as follows:

Digit Place Value

6 ones

4 tenths

0 hundredths

7 thousandths

Note that place values ending with the suffix ths refer to the decimal places to the right of the decimal point.

ENGAGE 1.4 In the number 8.034, how do you know the 0 is in the tenths place?

KEY MATH SKILL Identifying Place Values

PRACTICE PROBLEMS Try Practice Problems 1.15 and 1.16

4 8

Decimal Place Value Chart

2 . 5 7

T ho

us an

H un

dr ed

T en

O ne

D ec

im al

p oi

T en

th s

H un

dr ed

th s

T ho

us an

dt hs

SAMPLE PROBLEM 1.4 Identifying Place Values

TRY IT FIRST

A bullet found at a crime scene has a mass of 15.24 g. What are the place values for each of the digits in the mass of the bullet?

SOLUTION

Digit Place Value

1 tens

5 ones

2 tenths

4 hundredths

SELF TEST 1.4

Identify the place values for the digits in each of the following:

a. the victim’s height of 1.673 m b. the victim’s mass of 60.5 kg

ANSWER

a. Digit Place Value

1 ones

6 tenths

7 hundredths

3 thousandths

Digit Place Value

6 tens

0 ones

5 tenths

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1.4 Key Math Skills for Chemistry 11

Using Positive and Negative Numbers in Calculations A positive number is any number that is greater than zero and has a positive sign ( + ). Often the positive sign is understood and not written in front of the number. For example, the number + 8 is usually written as 8. A negative number is any number that is less than zero and is written with a negative sign ( - ). For example, a negative eight is written as - 8.

Multiplication and Division of Positive and Negative Numbers When two positive numbers or two negative numbers are multiplied, the answer is positive ( + ).

2 * 3 = 6 The + sign ( + 6) is understood. ( - 2) * ( - 3) = 6

When a positive number and a negative number are multiplied, the answer is negative ( - ).

2 * ( - 3) = - 6 ( - 2) * 3 = - 6

The rules for the division of positive and negative numbers are the same as the rules for multiplication. When two positive numbers or two negative numbers are divided, the answer is positive ( + ).

6 3

= 2 - 6 - 3

= 2

When a positive number and a negative number are divided, the answer is negative ( - ).

- 6 3

= - 2 6

- 3 = - 2

Addition of Positive and Negative Numbers When positive numbers are added, the sign of the answer is positive.

3 + 4 = 7 The + sign ( + 7) is understood.

When negative numbers are added, the sign of the answer is negative.

- 3 + ( - 4) = - 7

When a positive number and a negative number are added, the smaller number is subtracted from the larger number, and the result has the same sign as the larger number.

12 + ( - 15) = - 3

Subtraction of Positive and Negative Numbers When two numbers are subtracted, change the sign of the number to be subtracted and follow the rules for addition shown above.

12 - (+5) = 12 + ( - 5) = 7 - 12 - (−5) = - 12 + ( + 5) = - 7

Calculator Operations On your calculator, there are four keys that are used for basic mathematical operations. The change sign + / - key may be used to change the sign of a number.

To practice these basic calculations on the calculator, work through the problem going from the left to the right, doing the operations in the order they occur. On some calculators, a negative number is entered by pressing the number and then pressing the change sign + / - key. However, this may not work on all calculators. Because each type of calculator is slightly different, make sure that you know how your particular calculator works. At the end, press the equals = key or ANS or ENTER.

KEY MATH SKILL Using Positive and Negative

Numbers in Calculations

ENGAGE 1.5 Why does - 5 + 4 = - 1, whereas - 5 + ( - 4) = - 9?

PRACTICE PROBLEMS Try Practice Problems 1.17 and 1.18

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12 CHAPTER 1 Chemistry in Our Lives

Addition and Subtraction Multiplication and Division

Example 1:

Solution:

15 - 8 + 2 = 15 - 8 + 2 = 9

Example 3:

Solution:

2 * ( - 3) = 2 * 3 + / - = - 6

Example 2:

Solution:

4 + ( - 10) - 5 =

4 + 10 + / - - 5 = - 11

Example 4:

Solution:

8 * 3 4

8 * 3 , 4 = 6

Calculating Percentages To determine a percentage, divide the parts by the total (whole) and multiply by 100%. For example, if an aspirin tablet contains 325 mg of aspirin (active ingredient) and the tablet has a mass of 545 mg, what is the percentage of aspirin in the tablet?

325 mg aspirin

545 mg tablet * 100% = 59.6% aspirin

When a value is described as a percent (%), it represents the number of parts of an item in 100 of those items. If the percent of red balls is 5, it means there are 5 red balls in every 100 balls. If the percent of green balls is 50, there are 50 green balls in every 100 balls.

5% red balls = 5 red balls 100 balls

50% green balls = 50 green balls

100 balls

KEY MATH SKILL Calculating Percentages

ENGAGE 1.6 Why is the value of 100% used in the calculation of a percentage?

Multiplication

Division

Subtraction

Equals

Change sign Addition

SAMPLE PROBLEM 1.5 Calculating a Percentage

TRY IT FIRST

A bullet found at a crime scene may be used as evidence in a trial if the percentage of metals is a match to the composition of metals in a bullet from the suspect’s ammunition. A forensic scientist’s analysis of the bullet shows that it contains 13.9 g of lead, 0.3 g of tin, and 0.9 g of antimony. What is the percentage of each metal in the bullet? Express your answers to the ones place.

SOLUTION

A percentage is calculated by dividing the mass of each element by the total mass of the metals in the bullet and multiplying by 100%.

Total mass = 13.9 g + 0.3 g + 0.9 g = 15.1 g

Percentage of lead

13.9 g

15.1 g * 100% = 92% lead

Percentage of tin

0.3 g

15.1 g * 100% = 2% tin

Percentage of antimony

0.9 g

15.1 g * 100% = 6% antimony

A bullet casing at a crime scene is marked as evidence.

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1.4 Key Math Skills for Chemistry 13

Solving Equations In chemistry, we use equations that express the relationship between certain variables. Let’s look at how we would solve for x in the following equation:

2x + 8 = 14

Our overall goal is to rearrange the items in the equation to obtain x on one side.

1. Place all like terms on one side. The numbers 8 and 14 are like terms. To remove the 8 from the left side of the equation, we subtract 8. To keep a balance, we need to subtract 8 from the 14 on the other side.

2x + 8 - 8 = 14 - 8 2x = 6

2. Isolate the variable you need to solve for. In this problem, we obtain x by dividing both sides of the equation by 2. The value of x is the result when 6 is divided by 2.

2x 2

= 6 2

x = 3

3. Check your answer. Check your answer by substituting your value for x back into the original equation.

2(3) + 8 = 14 6 + 8 = 14

14 = 14 Your answer x = 3 is correct.

Summary: To solve an equation for a particular variable, be sure you perform the same mathematical operations on both sides of the equation.

If you eliminate a symbol or number by subtracting, you need to subtract that same symbol or number from both sides.

If you eliminate a symbol or number by adding, you need to add that same symbol or number to both sides.

If you cancel a symbol or number by dividing, you need to divide both sides by that same symbol or number.

If you cancel a symbol or number by multiplying, you need to multiply both sides by that same symbol or number.

When we work with temperature, we may need to convert between degrees Celsius and degrees Fahrenheit using the following equation:

TF = 1.8(TC) + 32

KEY MATH SKILL Solving Equations

ENGAGE 1.7 Why is the number 8 subtracted from both sides of this equation?

SELF TEST 1.5

A bullet seized from the suspect’s ammunition has a composition of lead 11.6 g, tin 0.5 g, and antimony 0.4 g.

a. What is the percentage of each metal in the bullet? Express your answers to the ones place.

b. Could the bullet removed from the suspect’s ammunition be considered as evidence that the suspect was at the crime scene mentioned in Sample Problem 1.5?

ANSWER

a. The bullet from the suspect’s ammunition is lead 93%, tin 4%, and antimony 3%. b. The composition of this bullet does not match the bullet from the crime scene and

cannot be used as supporting evidence.

35 36 37 38 39 40

95 96.8 98.6 100.4 102.2 104

°C °C

°F °F

35 36 37 38 39 40

95 96.8 98.6 100.4 102.2 104

°C °C

°F °F

A plastic strip thermometer changes color to indicate body temperature.

PRACTICE PROBLEMS Try Practice Problems 1.23 and 1.24

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14 CHAPTER 1 Chemistry in Our Lives

To obtain the equation for converting degrees Fahrenheit to degrees Celsius, we subtract 32 from both sides.

TF = 1.8(TC) + 32 TF - 32 = 1.8(TC) + 32 - 32 TF - 32 = 1.8(TC)

To obtain TC by itself, we divide both sides by 1.8.

TF - 32 1.8

= 1.8(TC)

1.8 = TC

PRACTICE PROBLEMS Try Practice Problems 1.19 and 1.20

ANSWER

a. m = q

∆T * SH b. m = D * V

SAMPLE PROBLEM 1.6 Solving Equations

TRY IT FIRST

Solve the following equation for V2:

P1V1 = P2V2

SOLUTION

P1V1 = P2V2

To solve for V2, divide both sides by the symbol P2.

P1V1 P2

= P2V2 P2

V2 = P1V1 P2

SELF TEST 1.6

Solve each of the following equations for m:

a. q = m * ∆T * SH b. D = m V

INTERACTIVE VIDEO

Solving Equations

ENGAGE 1.8 Why is the numerator divided by P2 on both sides of the equation?

Interpreting Graphs A graph is a diagram that represents the relationship between two variables. These quantities are plotted along two perpendicular axes, which are the x axis (horizontal) and y axis (vertical).

Example In the graph Volume of a Balloon versus Temperature, the volume of a gas in a balloon is plotted against its temperature.

Title Look at the title. What does it tell us about the graph? The title indicates that the volume of a balloon was measured at different temperatures.

Vertical Axis Look at the label and the numbers on the vertical (y) axis. The label indicates that the volume of the balloon was measured in liters (L). The numbers, which are chosen to include the low and high measurements of the volume of the gas, are evenly spaced from 22.0 L to 32.0 L.

Horizontal Axis The label on the horizontal (x) axis indicates that the temperatures of the balloon, measured in kelvins (K), are evenly spaced from 270 K to 390 K.

KEY MATH SKILL Interpreting Graphs

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1.4 Key Math Skills for Chemistry 15

Points on the Graph Each point on the graph represents a volume in liters that was measured at a specific temperature. When these points are connected, a line is obtained.

Interpreting the Graph From the graph, we see that the volume of the gas increases as the temperature of the gas increases. This is called a direct relationship. Now we use the graph to determine the volume at various temperatures. For example, suppose we want to know the volume of the gas at 320 K. We would start by finding 320 K on the x axis and then drawing a line up to the plotted line. From there, we would draw a horizontal line that intersects the y axis and read the volume value where the line crosses the y axis as shown on the graph above.

ENGAGE 1.9 Why are the numbers on the vertical and horizontal axes placed at regular intervals?

PRACTICE PROBLEMS Try Practice Problems 1.21 and 1.22, 1.25 and 1.26

y axis (vertical axis)

x axis (horizontal axis)

22.0 270 290 310 330 350 370 390

24.0

26.0V ol

um e

(L )

28.0

30.0

32.0

Temperature (K)

Volume of a Balloon versus Temperature

ANSWER

a. 37.6 °C b. 8 min c. 0.9 °C

SAMPLE PROBLEM 1.7 Interpreting a Graph

TRY IT FIRST

A nurse administers Tylenol to lower a child’s fever. The graph shows the body temperature of the child plotted against time.

a. What is measured on the vertical axis? b. What is the range of values on the vertical axis? c. What is measured on the horizontal axis? d. What is the range of values on the horizontal axis?

SOLUTION

a. body temperature, in degrees Celsius b. 37.0 °C to 39.8 °C c. time, in minutes, after Tylenol was given d. 0 min to 30 min

SELF TEST 1.7

a. Using the graph in Sample Problem 1.7, what was the child’s temperature 15 min after Tylenol was given?

b. How many minutes elapsed for the temperature to decrease from 39.4 °C to 38.0 °C? c. What was the decrease, in degrees Celsius, between 5 min and 20 min?

0 5 10 15 20 25 30

37.4

37.0

37.8

38.2

38.6

39.0

39.4

39.8

Time (min) After Tylenol was Given

Child’s Body Temperature versus Time

B od

y T

em pe

ra tu

re (

°C )

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16 CHAPTER 1 Chemistry in Our Lives

PRACTICE PROBLEMS

1.4 Key Math Skills for Chemistry

1.15 What is the place value for the bold digit? a. 7.3288 b. 16.1234 c. 0.280 d. 4675.99 e. 0.0901

1.16 What is the place value for the bold digit? a. 975.689 b. 375.88 c. 46.1000 d. 0.8128 e. 2.710

1.17 Evaluate each of the following: a. 15 - ( - 8) = _______ b. - 8 + ( - 22) = _______ c. 4 * ( - 2) + 6 = ______ d. 75 - ( - 44) - 65 = _____

e. - 25 + ( - 11)

- 3 + 6 = _______

1.18 Evaluate each of the following: a. - 11 - ( - 9) = _______ b. 34 + ( - 55) = _______

c. - 56

8 = _______ d. 0.04 + ( - 0.08) = _______

e. - 2 * ( - 4)

2 + 12 = _______

1.19 Solve each of the following for a:

a. 4a + 4 = 40 b. a 6

= 7

c. 55 - a + 15

4 = a d.

6a - 27 3

= - a 1.20 Solve each of the following for b: a. 2b + 7 = b + 10 b. 3b - 4 = 24 - b

c. - 16 - 2b + 8b

2 = b d.

