chemistry Lad

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Lab 1: Scientific Measurements & Introduction to the Lab Introduction This lab will introduce you to the lab in which you will be working this semester. You will also become familiar with the correct way to make a measurement in the chemical laboratory, including the use and manipulation of common units, and how chemists indicate their degree of (un)certainty. You will learn about significant figures, and how to manipulate them, and perform some simple calculations to practice the above skills. Background Along with qualitative observations, some of the most important data that chemists collect is in the form of quantitative measurements. When chemists in different labs want to compare results, it is important that the quantities are comparable. To facilitate this, we work in the metric system, report units (always!) and are very intentional about the way we record and report data. When you are making a scientific measurement, you should utilize all of the accuracy which can be obtained from the instrument you are using, and results should be reported to reflect this level of accuracy. Results of calculations using these measurements should also reflect the accuracy of the measurements and the subsequent impact on any calculations. In order to accomplish this, simple rules regarding significant figures (which tell another scientist which numbers are meaningful) should be followed. In this experiment, significant figures will be introduced and emphasized. We will also practice this some in lecture, and you should be mindful of significant figures (sig figs) in all of your work for this course. The Metric System If you’re not familiar with the metric system, more detail can be found on pages 12-16 of your Brown and Holme text. A brief introduction of the pieces relevant to this lab is given here. The metric system is based on the units of meter for length, gram for mass, and liter for volume. Prefixes may be added to indicate multiples in base 10 of these units, which allows use of the same scale to describe very large and very small quantities. Common prefixes include kilo- (1000 units, there are 1000 meters in a kilometer), centi- (0.01 units, there are 0.01 meters in a centimeter, but it can be easier to remember this as 100 centimeters in a meter), milli- (0.001 units- there are 0.001 liters in a milliliter, but this can be easier to remember as 1000 milliliters per liter), and micro- (0.000001 units or 10-6 units, there are 10-6 meters in a micrometer, but this can be easier to remember as 106 micrometers in a meter.) Both ways of thinking of the units are pointed out here, because you always want to stop and make sure your units make sense when converting them for comparison. You probably know from life experience that a centimeter is smaller than a meter; it should make sense to think that there are 100 centimeters per meter. Keeping this type of perspective can make the metric system easier to manipulate until it becomes more familiar. In lab, you should use the prefix that is appropriate for the scale of your measurement. For example, if you have a penny that weighs 3.164 g, you should report it as such, rather than 0.003164 kg (kilograms) or 3164000 µg (micrograms), though all three technically represent the same mass.

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Precision of Measurement and Significant Figures The precision of your measurement depends heavily on the instrument that you are using. As a rule of thumb, the markings given on the instrument are known, and you should estimate one place beyond the markings. However, you may ONLY estimate the final digit. If the measurement appears to fall exactly on the line, you can estimate the final digit as zero. This zero is still meaningful, as we will see. This is demonstrated in Figure 1, where the same item is measured on two different rulers.

Figure 1. The same measurement made with two different rulers.

Using metric ruler “A”, you can tell for certain that the object falls between 12 and 13, but you have to estimate the next digit. It appears to be about halfway, but it might be closer to 0.6 than 0.5; the decimal place cannot be reported with certainty. However, we should report it because we know it’s NOT 12.0 or 12.1. We know something about the value, so we can report a significant digit, acknowledging that there is some uncertainty. In the case of ruler A, this would be indicated by recording a value of 12.5 +/- 0.1 cm. Notice the value includes only numbers that are significant, as many significant digits as possible, a measure of the uncertainty of the value, and units. This should be the case for every measurement you record in your notebook! Following the same reasoning for ruler “B”, we now have more markings, which will allow us to report the measurement with greater precision. A closer view of ruler B appears in Figure 2. Here, we can see that the end of the item is quite close to the fifth marking between the 12 and 13, perhaps even right on the line. If the measurement appears to fall exactly on the line, you can estimate the final digit as zero. This zero is still meaningful, and it tells anyone using your data that the measurement was quite close to the line. While it may not be exactly zero, you know it was not half way to the next line!

https://sites.google.com/site/ivytechchemistry/lab-1

Figure 2. A closer look at ruler B.

