Week 1 Lecture Video and Homework

Chris Pool

Chapter1MathToolboxstudents.pdf

Home >Chemistry homework help >Week 1 Lecture Video and Homework

Math Review

In chemistry you will encounter very large and very small numbers.

602,200,000,000,000,000,000,000 atoms

0.000000000166 m radius of a gold atom

How do scientists simplify very large or very small values containing many digits?

Scientific Notation

A number written in scientific notation is expressed as:

C x 10n where C is the coefficient (a number between 1- 9) and n is the exponent (a positive or negative integer)

602,200,000,000,000,000,000,000 atoms

0.000000000166 m radius of a gold atom

Practice – Scientific Notation

Calculations with Exponents

1. (6 x 103)(5 x 10-5) = ________________________ 2. (7 x 103)4 = _______________________________ 3. (6 x 103) + (1 x 104) = ________________________

Normal Notation Scientific Notation Diameter of the Earth 12800000 m

Length of a virus 0.00003 cm

Mass of a human 68 kg

Accuracy vs. Precision

How do scientists express the accuracy or precision of measurement?

Accuracy vs. Precision

Accuracy of a measured number is the how close it is to its expected or true value.

Precision of measurement is the extent of the agreement between repeated measurements of its value.

Trial Mass (grams) 1 100.01 2 99.99 3 100.00

Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other

Practice

Actual density = 19.32 g/cm3

Trial Student 1 Density (g/cm3)

Student 2 Density (g/cm3)

Student 3 Density (g/cm3)

Student 4 Density (g/cm3)

1 19.31 18.24 18.75 18.60 2 19.33 19.44 18.76 19.95 3 19.31 18.99 18.74 19.40

Average 19.32 18.89 18.75 19.32

Significant Figures

How do scientists know how many digits to record?

Exact vs. Measured Numbers

Significant Figures (SFs)

• The meaningful digits in a measured or calculated quantity

• All measurable digits plus one estimated

• Sig figs in a measurement depend on the measuring tool.

Practice

. l8. . . . l . . . . l9. . . . l . . . . l10. . cm What is the length of the red line?

What is the temperature?

All non-zero numbers in a measured number are significant.

Measurement Number of Significant Figures

38.15 cm

5.6 ft

65.6 lb

Counting Significant Figures

Leading zeros • Precede non-zero digits in a decimal number. • Are not significant.

Measurement Number of Significant Figures

0.008 mm

0.0156 oz

0.0042 lb

Leading Zeros

Trailing zeroes

Trailing zeros • Following non-zero numbers are significant in numbers

with decimal points.

Measurement Number of Significant Figures

25.000 cm

20.0 kg

48600 mL

Sandwiched zeros • Occur between nonzero numbers. • Are significant.

Measurement Number of Significant Figures

50.8 mm

2001 min

0.0702 lb

Sandwiched Zeros

Significant Figures in Scientific Notation

In scientific notation all digits including zeros in the coefficient are significant.

Scientific Notation Number of Significant Figures

8 x 104 m

8.0 x 104 m

8.00 x 104 m

State the number of significant figures in each of the following measurements:

A. 0.030 m B. 4.050 L

C. 0.0008 g

Practice

Calculated Answers

In calculations, § Answers must have the

same number of significant figures as the least precise measured number(s).

§ Calculator answers must often be rounded off.

§ Rounding rules are used to obtain the correct number of significant figures.

Practice

Adjust the following calculated answers to give answers with three significant figures:

A. 824.75143 cm

B. 0.112486 g

RULE 1. In carrying out a multiplication or division, the answer cannot have more significant figures than either of the original numbers.

Give an answer for the following with the correct number of significant figures: A. 2.19 x 4.2 =

1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 = 1) 61.59 2) 62 3) 60

Practice

RULE 2. In carrying out an addition or subtraction, the answer cannot have more digits after the decimal point than either of the original numbers or more digits after the leftmost uncertain digit than either of the original numbers.

4320 cm (10th place) - 1100 cm (100th place)

3220 cm (100th place) à 3200 cm

For each calculation, round the answer to give the correct number of significant figures.