3 * ( - 4b) + 32 2

= - 4b

Use the following graph for problems 1.21 and 1.22:

Applications 1.23 a. A clinic had 25 patients on Friday morning. If 21 patients

were given flu shots, what percentage of the patients received flu shots? Express your answer to the ones place.

b. An alloy contains 56 g of pure silver and 22 g of pure copper. What is the percentage of silver in the alloy? Express your answer to the ones place.

c. A collection of coins contains 11 nickels, 5 quarters, and 7 dimes. What is the percentage of dimes in the collection? Express your answer to the ones place.

d. A saline solution has a mass of 44 g, of which 2.2 g is sodium chloride. What percent of the solution is sodium chloride? Express your answer to the ones place.

1.24 a. At a local hospital, 35 babies were born in May. If 22 were boys, what percentage of the newborns were boys? Express your answer to the ones place.

b. An alloy contains 67 g of pure gold and 35 g of pure zinc. What is the percentage of zinc in the alloy? Express your answer to the ones place.

c. A collection of coins contains 15 pennies, 14 dimes, and 6 quarters. What is the percentage of pennies in the collection? Express your answer to the ones place.

d. In the hospital storeroom, 18 of 56 intravenous (IV) fluid bags contain dextrose solutions. The bags with dextrose are what percent of the total? Express your answer to the ones place.

Use the following graph for problems 1.25 and 1.26:

T em

pe ra

tu re

( °C

)

20 0 20 40

Time (min)

Temperature of Tea versus Time for Cooling

60 80 100

20 0 5 10

Time (h) Since Death

Post-Mortem Body Temperature versus Time

15 20 25

T em

pe ra

tu re

( °C

)

1.25 a. What does the title indicate about the graph? b. What is measured on the vertical axis? c. What is the range of values on the vertical axis? d. Does the temperature increase or decrease with an increase

in time?

1.26 a. What is measured on the horizontal axis? b. What is the range of values on the horizontal axis? c. How many hours were needed to reach a temperature of 28 °C? d. The coroner measured Gloria’s body temperature at 9 p.m. as

34 °C. What was the time of her death?

1.21 a. What does the title indicate about the graph? b. What is measured on the vertical axis? c. What is the range of values on the vertical axis? d. Does the temperature increase or decrease with an increase

in time?

1.22 a. What is measured on the horizontal axis? b. What is the range of values on the horizontal axis? c. What is the temperature of the tea after 20 min? d. How many minutes were needed to reach a temperature of

45 °C?

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1.5 Writing Numbers in Scientific Notation 17

1.5 Writing Numbers in Scientific Notation LEARNING GOAL Write a number in scientific notation.

In chemistry, we often work with numbers that are very large and very small. We might measure something as tiny as the width of a human hair, which is about 0.000 008 m. Or perhaps we want to count the number of hairs on the average human scalp, which is about 100 000 hairs. In this text, we add spaces between sets of three digits when it helps make the places easier to count. However, we will see that it is more convenient to write large and small numbers in scientific notation.

8 * 10-6 m1 * 105 hairs

Humans have an average of 1 * 10 5 hairs on their scalps. Each hair is about 8 * 10 -6 m wide.

A number written in scientific notation has two parts: a coefficient and a power of 10. For example, the number 2400 is written in scientific notation as 2.4 * 103. The coefficient, 2.4, is obtained by moving the decimal point to the left to give a number that is at least 1 but less than 10. Because we moved the decimal point three places to the left, the power of 10 is a positive 3, which is written as 103. When a number greater than 1 is converted to scientific notation, the power of 10 is positive.

KEY MATH SKILL Writing Numbers in Scientific

Notation

ENGAGE 1.10 Why is 530 000 written as 5.3 * 10 5 in scientific notation?

Standard Number Scientific Notation

0.000 008 m 8 * 10-6 m

100 000 hairs 1 * 105 hairs

= 3 places Coefficient Power

of 10

Standard Number Scientific Notation

2 4 0 0. 2.4 * 103

Standard Number Scientific Notation

0.0 0 0 8 6 = 8.6 10-4

4 places Coefficient Power of 10

In another example, 0.000 86 is written in scientific notation as 8.6 * 10-4. The coefficient, 8.6, is obtained by moving the decimal point to the right. Because the decimal point is moved four places to the right, the power of 10 is a negative 4, written as 10-4. When a number less than 1 is written in scientific notation, the power of 10 is negative.

ENGAGE 1.11 Why is 0.000 053 written as 5.3 * 10 -5 in scientific notation?

TABLE 1.2 gives some examples of numbers written as positive and negative powers of 10. The powers of 10 are a way of keeping track of the decimal point in the number. TABLE 1.3 gives several examples of writing measurements in scientific notation.

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18 CHAPTER 1 Chemistry in Our Lives

Standard Number Multiples of 10 Scientific Notation

10 000 10 * 10 * 10 * 10 1 * 104 Some positive powers of 10

1000 10 * 10 * 10 1 * 103

100 10 * 10 1 * 102

10 10 1 * 101

1 0 1 * 100

0.1 1 10

1 * 10-1 Some negative powers of 10

0.01 1 10

* 1 10

= 1

100 1 * 10-2

0.001 1 10

* 1 10

= 1

1000 1 * 10-3

0.0001 1 10

* 1 10

= 1

10 000 1 * 10-4

TABLE 1.2 Some Powers of 10

Measured Quantity Standard Number Scientific Notation

Volume of gasoline used in the United States each year 550 000 000 000 L 5.5 * 1011 L

Diameter of Earth 12 800 000 m 1.28 * 107 m

Average volume of blood pumped in 1 day 8500 L 8.5 * 103 L

Time for light to travel from the Sun to Earth 500 s 5 * 102 s

Mass of a typical human 68 kg 6.8 * 101 kg

Mass of stirrup bone in ear 0.003 g 3 * 10-3 g

Diameter of a chickenpox (Varicella zoster) virus 0.000 000 3 m 3 * 10-7 m

Mass of bacterium (mycoplasma) 0.000 000 000 000 000 000 1 kg 1 * 10-19 kg

TABLE 1.3 Some Measurements Written as Standard Numbers and in Scientific Notation

A chickenpox virus has a diameter of 3 * 10 -7 m .

SAMPLE PROBLEM 1.8 Writing a Number in Scientific Notation

TRY IT FIRST

Write each of the following in scientific notation:

a. 3500 b. 0.000 016

SOLUTION

ANALYZE THE PROBLEM

Given Need Connect

standard number scientific notation coefficient is at least 1 but less than 10

a. 3500

STEP 1 Move the decimal point to obtain a coefficient that is at least 1 but less than 10. For a number greater than 1, the decimal point is moved to the left three places to give a coefficient of 3.5.

STEP 2 Express the number of places moved as a power of 10. Moving the decimal point three places to the left gives a power of 3, written as 103.

STEP 3 Write the product of the coefficient multiplied by the power of 10. 3.5 * 103

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1.5 Writing Numbers in Scientific Notation 19

Scientific Notation and Calculators You can enter a number in scientific notation on many calculators using the EE or EXP key. After you enter the coefficient, press the EE or EXP key and enter the power 10. To enter a negative power of 10, press the + / - key or the - key, depending on your calculator.

Number to Enter Procedure Calculator Display

4 * 106 4 EE or EXP 6

2.5 * 10-4 2.5 EE or EXP + / - 4

When a calculator answer appears in scientific notation, the coefficient is shown as a number that is at least 1 but less than 10, followed by a space or E and the power of 10. To express this display in scientific notation, write the coefficient value, write * 10, and use the power of 10 as an exponent.

Calculator Display Expressed in Scientific Notation

7.52 * 104

5.8 * 10-2

On many calculators, a number is converted into scientific notation using the appropriate keys. For example, the number 0.000 52 is entered, followed by pressing the 2nd or 3rd function key (2nd F) and the SCI key. The scientific notation appears in the calculator display as a coefficient and the power of 10.

or or

4 06

2.5 — 04 2.5 E — 042.5 —04

4 E064 06

ENGAGE 1.12 Describe how you enter a number in scientific notation on your calculator.

or or

7.52 04

5.8 — 02 5.8 E — 025.8 —02

7.52 E047.52 04

b. 0.000 016

STEP 1 Move the decimal point to obtain a coefficient that is at least 1 but less than 10. For a number less than 1, the decimal point is moved to the right five places to give a coefficient of 1.6.

STEP 2 Express the number of places moved as a power of 10. Moving the decimal point five places to the right gives a power of negative 5, written as 10-5.

STEP 3 Write the product of the coefficient multiplied by the power of 10. 1.6 * 10-5

SELF TEST 1.8

Write each of the following in scientific notation:

a. 425 000 b. 0.000 000 86 c. 0.007 30 d. 978 * 105

ANSWER

a. 4.25 * 105 b. 8.6 * 10-7 c. 7.30 * 10-3 d. 9.78 * 107 PRACTICE PROBLEMS

Try Practice Problems 1.27 and 1.28

0.000 52 5.2 10-4* Calculator display

2ndF SCI oror == 5.2— 04 5.2 E— 045.2 —04

Converting Scientific Notation to a Standard Number When a number written in scientific notation has a positive power of 10, the standard number is obtained by moving the decimal point to the right for the same number of places as the power of 10. Placeholder zeros are used, as needed, to give additional places.

Scientific Notation Standard Number

4.3 0 430= =4.3 102*

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20 CHAPTER 1 Chemistry in Our Lives

For a number with a negative power of 10, the standard number is obtained by moving the decimal point to the left for the same number of places as the power of 10. Placeholder zeros are added in front of the coefficient as needed.

PRACTICE PROBLEMS Try Practice Problems 1.29 and 1.30

Scientific Notation Standard Number

0 0 0 0 0 2.5= 0.000 025=2.5 10-5*

SAMPLE PROBLEM 1.9 Writing Scientific Notation as a Standard Number

TRY IT FIRST

Write each of the following as a standard number:

a. 7.2 * 10-3 b. 2.4 * 105

SOLUTION

a. To write the standard number for an exponential number with a negative power of 10, move the decimal point to the left the same number of places (three) as the power of 10. Add placeholder zeros before the coefficient as needed.

ANSWER

a. 0.000 725 b. 3 050 000

2.4 0 0 0 0= 240 000=2.4 105*

0 0 0 7.2 m= 0.0072=7.2 10-3*

b. To write the standard number for an exponential number with a positive power of 10, move the decimal point to the right the same number of places (five) as the power of 10. Add placeholder zeros following the coefficient as needed.

SELF TEST 1.9

Write each of the following as a standard number:

a. 7.25 * 10-4 b. 3.05 * 106

PRACTICE PROBLEMS

1.5 Writing Numbers in Scientific Notation

1.27 Write each of the following in scientific notation: a. 55 000 b. 480 c. 0.000 005 d. 0.000 14 e. 0.0072 f. 670 000

1.28 Write each of the following in scientific notation: a. 180 000 000 b. 0.000 06 c. 750 d. 0.15 e. 0.024 f. 1500

1.29 Write each of the following as a standard number: a. 1.2 * 104 b. 8.25 * 10-2 c. 4 * 106 d. 5.8 * 10-3

1.30 Write each of the following as a standard number: a. 3.6 * 10-5 b. 8.75 * 104 c. 3 * 10-2 d. 2.12 * 105

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Concept Map 21

UPDATE Forensic Evidence Helps Solve the Crime

Using a variety of laboratory tests, Sarah finds ethylene glycol in Gloria’s blood. The quantitative tests indicate that Gloria had ingested 125 g of ethylene glycol. Sarah determines that the liquid in a glass found in Gloria’s home was ethylene glycol that had

been added to an alcoholic beverage. Ethylene glycol is a clear, sweet-tasting, thick liquid that is odorless and mixes with water. It is easy to obtain since it is used as antifreeze in automobiles and in brake fluid. Because the initial symptoms of ethylene glycol poisoning are similar to being intoxicated, the victim is often unaware of its presence.

If ingestion of ethylene glycol occurs, it can cause depression of the central nervous system, cardiovascular damage, and kidney failure. If discovered quickly, hemodialysis may be used to remove ethylene glycol from the blood. A toxic amount of ethylene glycol is 1.5 g of ethylene glycol/kg of body mass. Thus, 75 g could be fatal for a 50-kg (110-lb) person.

Sarah determines that fingerprints on the glass containing the ethylene glycol were those of Gloria’s

husband. This evidence along with the container of antifreeze found in the home led to the arrest and conviction of the husband for poisoning his wife.

Applications

1.31 Identify each of the following comments in the police report as an observation, a hypothesis, an experiment, or a conclusion: a. Gloria may have had a heart attack. b. Test results indicate that Gloria was poisoned. c. The liquid in the glass was analyzed. d. The antifreeze in the pantry was the same color as the

liquid in the glass.

1.32 Identify each of the following comments in the police report as an observation, a hypothesis, an experiment, or a conclusion: a. Gloria may have committed suicide. b. Sarah ran blood tests to identify any toxic substances. c. The temperature of Gloria’s body was 34 °C. d. The fingerprints found on the glass were determined to

be her husband’s.

1.33 A container was found in the home of the victim that contained 120 g of ethylene glycol in 450 g of liquid. What was the percentage of ethylene glycol? Express your answer to the ones place.

1.34 If the toxic quantity is 1.5 g of ethylene glycol per 1000 g of body mass, what percentage of ethylene glycol is fatal?

Substances

CHEMISTRY IN OUR LIVES

deals with uses the is learned by uses key math skills

Hypothesis

Experiments

Conclusion

Reading the Text

Practicing Problem Solving

Working with a Group

Self-Testing

Answering the Engage Questions

Trying It First

Chemicals

Scientific Method

Observations

Identifying Place Values

Using Positive and Negative Numbers

Calculating Percentages

Solving Equations

Converting Between Standard

Numbers and Scientific Notation

called starting with

that lead to

CONCEPT MAP

M01_TIMB8119_06_SE_C01.indd 21 11/29/18 9:24 AM

22 CHAPTER 1 Chemistry in Our Lives

CHAPTER REVIEW

1.1 Chemistry and Chemicals LEARNING GOAL Define the term chemistry, and identify chemicals. • Chemistry is the study of the composition,

structure, properties, and reactions of matter. • A chemical always has the same compo-

sition and properties wherever it is found.