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Again, you should report that your uncertainty is in the last recorded digit. Thus, you would reflect the greater level of precision by recording this measurement as 12.50 +/- 0.01 cm. 12.50 +/- 0.02 may also be appropriate here, depending on how confident you are in your measurement. Do you believe you could tell the difference between 12.50 and 12.52 cm in this image? When a measurement is recorded as described above, all of the reported numbers have meaning, or are significant, and there is uncertainly only in the final digit. Likewise, when you see a value correctly reported, you can assume that every number is meaningful, and that the uncertainty is in the final digit. It is important to note that when using a digital instrument for a measurement, this same rule is followed. There is some uncertainty in the last number displayed, but it is significant, and all numbers should be recorded. Sometimes, it is necessary to further manipulate your raw data, and it is important to consider the number of significant figures when doing so. The method of handling them depends on what you are doing. For this course, we will limit our discussion to two different possibilities: addition/subtraction and multiplication/division. Let us begin with the first scenario. First, when you are adding and subtracting values, all of the values must have the same units. It should make sense to you that 4 L minus 1 mL is not 3! To see where we go from there, let’s consider a specific example. Say you were interested in a total volume of water from three separate measurements. The first measurement was 234 mL, which was read in a graduated cylinder to +/- 1 mL and contains 3 significant figures. The second and third measurements were made in a slightly more precise graduated cylinder that allowed you to estimate the first decimal place. They were 21.5 and 1.7 mL, with an uncertainty of +/- 0.1 mL, and contain 3 and 2 significant figures respectively. In this example, all of the values are reported with the same units, so we can combine the volumes, but let’s consider the values in liters, as well: 234 mL or 0.234 L 21.5 mL 0.0215 L 1.7 mL 0.0017 L 257.2 mL 0.2572 L Rounds to 257 mL 0.257 L

Here, it is important to note that the uncertainty in the initial measurement was +/- 1 mL. Thus, our overall volume is only certain to the mL. Therefore, we round to the nearest mL. When adding and subtracting values, your answer is certain only to the number of decimal places in your least certain value. Note also, that while the two values, while they appear to be different at a first glance, represent the same volume reported to the same number of significant digits. Without using scientific notation, there is no way to report this value in liters without that initial zero - it is simply a placeholder. Thus, both reported values have three significant digits. Converting 0.257 L into scientific notation yields 2.57 x 10-1, confirming that there are three significant

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figures (this is one of the strengths of scientific notation). When you see a zero at the beginning of a number, it is not significant.

For further example, consider the following: 10.1 mm or 10.1 mm or 0.0101 m 0.105 m 105 mm 0.105 m 1.284 cm 12.84 mm 0.01284 m Cannot be added

as written 127.94 mm 0.12794 m

Rounds to 128 mm 0.128 m

When multiplying and dividing, the rules are slightly different. Rather than considering the number of decimal places, we consider the number of significant figures in our least precise value. When multiplying or dividing, report your answer with the same number of significant figures as your least precise starting value. You should also be aware of units, but they need not necessarily match. Units that do match may cancel out, and you should do so when you are able, but they can be carried forward with the number if that is not the case. For example:

(0.825 g/mL)(12.5 mL) = 10.3 g

Here, the units would have been (g•mL)/mL. Because mL appears on both the top and bottom, it may be cancelled to give g as the final answer. Both values had three significant figures, leading to three in the final answer.

22.4 𝐿 (1.00 𝑎𝑡𝑚) (1.00 𝑚𝑜𝑙)(273.15 𝐾)

= 0.0820 𝐿 𝑎𝑡𝑚 𝑚𝑜𝑙 𝐾

Sometimes, the units are so different that none cancel, and they are all carried forward. The least precise of the starting values have three significant figures, so the answer is again reported with three significant figures (recall that the leading zeroes are not significant, and we will discuss terminal zeroes shortly).

52.4 𝑚𝐿 𝑠𝑜𝑙𝑛 × 40.0 𝑔 𝑁𝑎𝑂𝐻 1000.𝑚𝐿 𝑠𝑜𝑙𝑛

× 60.0 𝑔 𝑎𝑐𝑒𝑡𝑖𝑐 𝑎𝑐𝑖𝑑 40.0 𝑔 𝑁𝑎𝑂𝐻

= 3.14 𝑔 𝑎𝑐𝑒𝑡𝑖𝑐 𝑎𝑐𝑖𝑑

In other cases, multiplication and division can occur over many steps to intentionally cancel the units. Here, the final units would have been mL g2/ mL g, but this is simplified to cancel when possible to leave only g in the final answer. Note the strange decimal at the end of 1000. That tells us something about those zeroes, and we will discuss that shortly.