A. 235.05 + 19.6 + 2 =

1) 257 2) 256.7 3) 256.65

B. 58000 - 1880 =

1) 56,120 2) 56,100 3) 56,000

Practice

More Practice – Sig Figs

Calculate the following: 1. 14.6608 + 12.2 + (1.500000 x 102) = ____________________

2. (5.5 x 10-8)(4 x 1010) = _______________________________ 6.65 x 1045

Given number # of significant digits 26

19628.00 0.003416 9 x 1019

1.2407661 x 10-2

Math Review Units and Conversions

How do scientists show the unit conversion process in an organized manner ?

Equalities • Use two different units to describe the same

measured amount. • Examples,

1 min = 60 seconds 1 lb = 16 oz 2.20 lb = 1 kg

Equalities and Conversion Factors

Converting a Quantity from One Unit to Another

Dimensional Analysis: A quantity in one unit is converted to an equivalent quantity in a different unit by using conversion factors that express the relationship between units.

(Starting quantity) x (Conversion factor) = Equivalent quantity

Dimensional Analysis

Old UNIT

New UNIT New UNIT

Conversion Ratio = the ratio of equivalent quantities

2 dozen

1 dozen

12 donuts 24 donuts

The Metric System

Why do scientists use the metric system? Length One meter= 1/107 the distance from the equator to the north pole

Volume and Mass

Volume Mass

Prefixes of Metric System

1 m 10 dm

Basic Units

meter (m) gram (g) Liter (L)

second (s) mole (mol) calorie (cal)

Joule (J)

deci (d) centi (c) milli (m) micro (µ) nano (n)Giga (G) Mega (M) kilo (k) hecto (h) deca (da)

1 m

1 m 100 cm

1 m 1000 mm

1 m 1 x106 µm

1 m 1 x109 nm

10 dm 1 m 1 m

1 x106 µm

10 m 1 dam

10 m

1 dam

100 m 1 hm

1 hm

1000 m 1 km

1000 m

1 km

100 m

1 x106 m 1 Mm

1 Mm

1 x106 m

1 x109 m 1 Gm

1 Gm

1 x109 m

Metric System

100 cm 1000 mm 1 x109 nm 1 m 1 m

Scale of the Universe31

Problem Solving

STEP 1: Identify the information given and the information needed to answer.

STEP 2: Find the relationship(s) between the known information and unknown answer, and plan a series of steps, including conversion factors, for getting from one to the other.

STEP 3: Solve the problem by canceling units. STEP 4: Check the answer to make sure it makes

sense, both in magnitude and units.

https://scaleofuniverse.com/

1. A rattlesnake is 2.44 m long. How many centimeters long is the snake?

2. The African Elephant is the largest land mammal. Males can weigh up to 9,100 kg. How many dekagrams is this?

Practice

In most other countries, the maximum speed limit is 100 km/h. Convert this quantity to mi/h (mph).

Convert this quantity to meters/second (m/s).

A conversion factor • may be obtained from information in a word problem. • is written for that problem only. Example 1: The price of one pound (1 lb) of red peppers is $2.39.

1 lb red peppers and $2.39 $2.39 1 lb red peppers

Example 2: A tablet contains 250 mg of aspirin.

1 tablet and 250 mg aspirin 250 mg aspirin 1 tablet

Conversion Factors in a Problem

If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet? (1 in = 2.54 cm)

Practice

The doctor asks for an infusion of procainamide at a rate of 2.5mg/min. The pharmacy has mixed 3.0 g of procainamide in 1.0 L of solution. How many mL/hr would you set the IV pump?

A light year is the distance light travels in one year. Sirrus Dog Star is the brightest star in the sky, is approximately 8.6 light years from Earth. How far (in miles) from Earth is it if light travels 3.0 x 108 m/s?

1 km = 0.6214 mi

Practice!

Practice – Dimensional Analysis

1. How many inches are in 2 kilometers? [1 in = 2.54 cm; 100 cm = 1 m; 1000 m = 1 km]

2. What is the volume of a 14 lb block of gold? [1 lb = 453.6 g; dAu = 19.3 g/cm3]

3. Dan regularly runs a 5-minute mile. How fast is Dan running in feet per second? [1 min = 60 s; 1 mile = 1760 yds; 1 yd = 3 ft]