1.2 Scientific Method: Thinking Like a Scientist LEARNING GOAL Describe the scientific method. • The scientific method is a process of

explaining natural phenomena beginning with making observations, forming a hypothesis, and performing experiments.

• After repeated successful experiments, a conclusion may be drawn that the hypothesis is valid.

1.3 Studying and Learning Chemistry LEARNING GOAL Identify strategies that are effective for learning. Develop a study plan for learning chemistry. • A plan for learning chemistry utilizes

the features in the text that help develop a successful approach to learning chemistry.

• By using the Learning Goals, Reviews, Engage questions, Analyze the Problems, Try It First, Sample Problems, and Self Tests in the chapter, and Practice Problems at the end of each section, you can successfully learn the concepts of chemistry.

1.4 Key Math Skills for Chemistry LEARNING GOAL Review math concepts used in chemistry: place values, positive and negative numbers, percentages, solving equations, and interpreting graphs. • Solving chemistry problems involves a

number of math skills: identifying place values, using positive and negative numbers, calculating percentages, solving equations, and interpreting graphs.

1.5 Writing Numbers in Scientific Notation LEARNING GOAL Write a number in scientific notation. • A number written in

scientific notation has two parts, a coefficient and a power of 10.

• When a number greater than 1 is converted to scientific notation, the power of 10 is positive.

• When a number less than 1 is written in scientific notation, the power of 10 is negative.

1 * 105 hairs 8 * 10-6 m

chemical A substance that has the same composition and properties wherever it is found.

chemistry The study of the composition, structure, properties, and reactions of matter.

conclusion An explanation of an observation that has been validated by repeated experiments that support a hypothesis.

experiment A procedure that tests the validity of a hypothesis. hypothesis An unverified explanation of a natural phenomenon. observation Information determined by noting and recording a

natural phenomenon.

scientific method The process of making observations, proposing a hypothesis, and testing the hypothesis; after repeated experiments validate the hypothesis, a conclusion may be drawn as to its validity.

scientific notation A form of writing large and small numbers using a coefficient that is at least 1 but less than 10, followed by a power of 10.

KEY TERMS

The chapter section containing each Key Math Skill is shown in parentheses at the end of each heading.

Identifying Place Values (1.4) • The place value identifies the numerical value of each digit in a

number.

Example: Identify the place value for each of the digits in the number 456.78.

KEY MATH SKILLS

Answer: Digit Place Value

4 hundreds

5 tens

6 ones

7 tenths

8 hundredths

M01_TIMB8119_06_SE_C01.indd 22 11/29/18 9:24 AM

Key Math Skills 23

Using Positive and Negative Numbers in Calculations (1.4)

• A positive number is any number that is greater than zero and has a positive sign ( + ), which is often omitted. A negative number is any number that is less than zero and is written with a negative sign ( - ).

• When two positive numbers are added, multiplied, or divided, the answer is positive.

• When two negative numbers are multiplied or divided, the answer is positive. When two negative numbers are added, the answer is negative.

• When a positive and a negative number are multiplied or divided, the answer is negative.

• When a positive and a negative number are added, the smaller number is subtracted from the larger number, and the result has the same sign as the larger number.

• When two numbers are subtracted, change the sign of the number to be subtracted, then follow the rules for addition.

Example: Evaluate each of the following: a. - 8 - 14 = b. 6 * ( - 3) = Answer: a. - 22 b. - 18

Calculating Percentages (1.4) • A percentage is the part divided by the total (whole) multiplied

by 100%.

Example: A drawer contains 6 white socks and 18 black socks. What is the percentage of white socks?

Answer: 6 white socks 24 total socks

* 100% = 25% white socks

Solving Equations (1.4) An equation in chemistry often contains an unknown. To rearrange an equation to obtain the unknown factor by itself, you keep it balanced by performing matching mathematical operations on both sides of the equation.

• If you eliminate a number or symbol by subtracting, subtract that same number or symbol from both sides.

• If you eliminate a number or symbol by adding, add that same number or symbol to both sides.

• If you cancel a number or symbol by dividing, divide both sides by that same number or symbol.

• If you cancel a number or symbol by multiplying, multiply both sides by that same number or symbol.

Example: Solve the equation for a: 3a - 8 = 28 Answer: Add 8 to both sides 3a - 8 + 8 = 28 + 8

3a = 36

Divide both sides by 3 3a 3

= 36 3

a = 12 Check: 3(12) - 8 = 28

36 - 8 = 28 28 = 28

Your answer a = 12 is correct.

500

450

400

350

300

250

200

150

100

0 20 40 60 80 100

S ol

ub il

it y

(g s

ug ar

/1 00

m L

w at

er )

Temperature (°C)

Solubility of Sugar in Water versus Temperature

Interpreting Graphs (1.4)

• A graph represents the relationship between two variables. • The quantities are plotted along two perpendicular axes, which are

the x axis (horizontal) and y axis (vertical). • The title indicates the components of the x and y axes. • Numbers on the x and y axes show the range of values of the

variables. • The graph shows the relationship between the component on the

y axis and that on the x axis.

Example:

a. Does the amount of sugar that dissolves in 100 mL of water increase or decrease when the temperature increases?

b. How many grams of sugar dissolve in 100 mL of water at 70 °C?

c. At what temperature (°C) will 275 g of sugar dissolve in 100 mL of water?

Answer: a. increase b. 320 g c. 55 °C

Writing Numbers in Scientific Notation (1.5) • A number written in scientific notation consists of a coefficient

and a power of 10. A number is written in scientific notation by:

• Moving the decimal point to obtain a coefficient that is at least 1 but less than 10.

• Expressing the number of places moved as a power of 10. The power of 10 is positive if the decimal point is moved to the left, negative if the decimal point is moved to the right.

Example: Write the number 28 000 in scientific notation. Answer: Moving the decimal point four places to the left gives

a coefficient of 2.8 and a positive power of 10, 104. The number 28 000 written in scientific notation is 2.8 * 104.

M01_TIMB8119_06_SE_C01.indd 23 11/29/18 9:24 AM

24 CHAPTER 1 Chemistry in Our Lives

UNDERSTANDING THE CONCEPTS

The chapter sections to review are shown in parentheses at the end of each problem.

1.35 A “chemical-free” shampoo includes the following ingredients: water, cocamide, glycerin, and citric acid. Is the shampoo truly “chemical-free”? (1.1)

1.36 A “chemical-free” sunscreen includes the following ingredients: titanium dioxide, vitamin E, and vitamin C. Is the sunscreen truly “chemical-free”? (1.1)

1.37 According to Sherlock Holmes, “One must follow the rules of scientific inquiry, gathering, observing, and testing data, then formulating, modifying, and rejecting hypotheses, until only one remains.” Did Holmes use the scientific method? Why or why not? (1.2)

1.38 In A Scandal in Bohemia, Sherlock Holmes receives a mysterious note. He states, “I have no data yet. It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” What do you think Holmes meant? (1.2)

1.39 For each of the following, indicate if the answer has a positive or negative sign: (1.4)

a. Two negative numbers are added. b. A positive and negative number are multiplied.

1.40 For each of the following, indicate if the answer has a positive or negative sign: (1.4)

a. A negative number is subtracted from a positive number. b. Two negative numbers are divided.

Applications

1.41 Classify each of the following statements as an observation or a hypothesis: (1.2)

a. A patient breaks out in hives after receiving penicillin. b. Dinosaurs became extinct when a large meteorite struck

Earth and caused a huge dust cloud that severely decreased the amount of light reaching Earth.

c. A patient’s blood pressure was 110/75.

1.42 Classify each of the following statements as an observation or a hypothesis: (1.2)

a. Analysis of 10 ceramic dishes showed that four dishes contained lead levels that exceeded federal safety standards.

b. Marble statues undergo corrosion in acid rain. c. A child with a high fever and a rash may have chickenpox.

1.43 Select the correct phrase(s) to complete the following statement: If experimental results do not support your hypothesis, you should (1.2)

a. pretend that the experimental results support your hypothesis

b. modify your hypothesis c. do more experiments

1.44 Select the correct phrase(s) to complete the following statement: A hypothesis is supported when (1.2)

a. one experiment proves the hypothesis b. many experiments validate the hypothesis c. you think your hypothesis is correct

1.45 Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion: (1.2)

a. During an assessment in the emergency room, a nurse writes that the patient has a resting pulse of 30 beats/min.

b. A nurse thinks that an incision from a recent surgery that is red and swollen is infected.

c. Repeated studies show that lowering sodium in the diet leads to a decrease in blood pressure.

1.46 Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion: (1.2)

a. Drinking coffee at night keeps me awake. b. If I stop drinking coffee in the afternoon, I will be able to

sleep at night. c. I will try drinking coffee only in the morning.

1.47 Which of the following would be part of a successful study plan? (1.3)

a. skipping class and just reading the text b. working the Sample Problems as you go through a chapter

c. self-testing d. reading through the chapter, but working the problems later e. reading the assignment before class

1.48 Which of the following would be part of a successful study plan? (1.3)

a. studying all night before the exam b. highlighting important ideas in the text c. working problems in a notebook for easy reference d. forming a study group and discussing the problems together e. reviewing Key Math Skills and Core Chemistry Skills

1.49 Evaluate each of the following: (1.4)

a. 4 * ( - 8) = _______ b. - 12 - 48 = _______

c. - 168 - 4

= _______

1.50 Evaluate each of the following: (1.4)

a. - 95 - ( - 11) = _______ b. 152 - 19

= _______

c. 4 - 56 = _______ 1.51 A bag of gumdrops contains 16 orange gumdrops, 8 yellow

gumdrops, and 16 black gumdrops. (1.4)

a. What is the percentage of yellow gumdrops? Express your answer to the ones place.

b. What is the percentage of black gumdrops? Express your answer to the ones place.

1.52 On the first chemistry test, 12 students got As, 18 students got Bs, and 20 students got Cs. (1.4)

a. What is the percentage of students who received Bs? Express your answer to the ones place.

b. What is the percentage of students who received Cs? Express your answer to the ones place.

ADDITIONAL PRACTICE PROBLEMS

M01_TIMB8119_06_SE_C01.indd 24 11/29/18 9:24 AM

Answers to Engage Questions 25

1.53 Write each of the following in scientific notation: (1.5)

a. 120 000 b. 0.000 000 34 c. 0.066 d. 2700

1.54 Write each of the following in scientific notation: (1.5)

a. 0.0042 b. 310 c. 890 000 000 d. 0.000 000 056

1.55 Write each of the following as a standard number: (1.5)

a. 2.6 * 10-5 b. 6.5 * 102 c. 3.7 * 10-1 d. 5.3 * 105

1.56 Write each of the following as a standard number: (1.5)

a. 7.2 * 10-2 b. 1.44 * 103 c. 4.8 * 10-4 d. 9.1 * 106

Applications

1.57 Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion: (1.2)

a. A patient has a high fever and a rash on her back. b. A nurse tells a patient that her baby who gets sick after

drinking milk may be lactose intolerant. c. Numerous studies have shown that omega-3 fatty acids

lower triglyceride levels.

1.58 Identify each of the following as an observation, a hypothesis, an experiment, or a conclusion: (1.2)

a. Every spring, you have congestion and a runny nose. b. An overweight patient decides to exercise more to lose weight. c. Many research studies have linked obesity to heart disease.

ANSWERS TO ENGAGE QUESTIONS 1.8 Dividing both sides of the equation solves the equation for the

unknown V2.

1.9 A graph represents the relationship between two variables plotted in equal intervals along the x axis (horizontal) and the y axis (vertical).

1.10 The decimal point is moved five places to the left to give a coefficient that is at least 1 but less than 10 and a power of 10 that is a positive 5.

1.11 The decimal point is moved five places to the right to give a coefficient that is at least 1 but less than 10, and a power of 10 that is a negative 5.

1.12 Enter the coefficient, press the EE or EXP key, and enter the power of 10. To enter a negative power of 10, press the + / - key or the - key.

1.1 A chemical has the same composition and properties wherever it is found.

1.2 An experiment is done to find a relationship between the hypothesis and the observations.

1.3 Self-testing practices the retrieval of new information and helps connect to prior knowledge.

1.4 The value 0 is located in the first place to the right of the decimal point, which is the tenths place.

1.5 Addition of a negative number and a positive number gives an answer that has the sign of the larger value. Addition of two negative numbers gives a larger number with a negative sign.

1.6 The value of 100% represents exactly 100 units of the whole.

1.7 Subtracting 8 from both sides of the equation places like terms on the same sides.

The following problems are related to the topics in this chapter. However, they do not all follow the chapter order, and they require you to combine concepts and skills from several sections. These problems will help you increase your critical thinking skills and prepare for your next exam.

1.59 Classify each of the following as an observation, a hypothesis, an experiment, or a conclusion: (1.2)

a. The bicycle tire is flat. b. If I add air to the bicycle tire, it will expand to the proper size. c. When I added air to the bicycle tire, it was still flat. d. The bicycle tire has a leak in it.

1.60 Classify each of the following as an observation, a hypothesis, an experiment, or a conclusion: (1.2)

a. A big log in the fire does not burn well. b. If I chop the log into smaller wood pieces, it will burn better. c. The small wood pieces burn brighter and make a hotter fire. d. The small wood pieces are used up faster than burning the

big log.

1.61 Solve each of the following for x: (1.4)

a. 2x + 5 = 41 b. 5x 3

= 40

1.62 Solve each of the following for z: (1.4)

a. 3z - ( - 6) = 12 b. 4z

- 12 = - 8

Use the following graph for problems 1.63 and 1.64:

CHALLENGE PROBLEMS

0.35

0.30 0.25 0.20

S ol

ub il

it y

(g C

O 2/

10 0

g w

at er

) 0.15

0.10 0.05

0 0 10 20

Temperature (°C)

Solubility of Carbon Dioxide in Water versus Temperature

30 40 50 60

1.63 a. What does the title indicate about the graph? (1.4) b. What is measured on the vertical axis? c. What is the range of values on the vertical axis? d. Does the solubility of carbon dioxide increase or decrease

with an increase in temperature?