Let’s revisit zero for a moment. When considering a properly reported number, any non-zero digits are significant, but (as demonstrated in the last set of examples) zero has some nuances you should be aware of.

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• As noted before, leading zeroes are not significant. • Zeroes occurring in the middle of a number are always significant. • Trailing zeroes may or may not be significant. Trailing zeroes after a decimal place are

always significant. Thus, 1.000 L has 4 significant figures. You should recognize from the discussion of measurement that those trailing zeroes would not have been recorded unless the precision of the instrument allowed it; they are meaningful. When converting that number to mL, though, it gets tricky because trailing zeroes with no decimal place are not significant. Thus, writing 1000 mL would imply that we only knew that value to one significant figure, which was not the case! Thus, we would use a decimal place to indicate that those zeroes were significant, and write 1000. mL as shown in the example above. Trailing zeroes prior to a decimal place are significant, so this notation correctly conveys that we have 4 significant figures in that value.

For more examples, a summary of the rules, and practice problems regarding significant figures, see pages 16-18 in your text. Experimental Procedure: Part I: Get to know your lab and safety equipment! Provide a full page sketch of the lab, indicating the location of the following (you may work in small groups or teams to explore and find these items): Eye washes Fire blanket Fire extinguishers Sinks First aid kit Fume hoods Emergency showers Emergency numbers Glassware closet Goggles Part II: Measure the linear dimensions of your notebook. You will use both English and metric units to calculate the volume of your lab notebook and compare the two. To accomplish this, obtain the dimensions of your lab notebook in both metric and English units. You should enter this date in your notebook using a table similar to the following:

English Metric

Length

Width

Thickness

Remember units and significant figures! The metric measurements should be in centimeters, and the English in inches. Part III: Sugar! You will measure the volume and mass of a single sugar cube in order to determine its density and perform some calculations. The density of an object is its mass per unit volume (d=m/V)

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and can be obtained through simple measurements. This will require that you measure the length of the three dimensions and use a balance to obtain the mass. Record all data in your notebook for use in future calculations. Part IV: Density of a metallic solid For part IV, you will find the density of a metallic solid by two different methods, compare the two, and attempt to identify the metal with this information. Start by recording the mass of your metal rod, which will be needed for both methods. Make any observations on the rod that may help you to identify it as part of your post-lab. Method 1: Measure the dimensions to find the volume. Recall that the volume of a cylinder is described by V=πr2h. With a ruler, measure the length of the rod five times, adjusting it slightly each time to compensate for irregularities in the length. Again using a ruler, measure the diameter of the rod five times by a similar method. Method 2: Find the volume by the water displacement method. Fill a small graduated cylinder partway with water, leaving enough space for the water to rise when the rod is added. Record the initial volume of water in the graduated cylinder. Add the metal rod to the cylinder, and record the final volume in the cylinder. The difference in these values (Vf – Vi) is the volume of the rod. Before you leave the lab: Calculate the volume of the metal rod by each method (this is also listed below). Report those values, as well as the mass of the rod, in the spreadsheet open in lab. Your post-lab will require you to access the class data (that will be posted on the course Moodle) to answer some questions. Because your contribution to the class data is vital, a small portion of your grade for this lab will be attached to doing so! Calculations: You may find the useful relationships on the inside of your text to be particular useful for this activity. Calculate the following in your notebook from your data, report the correct number of significant figures, and show your work: The volume of the book in cubic centimeters. The volume of the book in cubic inches. The volume of the book in gallons. The volume of the book in liters. The volume of a sugar cube in mL. The density of a sugar cube in g/mL. The number of sugar cubes in one pound of sugar. Start by calculating the average height and diameter of your rod. Using the average height and diameter you’ve calculated, determine the volume of the metal rod.

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Using the volume measurement you trust the most (you should defend this choice in your discussion), calculate the density of the metal rod. REMEMBER TO CONSULT THE LAB EXPECTATIONS AND COMPLETE ALL PORTIONS OF THE POST-LAB! Post-lab questions:

1. Access the class data for this lab on the Moodle for this course. Which method seemed to provide the most consistent results.

2. Use the calculated value of the rod’s density to suggest any possible substance of which the rod might be composed. Does it make a difference if you use the class data or your own? Which would you deem more reliable? Why?

3. What is the most likely element that was used to make the rod? Defend your answer. Hint: Tables of densities are available online through a variety of sources, but you should cite whichever one you use to answer this question.