1.64 a. What is measured on the horizontal axis? (1.4) b. What is the range of values on the horizontal axis? c. What is the solubility of carbon dioxide in water at 25 °C? d. At what temperature does carbon dioxide have a solubility

of 0.20 g/100 g water?

M01_TIMB8119_06_SE_C01.indd 25 11/29/18 9:24 AM

26 CHAPTER 1 Chemistry in Our Lives

ANSWERS TO SELECTED PROBLEMS 1.25 a. This graph shows the relationship between body

temperature and time since death. b. temperature, in °C c. 20 °C to 44 °C d. decrease

1.27 a. 5.5 * 104 b. 4.8 * 102 c. 5 * 10-6 d. 1.4 * 10-4 e. 7.2 * 10-3 f. 6.7 * 105

1.29 a. 12 000 b. 0.0825 c. 4 000 000 d. 0.0058

1.31 a. hypothesis b. conclusion c. experiment d. observation

1.33 27% ethylene glycol

1.35 No. All of the ingredients are chemicals.

1.37 Yes. Sherlock’s investigation includes making observations (gathering data), formulating a hypothesis, testing the hypothesis, and modifying it until one of the hypotheses is validated.

1.39 a. negative b. negative

1.41 a. observation b. hypothesis c. observation

1.43 b and c

1.45 a. observation b. hypothesis c. conclusion

1.47 b, c, and e

1.49 a. - 32 b. - 60 c. 42 1.51 a. 20% b. 40%

1.53 a. 1.2 * 105 b. 3.4 * 10-7 c. 6.6 * 10-2 d. 2.7 * 103

1.55 a. 0.000 026 b. 650 c. 0.37 d. 530 000

1.57 a. observation b. hypothesis c. conclusion

1.59 a. observation b. hypothesis c. experiment d. conclusion

1.61 a. 18 b. 24

1.63 a. The graph shows the relationship between the solubility of carbon dioxide in water and temperature.

b. solubility of carbon dioxide (g CO2/100 g water) c. 0 to 0.35 g of CO2/100 g of water d. decrease

1.1 a. Chemistry is the study of the composition, structure, properties, and reactions of matter.

b. A chemical is a substance that has the same composition and properties wherever it is found.

1.3 Many chemicals are listed on a multivitamin bottle, such as vitamin A, vitamin B3, vitamin B12, vitamin C, and folic acid.

1.5 Typical items found in a drugstore, and some of the chemicals they contain, are as follows:

Antacid tablets: calcium carbonate, cellulose, starch, stearic acid, silicon dioxide

Mouthwash: water, alcohol, thymol, glycerol, sodium benzoate, benzoic acid

Cough suppressant: menthol, beta-carotene, sucrose, glucose

1.7 a. observation b. hypothesis c. experiment d. observation e. observation f. conclusion

1.9 a. observation b. hypothesis c. experiment d. experiment

1.11 There are several things you can do that will help you successfully learn chemistry: forming a study group, retesting, working Sample Problems before reading the given answer, working the Self Test items, answering Engage questions as you study, working Practice Problems and checking Answers, reading the assignment ahead of class, and keeping a problem notebook.

1.13 a, c, and e

1.15 a. thousandths b. ones c. tenths d. hundreds e. hundredths

1.17 a. 23 b. - 30 c. - 2 d. 54 e. - 12 1.19 a. The graph shows the relationship between the temperature

of a cup of tea and time. b. temperature, in °C c. 20 °C to 90 °C d. decrease

1.21 a. 9 b. 42 c. 14 d. 3

1.23 a. 84% b. 72% c. 30% d. 5%

M01_TIMB8119_06_SE_C01.indd 26 11/29/18 9:24 AM

During the past few months, Greg has had an increased number of headaches, dizzy spells, and nausea. He goes to his doctor’s office, where Sandra, the registered nurse, completes the initial part of his exam by recording several measurements: weight 164 lb, height 5 ft 8 in., temperature 37.2 °C, and blood pressure 155/95. Normal blood pressure is 120/80 or lower.

When Greg sees his doctor, he is diagnosed with high blood pressure, or hypertension. The doctor prescribes 80. mg of Inderal (propranolol), which is available in 40.-mg tablets. Inderal is a beta blocker, which relaxes the muscles of the heart. It is used to treat hypertension, angina (chest pain), arrhythmia, and migraine headaches.

Two weeks later, Greg visits his doctor again, who determines that Greg’s blood pressure is now 152/90. The doctor increases the dosage of Inderal to 160. mg. Sandra informs Greg that he needs to increase his daily dosage from two tablets to four tablets.

CAREER

Registered Nurse In addition to assisting physicians, registered nurses work to promote patient health and prevent and treat disease. They provide patient care and help patients cope with illness. They take measurements such as a patient’s weight, height, temperature, and blood pressure; make conversions; and calculate drug dosage rates. Registered nurses also maintain detailed medical records of patient symptoms and prescribed medications.

Chemistry and Measurements

A few weeks later, Greg complains to his doctor that he is feel- ing tired. He has a blood test to determine if his iron level is low. You can see the results of Greg’s blood serum iron level in the UPDATE Greg’s Visit with His Doctor, page 59, and determine if Greg should be given an iron supplement.

UPDATE Greg’s Visit with His Doctor

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28 CHAPTER 2 Chemistry and Measurements

2.1 Units of Measurement LEARNING GOAL Write the names and abbreviations for the metric and SI units used in measurements of volume, length, mass, temperature, and time.

Think about your day. You probably took some measurements. Perhaps you checked your weight by stepping on a bathroom scale. If you made rice for dinner, you added two cups of water to one cup of rice. If you did not feel well, you may have taken your temperature. Whenever you take a measurement, you use a measuring device such as a scale, a measuring cup, or a thermometer.

Scientists and health professionals throughout the world use the metric system of measurement. It is also the common measuring system in all but a few countries in the world. The International System of Units (SI), or Système International, is the official system of measurement throughout the world except for the United States. In chemistry, we use metric units and SI units for volume, length, mass, temperature, and time, as listed in TABLE 2.1.

Measurement Metric SI

Volume liter (L) cubic meter (m3)

Length meter (m) meter (m)

Mass gram (g) kilogram (kg)

Temperature degree Celsius (°C) kelvin (K)

Time second (s) second (s)

TABLE 2.1 Units of Measurement and Their Abbreviations

Your weight on a bathroom scale is a measurement.

1.7 m (65 in.)

58.0 kg (128 lb)

2.1 km (1.3 mi) 12 kg (26 lb)

22 °C (72 °F)

There are many measurements in everyday life.

LOOKING AHEAD

2.1 Units of Measurement 28 2.2 Measured Numbers and

Significant Figures 31 2.3 Significant Figures in

Calculations 34 2.4 Prefixes and Equalities 39 2.5 Writing Conversion

Factors 42 2.6 Problem Solving Using

Unit Conversion 47 2.7 Density 53

FIGURE 2.1 In the metric system, volume is based on the liter.

946.4 mL = 1 qt 1000 mL = 1 L

Suppose you walked 1.3 mi to campus today, carrying a backpack that weighs 26 lb. The temperature was 72 °F. Perhaps you weigh 128 lb and your height is 65 in. These measurements and units may seem familiar to you because they are stated in the U.S. system of measurement. However, in chemistry, we use the metric system in making our measure- ments. Using the metric system, you walked 2.1 km to campus, carrying a backpack that has a mass of 12 kg, when the temperature was 22 °C. You have a mass of 58.0 kg and a height of 1.7 m.

Volume Volume (V ) is the amount of space a substance occupies. The metric unit for volume is the liter (L), which is slightly larger than a quart (qt). In a laboratory or a hospital, chemists work with metric units of volume that are smaller and more convenient, such as the milliliter (mL). There are 1000 mL in 1 L (see FIGURE 2.1). Some relationships between units for volume are

1 L = 1000 mL 1 L = 1.057 qt 946.4 mL = 1 qt

M02_TIMB8119_06_SE_C02.indd 28 11/27/18 11:38 AM

2.1 Units of Measurement 29

Length The metric and SI unit of length is the meter (m). The centimeter (cm), a smaller unit of length, is commonly used in chemistry and is about equal to the width of your little finger (see FIGURE 2.2). Some relationships between units for length are

1 m = 100 cm 1 m = 39.37 in. 1 m = 1.094 yd 2.54 cm = 1 in.

Mass The mass of an object is a measure of the quantity of material it contains. The SI unit of mass, the kilogram (kg), is used for larger masses such as body mass. In the metric system, the unit for mass is the gram (g), which is used for smaller masses. There are 1000 g in 1 kg. One pound (lb) is equal to 453.6 g. Some relationships between units for mass are

1 kg = 1000 g 1 kg = 2.205 lb 453.6 g = 1 lb

You may be more familiar with the term weight than with mass. Weight is a measure of the gravitational pull on an object. On Earth, an astronaut with a mass of 75.0 kg has a weight of 165 lb. On the Moon, where the gravitational pull is one-sixth that of Earth, the astronaut has a weight of 27.5 lb. However, the mass of the astronaut is the same as on Earth, 75.0 kg. Scientists measure mass rather than weight because mass does not depend on gravity. In a chemistry laboratory, an electronic balance is used to measure the mass in grams of a substance (see FIGURE 2.3).

Temperature Temperature tells us how hot something is, tells us how cold it is outside, or helps us deter- mine if we have a fever (see FIGURE 2.4). In the metric system, temperature is measured using Celsius temperature. On the Celsius (°C) temperature scale, water freezes at 0 °C and boils at 100 °C, whereas on the Fahrenheit (°F) scale, water freezes at 32 °F and boils at 212 °F. In the SI system, temperature is measured using the Kelvin (K) temperature scale on which the lowest possible temperature is 0 K, known as absolute zero. A unit on the Kelvin scale is called a kelvin (K) and is not written with a degree sign.

Time We typically measure time in units such as years (yr), days, hours (h), minutes (min), or seconds (s). Of these, the SI and metric unit of time is the second (s). The standard now used to determine a second is an atomic clock. Some relationships between units for time are

1 day = 24 h 1 h = 60 min 1 min = 60 s

FIGURE 2.2 Length in the metric system (SI) is based on the meter, which is slightly longer than a yard.

1 in. = 2.54 cm

Centimeters 1 2 3 4 5

10 20 30 40 50 60 70 80 90 100

12 36

1 ft 2 ft 3 ft

Meterstick

Yardstick

1 m = 39.37 in.

Inches24

FIGURE 2.3 On an electronic balance, the digital readout gives the mass of a nickel, which is 5.01 g.

FIGURE 2.4 A thermometer is used to determine temperature.

A stopwatch is used to measure the time of a race.

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30 CHAPTER 2 Chemistry and Measurements

2.2 Measured Numbers and Significant Figures LEARNING GOAL Identify a number as measured or exact; determine the number of significant figures in a measured number.

When you make a measurement, you use some type of measuring device. For example, you may use a meterstick to measure your height, a scale to check your weight, or a thermometer to take your temperature.

Measured Numbers Measured numbers are the numbers you obtain when you measure a quantity such as your height, weight, or temperature. Suppose you are going to measure the lengths of the objects in FIGURE 2.5. To report the length of the object, you observe the numerical values of the marked lines at the end of the object. Then you can estimate by visually dividing the space between the marked lines. This estimated value is the final digit in a measured number.

For example, in Figure 2.5a, the end of the object is between the marks of 4 cm and 5 cm, which means that the length is more than 4 cm but less than 5 cm. If you estimate that the end of the object is halfway between 4 cm and 5 cm, you would report its length as 4.5 cm. Another student might report the length of the same object as 4.4 cm because people do not estimate in the same way.

The metric ruler shown in Figure 2.5b is marked at every 0.1 cm. Now you can determine that the end of the object is between 4.5 cm and 4.6 cm. Perhaps you report its length as 4.55 cm, whereas another student reports its length as 4.56 cm. Both results are acceptable.

In Figure 2.5c, the end of the object appears to line up with the 3-cm mark. Because the end of the object is on the 3-cm mark, the estimated digit is 0, which means the measurement is reported as 3.0 cm.

Significant Figures In a measured number, the significant figures (SFs) are all the digits including the estimated digit. Nonzero numbers are always counted as significant figures. However, a zero may or may not be a significant figure depending on its position in a number. TABLE 2.2 gives the rules and examples of counting significant figures.

PRACTICE PROBLEMS Try Practice Problems 2.1 to 2.8

REVIEW Writing Numbers in Scientific

Notation (1.5)

CORE CHEMISTRY SKILL Counting Significant Figures

PRACTICE PROBLEMS Try Practice Problems 2.9 to 2.14

SAMPLE PROBLEM 2.1 Units of Measurement

TRY IT FIRST

On a typical day, a nurse encounters several situations involving measurement. State the name and type of measurement indicated by the units in each of the following:

a. A patient has a temperature of 38.5 °C. b. A physician orders 1.5 g of cefuroxime for injection. c. A physician orders 1 L of a sodium chloride solution to be given intravenously. d. A medication is to be given to a patient every 4 h.

SOLUTION

a. A degree Celsius is a unit of temperature. b. A gram is a unit of mass. c. A liter is a unit of volume. d. An hour is a unit of time.

SELF TEST 2.1

State the names and types of measurements for an infant that is 54.6 cm long with a mass of 5.2 kg.

PRACTICE PROBLEMS

2.1 Units of Measurement

2.1 Write the abbreviation for each of the following: a. gram b. degree Celsius c. liter d. pound e. second

2.2 Write the abbreviation for each of the following: a. kilogram b. kelvin c. quart d. meter e. centimeter

2.3 State the type of measurement in each of the following statements: a. I put 12 L of gasoline in my gas tank. b. My friend is 170 cm tall. c. Earth is 385 000 km away from the Moon. d. The horse won the race by 1.2 s.

2.4 State the type of measurement in each of the following statements: a. I rode my bicycle 15 km today. b. My dog weighs 12 kg. c. It is hot today. It is 30 °C. d. I added 2 L of water to my fish tank.

2.5 State the name of the unit and the type of measurement indicated for each of the following quantities:

a. 4.8 m b. 325 g c. 1.5 mL d. 4.8 * 102 s e. 28 °C

2.6 State the name of the unit and the type of measurement indicated for each of the following quantities:

a. 0.8 L b. 3.6 cm c. 4 kg d. 3.5 h e. 373 K

Applications

2.7 On a typical day, medical personnel may encounter several situations involving measurement. State the name and type of measurement indicated by the units in each of the following: a. The clotting time for a blood sample is 12 s. b. A premature baby weighs 2.0 kg. c. An antacid tablet contains 1.0 g of calcium carbonate. d. An infant has a temperature of 39.2 °C.

2.8 On a typical day, medical personnel may encounter several situations involving measurement. State the name and type of measurement indicated by the units in each of the following: a. During open-heart surgery, the temperature of a patient is

lowered to 29 °C. b. The circulation time of a red blood cell through the body

is 20 s. c. A patient with a persistent cough is given 10. mL of cough

syrup. d. The amount of iron in the red blood cells of the body

is 2.5 g.

ANSWER

A centimeter (cm) is a unit of length. A kilogram (kg) is a unit of mass.

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2.2 Measured Numbers and Significant Figures 31

2.2 Measured Numbers and Significant Figures LEARNING GOAL Identify a number as measured or exact; determine the number of significant figures in a measured number.

PRACTICE PROBLEMS Try Practice Problems 2.1 to 2.8

REVIEW Writing Numbers in Scientific

Notation (1.5)

CORE CHEMISTRY SKILL Counting Significant Figures

PRACTICE PROBLEMS Try Practice Problems 2.9 to 2.14

FIGURE 2.5 The lengths of the rectangular objects are measured in centimeters.

10 cm

2 3 4 5

10 cm

2 3 4 5

10 cm

2 3 4 5

(a) 4.5 cm

(b) 4.55 cm

Rule Measured Number Number of Significant Figures

1. A number is a significant figure if it is

a. a nonzero digit 4.5 g 122.35 m

2 5

b. a zero between nonzero digits 205 °C 5.008 kg

3 4

c. a zero at the end of a decimal number 50. L 16.00 mL

2 4

d. in the coefficient of a number written in scientific notation

4.8 * 105 m 5.70 * 10-3 g

2 3

2. A zero is not significant if it is

a. at the beginning of a decimal number 0.0004 s 0.075 cm

1 2

b. used as a placeholder in a large number without a decimal point

850 000 m 1 250 000 g

2 3

TABLE 2.2 Significant Figures in Measured Numbers

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32 CHAPTER 2 Chemistry and Measurements

Significant Zeros and Scientific Notation In this text, we will place a decimal point after a significant zero at the end of a number. For example, if a measurement is written as 500. g, the decimal point after the second zero indicates that both zeros are significant. To show this more clearly, we can write it as 5.00 * 102 g. When the first zero in the measurement 300 m is a significant zero, but the second zero is not, the measurement is written as 3.0 * 102 m. We will assume that all zeros at the end of large standard numbers without a decimal point are not significant. Therefore, we write 400 000 g as 4 * 105 g, which has only one significant figure.

ENGAGE 2.1 Why is the zero in the coefficient of 3.20 * 104 cm a significant figure?

PRACTICE PROBLEMS Try Practice Problems 2.15 to 2.18

Counted Numbers Defined Equalities

Items Metric System U.S. System

8 doughnuts 1 L = 1000 mL 1 ft = 12 in. 2 baseballs 1 m = 100 cm 1 qt = 4 cups 5 capsules 1 kg = 1000 g 1 lb = 16 oz

TABLE 2.3 Examples of Some Exact Numbers

Exact Numbers Exact numbers are those numbers obtained by counting items or using a definition that c ompares two units in the same measuring system. Suppose a friend asks you how many classes you are taking. You would answer by counting the number of classes in your schedule. Suppose you want to state the number of seconds in one minute. Without using any measuring device, you would give the definition: There are 60 s in 1 min. Exact numbers are not measured, do not have a limited number of significant figures, and do not affect the number of significant figures in a calculated answer. For more examples of exact numbers, see TABLE 2.3.

The number of baseballs is counted, which means 2 is an exact number.

SAMPLE PROBLEM 2.2 Significant Figures

TRY IT FIRST

Write the number of significant figures in each of the following measured numbers:

a. 0.000 250 m b. 70.040 g c. 1.020 * 106 L

SOLUTION

ANALYZE THE PROBLEM

Given Need Connect

measured number number of significant figures

Table 2.2, rules for significant figures

a. Nonzero digits and zeros at the end of a decimal number are significant. 0.000 250 m has three SFs (Rules 1a, 1c).

b. Nonzero digits, zeros between nonzero digits, or at end of a decimal number are significant. 70.040 g has five SFs (Rules 1a, 1b, 1c).

c. All digits in the coefficient of a number written in scientific notation are significant. 1.020 * 106 L has four SFs (Rule 1d).

SELF TEST 2.2

Write the number of significant figures in each of the following measured numbers:

a. 0.040 08 m b. 6.00 * 103 g ANSWER

a. four SFs (Rules 1a, 1b) b. three SFs (Rule 1d)

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2.2 Measured Numbers and Significant Figures 33

For example, a mass of 42.2 g and a length of 5.0 * 10-3 cm are measured numbers because they are obtained using measuring tools. There are three SFs in 42.2 g because all nonzero digits are always significant. There are two SFs in 5.0 * 10-3 cm because all the digits in the coefficient of a number written in scientific notation are significant. However, a quantity of three eggs is an exact number that is obtained by counting. In the equality 1 kg = 1000 g, the masses of 1 kg and 1000 g are both exact numbers because this is a definition in the metric system.

ENGAGE 2.2 Why is the 4 in 4 hats an exact number, whereas the 6.24 in 6.24 cm has three significant figures?

PRACTICE PROBLEMS Try Practice Problems 2.19 to 2.24

SAMPLE PROBLEM 2.3 Measured and Exact Numbers

TRY IT FIRST

Identify each of the following numbers as measured or exact, give the number of significant figures (SFs) in each of the measured numbers, and explain:

a. 0.170 L b. 4 knives c. 6.3 * 10-6 s d. 1 m = 100 cm

SOLUTION

ANALYZE THE PROBLEM

Given Need Connect

numbers identify exact or measured, number of SFs

Table 2.2, rules for SFs in measured numbers

STEP 1 A measured number is the result of a measurement. An exact number is obtained by counting or by definition.

a. measured b. exact, counted c. measured d. exact, definition

STEP 2 Significant figures are the nonzero digits and any zeros after nonzero digits in a decimal number. In numbers written in scientific notation, the numbers in the coefficient are all significant.

a. three SFs c. two SFs

SELF TEST 2.3

Identify each of the following numbers as measured or exact, and give the number of significant figures (SFs) in each of the measured numbers:

a. 0.020 80 kg b. 5.06 * 104 h c. 4 chemistry books ANSWER

a. measured; four SFs b. measured; three SFs c. exact

PRACTICE PROBLEMS

2.2 Measured Numbers and Significant Figures

2.9 Use the metric ruler to measure the length in each of the following, and write the measurement, the estimated digit, and the number of significant figures:

10 cm

2 3 4 5 10 cm

2 3 4 5

(a) (b) (c)

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34 CHAPTER 2 Chemistry and Measurements

2.10 Determine the volume, in milliliters, of each liquid in the graduated cylinders by reading the lowest point of the curve of the liquid in the diagrams (a), (b), and (c) using the correct number of significant figures.

2.11 How many significant figures are in each of the following? a. 11.005 g b. 0.000 32 m c. 36 000 000 km d. 1.80 * 104 kg e. 0.8250 L f. 30.0 °C

2.12 How many significant figures are in each of the following? a. 20.60 mL b. 1036.48 kg c. 4.00 m d. 20 °C e. 60 800 000 g f. 5.0 * 10-3 L 2.13 In which of the following pairs do both numbers contain the

same number of significant figures? a. 11.0 m and 11.00 m b. 0.0250 m and 0.205 m c. 0.000 12 s and 12 000 s d. 250.0 L and 2.5 * 10-2 L

2.14 In which of the following pairs do both numbers contain the same number of significant figures? a. 0.005 75 g and 5.75 * 10-3 g b. 405 K and 405.0 K c. 150 000 s and 1.50 * 104 s d. 3.8 * 10-2 L and 3.80 * 105 L

2.15 Indicate if the zeros are significant in each of the following measurements:

a. 0.0038 m b. 5.04 cm c. 800. L d. 3.0 * 10-3 kg e. 85 000 g

2.16 Indicate if the zeros are significant in each of the following measurements:

a. 20.05 °C b. 5.00 m c. 0.000 02 g d. 120 000 yr e. 8.05 * 102 L 2.17 Write each of the following in scientific notation with two

significant figures: a. 5000 L b. 30 000 g c. 100 000 m d. 0.000 25 cm

2.18 Write each of the following in scientific notation with two significant figures:

a. 5 100 000 g b. 26 000 s c. 40 000 m d. 0.000 820 kg

2.19 Identify the numbers in each of the following statements as measured or exact: a. A patient has a mass of 67.5 kg. b. A patient is given 2 tablets of medication. c. In the metric system, 1 L is equal to 1000 mL. d. The distance from Denver, Colorado, to Houston, Texas, is

1720 km.

2.20 Identify the numbers in each of the following statements as measured or exact: a. There are 31 students in the laboratory. b. The oldest known flower lived 1.20 * 108 yr ago. c. The largest gem ever found, an aquamarine, has a mass of

104 kg. d. A laboratory test shows a blood cholesterol level of

184 mg/dL.

2.21 Identify the measured number(s), if any, in each of the following pairs of numbers: a. 3 hamburgers and 6 oz of hamburger b. 1 table and 4 chairs c. 0.75 lb of grapes and 350 g of butter d. 60 s = 1 min

2.22 Identify the exact number(s), if any, in each of the following pairs of numbers: a. 5 pizzas and 50.0 g of cheese b. 6 nickels and 16 g of nickel c. 3 onions and 3 lb of onions d. 5 miles and 5 cars

Applications

2.23 Identify each of the following as measured or exact, and give the number of significant figures (SFs) in each measured number: a. The mass of a neonate is 1.607 kg. b. The Daily Value (DV) for iodine for an infant is 130 mcg. c. There are 4.02 * 106 red blood cells in a blood sample. d. In November, 23 babies were born in a hospital.

2.24 Identify each of the following as measured or exact, and give the number of significant figures (SFs) in each measured number: a. An adult with the flu has a temperature of 103.5 °F. b. A blister (push-through) pack of prednisone contains

21 tablets. c. The time for a nerve impulse to travel from the feet to the

brain is 0.46 s. d. A brain contains 1.20 * 1010 neurons.

(a)

(b)

(c)

2.3 Significant Figures in Calculations LEARNING GOAL Give the correct number of significant figures for a calculated answer.

In the sciences, we measure many things: the length of a bacterium, the volume of a gas sample, the temperature of a reaction mixture, or the mass of iron in a sample. The number

REVIEW Identifying Place Values (1.4)

Using Positive and Negative Numbers in Calculations (1.4)

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2.3 Significant Figures in Calculations 35

of significant figures in measured numbers determines the number of significant figures in the calculated answer.

Using a calculator will help you perform calculations faster. However, calculators cannot think for you. It is up to you to enter the numbers correctly, press the correct function keys, and give the answer with the correct number of significant figures.

Rounding Off Suppose you decide to buy carpeting for a room that has a length of 5.52 m and a width of 3.58 m. To determine how much carpeting you need, you would calculate the area of the room by multiplying 5.52 times 3.58 on your calculator. The calculator shows the number 19.7616 in its display. Because each of the original measurements has only three signifi- cant figures, the calculator display (19.7616) should be rounded off to three significant figures, 19.8.

5.52 m * 3.58 m = 19.7616 = 19.8 m2

Therefore, you can order carpeting that will cover an area of 19.8 m2. Each time you use a calculator, it is important to look at the original measurements and

determine the number of significant figures that can be used for the answer. You can use the following rules to round off the numbers shown in a calculator display.

Rules for Rounding Off

1. If the first digit to be dropped is 4 or less, it and all following digits are simply dropped from the number.

2. If the first digit to be dropped is 5 or greater, the last retained digit of the number is increased by 1.

KEY MATH SKILL Rounding Off

ENGAGE 2.3 Why is 10.072 rounded off to three significant figures equal to 10.1?

A technician uses a calculator in the laboratory.

Number to Round Off Three Significant Figures Two Significant Figures

8.4234 8.42 (drop 34) 8.4 (drop 234)

14.780 14.8 (drop 80, increase the last retained digit by 1)

15 (drop 780, increase the last retained digit by 1)

3256 3260* (drop 6, increase the last retained digit by 1, add 0) (3.26 * 103)

3300* (drop 56, increase the last retained digit by 1, add 00) (3.3 * 103)

*The value of a large number is retained by using placeholder zeros to replace dropped digits.

TABLE 2.4 Rules for Rounding Off

SAMPLE PROBLEM 2.4 Rounding Off

TRY IT FIRST

Round off each of the following numbers to three significant figures: a. 35.7823 m b. 0.002 621 7 L c. 3.8268 * 103 g

SOLUTION

ANALYZE THE PROBLEM

Given Need Connect

measured numbers

three significant figures

Table 2.4, rules for rounding off

Three SFs

Calculator display

Final answer, rounded off to three SFs

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36 CHAPTER 2 Chemistry and Measurements

Multiplication and Division with Measured Numbers In multiplication or division, the final answer is written so that it has the same number of significant figures (SFs) as the measurement with the fewest SFs.

Perform the following operations with measured numbers:

2.8 * 67.40 34.8

When the problem has multiple steps, the numbers in the numerator are multiplied and then divided by each of the numbers in the denominator.

2.8 * 67.40 , 34.8 = 5.422988506 = 5.4

Because the calculator display has more digits than the significant figures in the measured numbers allow, we need to round it off. Using the measured number that has the smallest number (two) of significant figures, 2.8, we round off the calculator display to an answer with two SFs.

Adding Significant Zeros Sometimes, a calculator display gives a small whole number. For example, suppose the calculator display is 4, but you used measurements that have three significant numbers. Then two significant zeros are added to give 4.00 as the correct answer.

8.00 2.00 = 4. = 4.00

PRACTICE PROBLEMS Try Practice Problems 2.25 to 2.28

CORE CHEMISTRY SKILL Using Significant Figures in

Calculations

ENGAGE 2.4 Why is the answer for the multiplication of 0.3 * 52.6 written with one significant figure?

PRACTICE PROBLEMS Try Practice Problems 2.29 and 2.30

ENGAGE 2.5 Why does the calculator answer of 5 in part c. require two significant zeros to give an answer of 5.00?

Three SFs

Three SFs Calculator display

Final answer, two zeros added to give three SFs

STEP 1 Identify the digits to be dropped.

a. drop 823 b. drop 17 c. drop 68

STEP 2 Increase the last retained digit by 1 if the first digit dropped is 5 or greater. Keep the last retained digit if the first digit dropped is 4 or less.

a. Increase the last retained digit by 1 to give 35.8 m. b. Retain digits to give 0.002 62 L. c. Increase the last retained digit by 1 to give 3.83 * 103 g.

SELF TEST 2.4

Round off each of the numbers in Sample Problem 2.4 to two significant figures.

ANSWER

a. 36 m b. 0.0026 L c. 3.8 * 103 g

A calculator is helpful in working problems and doing calculations faster.

SAMPLE PROBLEM 2.5 Significant Figures in Multiplication and Division

TRY IT FIRST

Perform the following calculations with measured numbers, and give the answers with the correct number of significant figures:

a. 56.8 * 0.37 b. (2.075) (0.585)

(8.42) (0.0245) c.

25.0 5.00

SOLUTION

ANALYZE THE PROBLEM

Given Need Connect

multiplication and division

answer with the correct number of SFs

rules for multiplication/ division

Two SFs Four SFs Three SFs

Calculator display

Answer, rounded off to two SFs

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2.3 Significant Figures in Calculations 37

Addition and Subtraction with Measured Numbers In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places.

2.045

+ 34.1 36.145

36.1

When numbers are added or subtracted to give an answer ending in zero, the zero does not appear after the decimal point in the calculator display. For example, 14.5 g - 2.5 g = 12.0 g. However, if you do the subtraction on your calculator, the display shows 12. To write the correct answer, a significant zero is written after the decimal point.

Thousandths place

Calculator display

Answer, rounded off to the tenths place

ENGAGE 2.6 Why is the answer 57.7 correct for the addition of 55.2 and 2.506?

Perform the following operations with measured numbers:

2.8 * 67.40 34.8

When the problem has multiple steps, the numbers in the numerator are multiplied and then divided by each of the numbers in the denominator.

2.8 * 67.40 , 34.8 = 5.422988506 = 5.4

8.00 2.00 = 4. = 4.00

PRACTICE PROBLEMS Try Practice Problems 2.25 to 2.28

CORE CHEMISTRY SKILL Using Significant Figures in

Calculations

ENGAGE 2.4 Why is the answer for the multiplication of 0.3 * 52.6 written with one significant figure?

PRACTICE PROBLEMS Try Practice Problems 2.29 and 2.30

ENGAGE 2.5 Why does the calculator answer of 5 in part c. require two significant zeros to give an answer of 5.00?

Three SFs

Three SFs Calculator display

Final answer, two zeros added to give three SFs

STEP 1 Determine the number of significant figures in each measured number.

a. 56.8 * 0.37 b. (2.075) (0.585)

(8.42) (0.0245) c.

25.0 5.00

STEP 2 Perform the indicated operations on the calculator.

a. 21.016 b. 5.884313345 c. 5.

STEP 3 Round off (or add zeros) to give the same number of significant figures as the measurement having the fewest significant figures.

a. 21 b. 5.88 c. 5.00

SELF TEST 2.5

Perform the following calculations with measured numbers, and give the answers with the correct number of significant figures:

a. 45.26 * 0.010 88 b. 2.6 , 324 c. 4.0 * 8.00

Three SFs Two SFs Four SFs Three SFs

Three SFs Three SFs

Three SFs

Calculator display

ANSWER

a. 0.4924 b. 0.0080 or 8.0 * 10-3 c. 2.0

Tenths place (fewer decimal places)

SAMPLE PROBLEM 2.6 Decimal Places in Addition and Subtraction

TRY IT FIRST

Perform the following calculations with measured numbers, and give each answer with the correct number of decimal places:

a. 104 + 7.8 + 40 b. 153.247 - 14.82

SOLUTION

ANALYZE THE PROBLEM

Given Need Connect

addition and subtraction

answer with the correct number of decimal places

rules for addition/ subtraction

STEP 1 Determine the number of decimal places in each measured number.

a. 104 7.8

+ 40

Ones place

Tenths place

Tens place (fewest decimal places)

b. 153.247 - 14.82

Thousandths place

Hundredths place

(fewer decimal places)

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38 CHAPTER 2 Chemistry and Measurements

ANSWER

a. 83.70 b. 0.5 PRACTICE PROBLEMS

Try Practice Problems 2.31 and 2.32

STEP 2 Perform the indicated operations on the calculator.

a. 151.8 b. 138.427

STEP 3 Round off (or add zeros) to give the same number of decimal places as the measured number having the fewest decimal places.

a. 150 b. 138.43

SELF TEST 2.6

Perform the following operations with measured numbers, and give each answer with the correct number of decimal places:

a. 82.45 + 1.245 + 0.000 56 b. 4.259 - 3.8

Rounded off to the tens place Rounded off to the hundredths place

Calculator display

PRACTICE PROBLEMS

2.3 Significant Figures in Calculations

2.25 Round off each of the following calculator answers to three significant figures:

a. 1.854 kg b. 88.2038 L c. 0.004 738 265 cm d. 8807 m e. 1.832 * 105 s 2.26 Round off each of the calculator answers in problem 2.25 to two

significant figures.

2.27 Round off or add zeros to each of the following to give three significant figures:

a. 56.855 m b. 0.002 282 g c. 11 527 s d. 8.1 L

2.28 Round off or add zeros to each of the following to give two significant figures:

a. 3.2805 m b. 1.855 * 102 g c. 0.002 341 mL d. 2 L

2.29 Perform each of the following operations, and give each answer with the correct number of significant figures:

a. 45.7 * 0.034 b. 0.002 78 * 5

c. 34.56 1.25

d. (0.2465) (25)

1.78

e. (2.8 * 104) (5.05 * 10-6) f. (3.45 * 10-2) (1.8 * 105)

(8 * 103) 2.30 Perform each of the following operations, and give each answer

with the correct number of significant figures: a. 400 * 185

b. 2.40

(4) (125)

c. 0.825 * 3.6 * 5.1

d. (3.5) (0.261)

(8.24) (20.0)

e. (5 * 10-5) (1.05 * 104)

(8.24 * 10-8)

f. (4.25 * 102) (2.56 * 10-3)

(2.245 * 10-3) (56.5)

2.31 Perform each of the following operations, and give each answer with the correct number of decimal places: a. 45.48 + 8.057 b. 23.45 + 104.1 + 0.025 c. 145.675 - 24.2 d. 1.08 - 0.585 e. 2300 + 196.11 f. 145.111 - 22.9 + 34.49

2.32 Perform each of the following operations, and give each answer with the correct number of decimal places: a. 5.08 + 25.1 b. 85.66 + 104.10 + 0.025 c. 24.568 - 14.25 d. 0.2654 - 0.2585 e. 66.77 + 17 - 0.33 f. 460 - 33.77

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2.4 Prefixes and Equalities 39

2.4 Prefixes and Equalities LEARNING GOAL Use the numerical values of prefixes to write a metric equality.

The special feature of the metric system is that a prefix can be placed in front of any unit to increase or decrease its size by some factor of 10. For example, the prefixes milli and micro are used to make the smaller units, milligram (mg) and microgram (mg).

The U.S. Food and Drug Administration (FDA) has determined the Daily Values (DV) for nutrients for adults and children age 4 or older. Examples of these recommended Daily Values, some of which use prefixes, are listed in TABLE 2.5.

The prefix centi is like cents in a dollar. One cent would be a “centidollar” or 0.01 of a dollar. That also means that one dollar is the same as 100 cents. The prefix deci is like dimes in a dollar. One dime would be a “decidollar” or 0.1 of a dollar. That also means that one dollar is the same as 10 dimes. TABLE 2.6 lists some of the metric prefixes, their symbols, and their numerical values.

(DV) for Selected Nutrients

Nutrient Amount Recommended

Calcium 1.0 g

Copper 2 mg

Iodine 150 mg (150 mcg)

Iron 18 mg

Magnesium 400 mg

Niacin 20 mg

Phosphorus 800 mg

Potassium 3.5 g

Selenium 70. mg (70. mcg)

Sodium 2.4 g

Zinc 15 mg

TABLE 2.5 Daily Values

TABLE 2.6 Metric and SI Prefixes

Prefix Symbol Numerical Value Scientific Notation Equality

Prefixes That Increase the Size of the Unit

peta P 1 000 000 000 000 000 1015 1 Pg = 1 * 1015 g 1 g = 1 * 10-15 Pg

tera T 1 000 000 000 000 1012 1 Ts = 1 * 1012 s 1 s = 1 * 10-12 Ts

giga G 1 000 000 000 109 1 Gm = 1 * 109 m 1 m = 1 * 10-9 Gm

mega M 1 000 000 106 1 Mg = 1 * 106 g 1 g = 1 * 10-6 Mg

kilo k 1 000 103 1 km = 1 * 103 m 1 m = 1 * 10-3 km

Prefixes That Decrease the Size of the Unit

deci d 0.1 10-1 1 dL = 1 * 10-1 L 1 L = 10 dL

centi c 0.01 10-2 1 cm = 1 * 10-2 m 1 m = 100 cm

milli m 0.001 10-3 1 ms = 1 * 10-3 s 1 s = 1 * 103 ms

micro m* 0.000 001 10-6 1 mg = 1 * 10-6 g 1 g = 1 * 106 mg

nano n 0.000 000 001 10-9 1 nm = 1 * 10-9 m 1 m = 1 * 109 nm

pico p 0.000 000 000 001 10-12 1 ps = 1 * 10-12 s 1 s = 1 * 1012 ps

femto f 0.000 000 000 000 001 10-15 1 fs = 1 * 10-15 s 1 s = 1 * 1015 fs

*In medicine, the abbreviation mc is used for the prefix micro because the symbol m may be misread, which could result in a medication error. Thus, 1 mg would be written as 1 mcg.

The relationship of a prefix to a unit can be expressed by replacing the prefix with its numerical value. For example, when the prefix kilo in kilometer is replaced with its value of 1000, we find that a kilometer is equal to 1000 m. Other examples follow:

1 kilometer (1 km) = 1000 meters (1000 m = 103 m)

1 kiloliter (1 kL) = 1000 liters (1000 L = 103 L)

1 kilogram (1 kg) = 1000 grams (1000 g = 103 g)

CORE CHEMISTRY SKILL Using Prefixes

PRACTICE PROBLEMS Try Practice Problems 2.33 to 2.40

ENGAGE 2.7 Why is 60. mg of vitamin C the same as 0.060 g of vitamin C?

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40 CHAPTER 2 Chemistry and Measurements

Equalities Between Prefixes Equalities can also be written for two prefix units. Suppose you need an equality for milliliters and deciliters. From Table 2.6, using L as the base unit, we can write the equalities 1 L = 10 dL and 1 L = 1000 mL and then write an equality for dL and mL.

1 L = 10 dL = 1000 mL or 1 dL = 100 mL

An endoscope has a video camera with a width of 1 mm attached to the end of a thin cable.

SAMPLE PROBLEM 2.7 Prefixes and Equalities

TRY IT FIRST

The camera in an endoscope has a width of 1 mm. Complete each of the following equalities involving millimeters:

a. 1 m = mm b. 1 cm = mm

SOLUTION

a. 1 m = 1000 mm b. 1 cm = 10 mm

SELF TEST 2.7

a. What is the relationship between liters and centiliters? b. What is the relationship between millimeters and micrometers? ANSWER

a. 1 L = 100 cL b. 1 mm = 1000 mm (mcm)

Measuring Length An ophthalmologist may measure the diameter of the retina of an eye in centimeters (cm), whereas a surgeon may need to know the length of a nerve in millimeters (mm). When the prefix centi is used with the unit meter, it becomes centimeter, a length that is one-hundredth of a meter (0.01 m). When the prefix milli is used with the unit meter, it becomes millimeter, a length that is one-thousandth of a meter (0.001 m). There are 100 cm and 1000 mm in a meter.

If we compare the lengths of a millimeter and a centimeter, we find that 1 mm is 0.1 cm; there are 10 mm in 1 cm. These comparisons are examples of equalities, which show the relationship between two units that measure the same quantity. Examples of equalities between different metric units of length follow:

1 m = 100 cm = 1 * 102 cm 1 m = 1000 mm = 1 * 103 mm

1 cm = 10 mm = 1 * 101 mm Some metric units for length are compared in FIGURE 2.6.

First quantity

unit+Number unit+Number

Second quantity

1 m 100 cm=

This example of an equality shows the relationship between meters and centimeters.

FIGURE 2.6 The metric length of 1 m is the same length as 10 dm, 100 cm, or 1000 mm.

10 20 30 40 50 60 70 80 90 100

m dm cm mm

1 10

100 1000

1 2 3 4

1 mm 1 cm = 10 mm

1 dm

ENGAGE 2.8 Why can the relationship of centimeters and meters be written as 1 m = 100 cm or 0.01 m = 1 cm?

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2.4 Prefixes and Equalities 41

When you see 1 cm, you are reading about length; when you see 1 cm3 or 1 cc or 1 mL, you are reading about volume. A comparison of units of volume is illustrated in FIGURE 2.8.

Substance in Blood Normal Range

Albumin 3.5–5.4 g/dL

Ammonia 20970 mg/dL (mcg/dL)

Calcium 8.5–10.5 mg/dL

Cholesterol 105–250 mg/dL

Iron (male) 809160 mg/dL (mcg/dL)

Protein (total) 6.0–8.5 g/dL

TABLE 2.7 Some Normal Laboratory Test Values

FIGURE 2.7 A plastic intravenous fluid container contains 1000 mL.

ENGAGE 2.9 Why is the volume 3.1 mL equal to the volume of 3.1 cm3?

Measuring Volume Volumes smaller than 1 L are common in the health sciences. When a liter is divided into 10 equal portions, each portion is a deciliter (dL). There are 10 dL in 1 L. Laboratory results for bloodwork are often reported in mass per deciliter. TABLE 2.7 lists normal laboratory test values for some substances in the blood.

When a liter is divided into a thousand parts, each of the smaller volumes is a milliliter (mL). In a 1-L container of physiological saline, there are 1000 mL of solution (see FIGURE 2.7). Examples of equalities between different metric units of volume follow:

1 L = 10 dL = 1 * 101 dL 1 L = 1000 mL = 1 * 103 mL

1 dL = 100 mL = 1 * 102 mL 1 mL = 1000 mL (mcL) = 1 * 103 mL (mcL) The cubic centimeter (abbreviated as cm3 or cc) is the volume of a cube whose

dimensions are 1 cm on each side. A cubic centimeter has the same volume as a milliliter, and the units are often used interchangeably.

1 cm3 = 1 cc = 1 mL

5 mL

1 cm

10 cm–=-1 dm

Volume–=-1 cm–*–1 cm–*–1 cm =-1 cm3–=-1 mL

Volume–=-10 cm–*–10 cm–*–10 cm =-1000 cm3 =-1000 mL =-1 L

10 c

10 cm

1.0 mL–= =-1.0 cc1.0 cm3

A cube measuring 10 cm on each side has a volume of 1000 cm3 or 1 L; a cube measuring 1 cm on each side has a volume of 1 cm3 (cc) or 1 mL.

FIGURE 2.8 Measurement of volume

A syringe contains 1.0 mL, which is the same as 1.0 cm3 and 1.0 cc.

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42 CHAPTER 2 Chemistry and Measurements

Measuring Mass When you go to the doctor for a physical examination, your mass is recorded in kilograms, whereas the results of your laboratory tests are reported in grams, milligrams (mg), or micrograms (mg or mcg). A kilogram is equal to 1000 g. One gram represents the same mass as 1000 mg, and one mg equals 1000 mg (or 1000 mcg). Examples of equalities between different metric units of mass follow:

1 kg = 1000 g = 1 * 103 g 1 g = 1000 mg = 1 * 103 mg

1 mg = 1000 mg (mcg) = 1 * 103 mg (mcg)

PRACTICE PROBLEMS Try Practice Problems 2.41 to 2.44

PRACTICE PROBLEMS

2.4 Prefixes and Equalities

2.33 Write the abbreviation for each of the following units: a. milligram b. deciliter c. kilometer d. picogram

2.34 Write the abbreviation for each of the following units: a. gigagram b. megameter c. microliter d. femtosecond

2.35 Write the complete name for each of the following units: a. cL b. kg c. ms d. Pm

2.36 Write the complete name for each of the following units: a. dL b. Ts c. mcg d. pm

2.37 Write the numerical value for each of the following prefixes: a. centi b. tera c. milli d. deci

2.38 Write the numerical value for each of the following prefixes: a. giga b. micro c. mega d. nano

2.39 Use a prefix to write the name for each of the following: a. 0.1 g b. 10-6 g c. 1000 g d. 0.01 g

2.40 Use a prefix to write the name for each of the following: a. 109 m b. 106 m c. 0.001 m d. 10-12 m

2.41 Complete each of the following metric relationships: a. 1 m = cm b. 1 m = nm c. 1 mm = m d. 1 L = mL 2.42 Complete each of the following metric relationships: a. 1 Mg = g b. 1 mL = mL c. 1 g = kg d. 1 g = mg 2.43 For each of the following pairs, which is the larger unit? a. milligram or kilogram b. milliliter or microliter c. m or km d. kL or dL e. nanometer or picometer

2.44 For each of the following pairs, which is the smaller unit? a. mg or g b. centimeter or nanometer c. millimeter or micrometer d. mL or dL e. centigram or megagram

2.5 Writing Conversion Factors LEARNING GOAL Write a conversion factor for two units that describe the same quantity.

Many problems in chemistry and the health sciences require you to change from one unit to another unit. Suppose you worked 2.0 h on your homework, and someone asked you how many minutes that was. You would answer 120 min. You must have multiplied 2.0 h * 60 min/h because you knew the equality (1 h = 60 min) that related the two units. When you expressed 2.0 h as 120 min, you changed only the unit of measurement used to express the time. Any equality can be written as fractions called conversion factors with one of the quantities in the numerator and the other quantity in the denominator. Two conversion factors are always possible from any equality. Be sure to include the units when you write the conversion factors.

Two Conversion Factors for the Equality: 1 h = 60 min

Numerator Denominator

h h

60 min

1 h and

1 h 60 min

These factors are read as “60 minutes per 1 hour” and “1 hour per 60 minutes.” The term per means “divide.” Some common relationships are given in TABLE 2.8.

The numbers in any definition between two metric units or between two U.S. system units are exact. Because numbers in a definition are exact, they are not used to determine

REVIEW Calculating Percentages (1.4)

CORE CHEMISTRY SKILL Writing Conversion Factors from

Equalities

PRACTICE PROBLEMS Try Practice Problems 2.45 and 2.46

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2.5 Writing Conversion Factors 43

significant figures. For example, the equality of 1 g = 1000 mg is a definition, which means that both of the numbers 1 and 1000 are exact.

When an equality consists of a metric unit and a U.S. unit, one of the numbers in the equality is obtained by measurement and counts toward the significant figures in the answer. For example, the equality of 1 lb = 453.6 g is obtained by measuring the grams in exactly 1 lb. In this equality, the measured quantity 453.6 g has four significant figures, whereas the 1 is exact. An exception is the relationship of 1 in. = 2.54 cm, which has been defined as exact.

Metric Conversion Factors We can write two metric conversion factors for any of the metric relationships. For example, from the equality for meters and centimeters, we can write the following factors:

Metric Equality Conversion Factors

1 m = 100 cm 100 cm 1 m

and 1 m

100 cm

Both are proper conversion factors for the relationship; one is just the inverse of the other. The usefulness of conversion factors is enhanced by the fact that we can turn a conversion factor over and use its inverse. The numbers 100 and 1 in this equality, and its conversion factors are both exact numbers.

Metric–U.S. System Conversion Factors Suppose you need to convert from pounds, a unit in the U.S. system, to kilograms in the metric system. A relationship you could use is

1 kg = 2.205 lb

The corresponding conversion factors would be

2.205 lb 1 kg

and 1 kg

2.205 lb

FIGURE 2.9 illustrates the contents of some packaged foods in both U.S. and metric units.

ENGAGE 2.10 Why does the equality 1 day = 24 h have two conversion factors?

Quantity Metric (SI) U.S. Metric–U.S.

Length 1 km = 1000 m 1 ft = 12 in. 2.54 cm = 1 in. (exact) 1 m = 1000 mm 1 yd = 3 ft 1 m = 39.37 in.

1 cm = 10 mm 1 mi = 5280 ft 1 m = 1.094 yd

1 km = 0.6214 mi

Volume 1 L = 1000 mL 1 qt = 4 cups 946.4 mL = 1 qt 1 dL = 100 mL 1 qt = 2 pt 1 L = 1.057 qt

1 mL = 1 cm3 1 gal = 4 qt 473.2 mL = 1 pt 1 mL = 1 cc* 3.785 L = 1 gal

5 mL = 1 tsp*

15 mL = 1 T (tbsp)*

Mass 1 kg = 1000 g 1 lb = 16 oz 1 kg = 2.205 lb 1 g = 1000 mg 453.6 g = 1 lb

1 mg = 1000 mcg* 28.35 g = 1 oz

Time 1 h = 60 min 1 h = 60 min

1 min = 60 s 1 min = 60 s

*Used in medicine.

TABLE 2.8 Some Common Equalities

FIGURE 2.9 In the United States, the contents of many packaged foods are listed in both U.S. and metric units.

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44 CHAPTER 2 Chemistry and Measurements

Equalities and Conversion Factors Stated Within a Problem An equality may also be stated within a problem that applies only to that problem. For example, the speed of a car in kilometers per hour or the price of onions in dollars per pound would be specific relationships for that problem only. From each of the following statements, we can write an equality and two conversion factors, and identify each number as exact or give the number of significant figures.

The car was traveling at a speed of 85 km/h.

Equality Conversion Factors Significant Figures or Exact

1 h = 85 km 85 km 1 h

and 1 h

85 km The 85 km is measured: It has two significant

figures. The 1 h is exact.

The price of onions is $1.24 per pound.

Equality Conversion Factors Significant Figures or Exact

1 lb = $1.24 $1.24 1 lb

and 1 lb

$1.24

The $1.24 is measured: It has three significant figures. The 1 lb is exact.

Conversion Factors from Dosage Problems Equalities stated within dosage problems for medications can also be written as conversion factors. Keflex (cephalexin), an antibiotic used for respiratory and ear infections, is available in 250-mg capsules. Vitamin C, an antioxidant, is available in 500-mg tablets. These dosage relationships can be used to write equalities from which two conversion factors can be derived.

One capsule contains 250 mg of Keflex.

Equality Conversion Factors Significant Figures or Exact

1 capsule = 250 mg of Keflex

250 mg Keflex

1 capsule and

1 capsule

250 mg Keflex

The 250 mg is measured: It has two significant figures. The 1 capsule is exact.

One tablet contains 500 mg of vitamin C.

Equality Conversion Factors Significant Figures or Exact

1 tablet = 500 mg of vitamin C

500 mg vitamin C

1 tablet and

1 tablet 500 mg vitamin C

The 500 mg is measured: It has one significant figure. The 1 tablet is exact.

Conversion Factors from a Percent, ppm, and ppb A percent (%) is written as a conversion factor by choosing a unit and expressing the numerical relationship of the parts of this unit to 100 parts of the whole. For example, a person might have 18% body fat by mass. The percent can be written as 18 mass units of body fat in every 100 mass units of body mass. Different mass units such as grams (g), kilograms (kg), or pounds (lb) can be used, but both units in the factor must be the same.

Equality Conversion Factors Significant Figures or Exact

100 kg of body mass = 18 kg of body fat

18 kg body fat

100 kg body mass and

100 kg body mass

18 kg body fat

The 18 kg is measured: It has two significant figures. The 100 kg is exact.

ENGAGE 2.11 How is a percent used to write an equality and two conversion factors?

Keflex (cephalexin), used to treat respiratory infections, is available in 250-mg capsules.

The thickness of the skin fold at the abdomen is used to determine the percentage of body fat.

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2.5 Writing Conversion Factors 45

When scientists want to indicate very small ratios, they use numerical relationships called parts per million (ppm) or parts per billion (ppb). The ratio of parts per million is the same as the milligrams of a substance per kilogram (mg/kg). The ratio of parts per billion equals the micrograms per kilogram (mg/kg, mcg/kg).

Ratio Units

parts per million (ppm) milligrams per kilogram (mg/kg)

parts per billion (ppb) micrograms per kilogram (mg/kg, mcg/kg)

For example, the maximum amount of lead that is allowed by the FDA in glazed pottery bowls is 2 ppm, which is 2 mg/kg.

Equality Conversion Factors Significant Figures or Exact

1 kg of glaze = 2 mg of lead

2 mg lead

1 kg glaze and

1 kg glaze

2 mg lead

The 2 mg is measured: It has one significant figure. The 1 kg is exact.

Conversion Factors with Powers Sometimes we use a conversion factor that is squared or cubed. This is the case when we need to calculate an area or a volume.

Distance = length

Area = length * length = length2

Volume = length * length * length = length3

Suppose you want to write the equality and the conversion factors for the relationship between an area in square centimeters and in square meters. To square the equality 1 m = 100 cm, we square both the number and the unit on each side.

Equality: 1 m = 100 cm

Area: (1 m)2 = (100 cm)2 or 1 m2 = (100)2 cm2

From the new equality, we can write two conversion factors as follows:

Conversion factors: (100 cm)2

(1 m)2 and

(1 m)2

(100 cm)2

In the following example, we show that the equality 1 in. = 2.54 cm can be squared to give area or can be cubed to give volume. Both the number and the unit must be squared or cubed.

Measurement Equality Conversion Factors

Length 1 in. = 2.54 cm 2.54 cm 1 in.

and 1 in.

2.54 cm

Area (1 in.)2 = (2.54 cm)2

(1 in.)2 = (2.54)2 cm2 = 6.45 cm2 (2.54 cm)2

(1 in.)2 and

(1 in.)2

(2.54 cm)2

Volume (1 in.)3 = (2.54 cm)3

(1 in.)3 = (2.54)3 cm3 = 16.4 cm3 (2.54 cm)3

(1 in.)3 and

(1 in.)3

(2.54 cm)3

SAMPLE PROBLEM 2.8 Equalities and Conversion Factors in a Problem

TRY IT FIRST

Write the equality and two conversion factors, and identify each number as exact or give the number of significant figures for each of the following:

a. The medication that Greg takes for his high blood pressure contains 40. mg of propranolol in 1 tablet.

b. Cold-water fish such as salmon contains 1.9% omega-3 fatty acids by mass.

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46 CHAPTER 2 Chemistry and Measurements

c. The U.S. Environmental Protection Agency (EPA) has set the maximum level for mercury in tuna at 0.5 ppm.

d. The area of (1 cm)2 is the same as (10 mm)2.

SOLUTION

a. Equality Conversion Factors Significant Figures or Exact 1 tablet = 40. mg of

propranolol 40. mg propranolol

1 tablet

and

1 tablet 40. mg propranolol

The 40. mg is measured: It has two significant figures. The 1 tablet is exact.

b. Equality Conversion Factors Significant Figures or Exact 100 g of salmon = 1.9 g

of omega-3 fatty acids 1.9 g omega@3 fatty acids

100 g salmon

and 100 g salmon

1.9 g omega@3 fatty acids

The 1.9 g is measured: It has two significant figures. The 100 g is exact.

c. Equality Conversion Factors Significant Figures or Exact 1 kg of tuna = 0.5 mg of

mercury 0.5 mg mercury

1 kg tuna

and 1 kg tuna

0.5 mg mercury

The 0.5 mg is measured: It has one significant figure. The 1 kg is exact.

d. Equality Conversion Factors Significant Figures or Exact

(1 cm)2 = (10 mm)2 (10 mm)2

(1 cm)2 and

(1 cm)2

(10 mm)2 Both 1 cm and 10 mm are exact,

by definition.

SELF TEST 2.8

Write the equality and its corresponding conversion factors, and identify each number as exact or give the number of significant figures for each of the following:

a. Levsin (hyoscyamine), used to treat stomach and bladder problems, is available as drops with 0.125 mg of Levsin per 1 mL of solution.

b. The EPA has set the maximum level of cadmium in rice as 0.4 ppm.

Propranolol is used to lower high blood pressure.

Salmon contains high levels of omega-3 fatty acids.

The maximum amount of mercury allowed in tuna is 0.5 ppm.

ANSWER

a. 1 mL of solution = 0.125 mg of Levsin

0.125 mg Levsin

1 mL solution and

1 mL solution 0.125 mg Levsin

The 0.125 mg is measured: It has three significant figures. The 1 mL is exact.

b. 1 kg of rice = 0.4 mg of cadmium

0.4 mg cadmium

1 kg rice and

1 kg rice

0.4 mg cadmium

The 0.4 mg is measured: It has one significant figure. The 1 kg is exact. PRACTICE PROBLEMS

Try Practice Problems 2.47 to 2.56

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2.6 Problem Solving Using Unit Conversion 47

PRACTICE PROBLEMS

2.5 Writing Conversion Factors

2.45 Why can two conversion factors be written for an equality such as 1 m = 100 cm?

2.46 How can you check that you have written the correct conversion factors for an equality?

2.47 Write the equality and two conversion factors for each of the following pairs of units: a. milligrams and kilograms b. nanograms and grams c. liters and kiloliters d. seconds and milliseconds e. millimeters and decimeters f. cubic meters and cubic centimeters

2.48 Write the equality and two conversion factors for each of the following pairs of units: a. centimeters and inches b. kilometers and miles c. pounds and grams d. liters and deciliters e. grams and picograms f. square centimeters and square inches

2.49 Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. One yard is 3 ft. b. One kilogram is 2.205 lb. c. A car goes 27 mi on 1 gal of gas. d. Sterling silver is 93% silver by mass. e. One minute is 60 s. f. One cubic meter is 1 * 106 cm3.

2.50 Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. One liter is 1.057 qt. b. At the store, oranges are $1.29 per lb. c. There are 7 days in 1 week. d. One deciliter contains 100 mL. e. An 18-carat gold ring contains 75% gold by mass. f. One square foot is 144 in.2

2.51 Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. A bee flies at an average speed of 3.5 m per second. b. The Daily Value (DV) for potassium is 3.5 g.

c. An automobile traveled 26.0 km on 1 L of gasoline. d. The pesticide level in plums was 29 ppb. e. Silicon makes up 28.2% by mass of Earth’s crust.

2.52 Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. The Daily Value (DV) for iodine is 150 mcg. b. The nitrate level in well water was 32 ppm. c. Gold jewelry contains 58% gold by mass. d. The price of a liter of milk is $1.65. e. A metric ton is 1000 kg.

Applications

2.53 Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. A calcium supplement contains 630 mg of calcium per

tablet. b. The Daily Value (DV) for vitamin C is 60 mg. c. The label on a bottle reads 50 mg of atenolol per tablet. d. A low-dose aspirin contains 81 mg of aspirin per tablet.

2.54 Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. The label on a bottle reads 10 mg of furosemide per 1 mL. b. The Daily Value (DV) for selenium is 70. mcg. c. An IV of normal saline solution has a flow rate of 85 mL per

hour. d. One capsule of fish oil contains 360 mg of omega-3 fatty

acids.

2.55 Write an equality and two conversion factors for each of the following medications: a. 10 mg of Atarax per 5 mL of Atarax syrup b. 0.25 g of Lanoxin per 1 tablet of Lanoxin c. 300 mg of Motrin per 1 tablet of Motrin

2.56 Write an equality and two conversion factors for each of the following medications: a. 2.5 mg of Coumadin per 1 tablet of Coumadin b. 100 mg of Clozapine per 1 tablet of Clozapine c. 1.5 g of Cefuroxime per 1 mL of Cefuroxime

2.6 Problem Solving Using Unit Conversion LEARNING GOAL Use conversion factors to change from one unit to another.

The process of problem solving in chemistry often requires one or more conversion factors to change a given unit to the needed unit. For the problem, the unit of the given and the unit of the needed are identified. From there, the problem is set up with one or more conversion factors used to convert the given unit to the needed unit as seen in Sample Problem 2.9.

Given unit * one or more conversion factors = needed unit

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48 CHAPTER 2 Chemistry and Measurements

SAMPLE PROBLEM 2.9 Using Conversion Factors

TRY IT FIRST

Greg’s doctor has ordered a PET scan of his heart. In radiological imaging, dosages of pharmaceuticals are based on body mass. If Greg weighs 164 lb, what is his body mass in kilograms?

SOLUTION

STEP 1 State the given and needed quantities.

ANALYZE THE PROBLEM

Given Need Connect

164 lb kilograms U.S.–metric conversion factor

STEP 2 Write a plan to convert the given unit to the needed unit.

2.205 lb and

1 kg = 2.205 lb

1 kg

2.205 lb

164 lb 74.4 kg=* 1 kg

2.205 lb Given Conversion factor

to cancel given unit

Unit for answer goes here

Answer

pounds kilograms U.S.– metric factor

STEP 3 State the equalities and conversion factors.

STEP 4 Set up the problem to cancel units and calculate the answer. Write the given, 164 lb, and multiply by the conversion factor that has lb in the denominator (bottom number) to cancel lb in the given.

ENGAGE 2.12 Why would you use the conversion

factor 1 lb

16 oz , not

16 oz 1 lb

, to convert

6.4 oz to pounds?

The given unit lb cancels out, and the needed unit kg is in the numerator. The unit you want in the final answer is the one that remains after all the other units have canceled out. This is a helpful way to check that you set up a problem properly.

lb * kg

lb = kg

The calculator display gives the numerical answer, which is adjusted to give a final answer with the proper number of significant figures (SFs). The value of 74.4 combined with the unit, kg, gives the final answer of 74.4 kg.

Unit needed for answer

2.205 2.205 7 4 . 3 7 6 4 1 7 2 3

1 164 74.4

Calculator display

Three SFs Four SFs

Exact

Three SFs (rounded off)

== =,164 * INTERACTIVE VIDEO

Conversion Factors

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2.6 Problem Solving Using Unit Conversion 49

SELF TEST 2.9

a. A total of 2500 mL of a boric acid antiseptic solution is prepared from boric acid concentrate. How many quarts of boric acid have been prepared?

b. A vial contains 65 mg of phenobarbital per 1 mL of solution. How many milliliters are needed for an order of 40. mg of phenobarbital?

PRACTICE PROBLEMS Try Practice Problems 2.57 to 2.62

ANSWER

a. 2.6 qt b. 0.62 mL

Using Two or More Conversion Factors In problem solving, two or more conversion factors are often needed to complete the change of units. In setting up these problems, one factor follows the other. Each factor is arranged to cancel the preceding unit until the needed unit is obtained. Once the problem is set up to cancel units properly, the calculations can be done without writing intermediate results. In this text, when two or more conversion factors are required, the final answer will be based on obtaining a final calculator display and rounding off (or adding zeros) to give the correct number of significant figures as shown in Sample Problem 2.10.

CORE CHEMISTRY SKILL Using Conversion Factors

ENGAGE 2.13 How are two conversion factors used in a problem setup?

SAMPLE PROBLEM 2.10 Using Two Conversion Factors

TRY IT FIRST

Greg has been diagnosed with diminished thyroid function. His doctor prescribes a dosage of 0.150 mg of Synthroid to be taken once a day. If tablets in stock contain 75 mcg of Synthroid, how many tablets are required to provide the prescribed medication?

SOLUTION

STEP 1 State the given and needed quantities.

ANALYZE THE PROBLEM

Given Need Connect

0.150 mg of Synthroid

number of tablets

metric conversion factor, clinical conversion factor

STEP 2 Write a plan to convert the given unit to the needed unit.

2 tablets= 1 tablet

75 mcg Synthroid *

Exact

Two SFs

0.150 mg Synthroid * 1000 mcg

1 mg

Three SFs Exact

Exact

milligrams number of tabletsmicrograms Metric factor

Clinical factor

STEP 3 State the equalities and conversion factors.

1 mg and

1 mg = 1000 mcg

1000 mcg

1 mg

1 tablet and

1 tablet = 75 mcg of Synthroid

75 mcg Synthroid

1 tablet

STEP 4 Set up the problem to cancel units and calculate the answer. The problem can be set up using the metric factor to cancel milligrams, and then the clinical factor to obtain the number of tablets as the final unit.

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50 CHAPTER 2 Chemistry and Measurements

ANSWER

a. 6 days b. 2.5 mL

SELF TEST 2.10

a. A bottle contains 120 mL of cough syrup. If one teaspoon (5 mL) is given four times a day, how many days will elapse before a refill is needed?

b. A patient is given a solution containing 0.625 g of calcium carbonate. If the calcium carbonate solution contains 1250 mg per 5 mL, how many milliliters of the solution were given to the patient?

One teaspoon of cough syrup is measured for a patient.

SAMPLE PROBLEM 2.11 Using a Percent as a Conversion Factor

TRY IT FIRST

A person who exercises regularly has 16% body fat by mass. If this person weighs 155 lb, what is the mass, in kilograms, of body fat?

SOLUTION

STEP 1 State the given and needed quantities.

ANALYZE THE PROBLEM

Given Need Connect

155 lb body weight kilograms of body fat

U.S.–metric conversion factor, percent conversion factor

STEP 2 Write a plan to convert the given unit to the needed unit.

Exercising regularly helps reduce body fat.

ANSWER

a. 160 g of fat b. 480 mg

2.205 lb body weight and

1 kg of body mass = 2.205 lb of body weight

1 kg body mass

2.205 lb body weight

16 kg body fat and

100 kg of body mass = 16 kg of body fat

100 kg body mass

16 kg body fat

pounds of body weight

kilograms of body mass

kilograms of body fat

U.S.–metric factor

Percent factor

155 lb body weight 11 kg of body fat* = 1 kg body mass

2.205 lb body weight

16 kg body fat

100 kg body mass *

Three SFs Four SFs Two SFsExact

Two SFsExact

STEP 3 State the equalities and conversion factors.

STEP 4 Set up the problem to cancel units and calculate the answer.

For problems that use several conversion factors, other plans may be possible. For exam- ple, for this problem, the pounds of body weight could be converted to pounds of body fat using the percent factor, which can be converted to kilograms of body fat using the metric–U.S. factor for kilograms and pounds.

SELF TEST 2.11

a. A package contains 2.4 lb of ground round. If it contains 15% fat, how many grams of fat are in the ground round?

b. A cream contains 4.0% (by mass) lidocaine to relieve back pain. If a patient uses 12 g of cream, how many milligrams of lidocaine are used?

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2.6 Problem Solving Using Unit Conversion 51

Conversion of Units in a Fraction Sometime units in an equality are written as a fraction that relates the two units. For example, we measure fuel consumption in a car in units of miles per gallon. Perhaps, the mileage for a car is 39.0 mi per gal (39.0 mi/gal). Someone driving a car in Europe would express the use of fuel in kilometers per liter (km/L). If we want to express mi/gal in units of km/L, we one use conversion factor to change miles to kilometers, and another to change gallons to liters as shown in Sample Problem 2.12.

SAMPLE PROBLEM 2.12 Conversion of Units in a Fraction

TRY IT FIRST

Your new car has a fuel consumption of 39.0 mi/gal. Convert this fuel consumption to km/L.

SOLUTION

STEP 1 State the given and needed quantities.

ANALYZE THE PROBLEM

Given Need Connect

39.0 mi 1 gal

km L

U.S.–metric conversion factors, km/mi, L/gal

ANSWER

a. 3 * 10-5 oz/lb b. 110 mi/h PRACTICE PROBLEMS

Try Practice Problems 2.63 to 2.68

0.6214 mi =

1 km = 0.6214 mi

1 km

0.6214 mi

3.785 L =

1 gal = 3.785 L

1 gal

3.785 L

miles gallon

kilometers gallon

kilometers liter

U.S.–metric factor

* = 1 km

0.6214 mi

39.0 mi

1 gal

3.785 L

16.6 km

1 L *

Exact

Three SFs

Four SFs Exact

Three SFs

Four SFs

ExactExact

STEP 2 Write a plan to convert the given unit to the needed unit.

STEP 3 State the equalities and conversion factors.

STEP 4 Set up the problem to cancel units and calculate the answer.

The problem can be set up using the U.S.–metric factor to convert miles to kilometers, and another U.S.–metric factor to convert gallons to liters to obtain the fraction km/L.

SELF TEST 2.12

Convert each of the following fractions to the indicated units:

a. 2 mg/kg to oz/lb b. 50. m/s to mi/h

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