Lab: Atomic Mass &
Average Atomic Mass

Background

Individual paper clips weigh significantly less than a gram and repeated measurements are unlikely to result in the same measured mass. Also, the lab balances are typically not sensitive enough to accurately weigh such small masses. Using a technique that is mathematically similar to that used by chemists with atoms, students measure the mass of paper clips by weighing a group and then dividing by the total number of items. In this way an average mass is measured.

In addition, the concepts (mathematical and chemical) that are needed for a full understanding of average atomic mass are explored using an extension of the idea of finding the atomic mass. Two sizes of paper clips are used as the heavier and lighter isotopes in several schemes representing different percent abundances and students predict and then measure the resulting average atomic mass.

Objective

To determine equivalent of the atomic mass of a several types of items too small to weigh individually. These values will be used to estimate the number of items in a sample.

To visually demonstrate the meaning of the term weighted average as it applies to the average atomic mass of elements due to the masses and percent abundances of their isotopes.

Materials

Part I, Atomic Mass

Procedure

In this section of the lab activity you will establish the mass of two different sized paper clips. You will then use this information to count items. Finally, you will calculate the percent error in your counting-by-weighing procedure. This process is very similar to the process used by chemists to find atomic masses and to count atoms and molecules.

1. Weigh an empty weighing boat.
2. Find the mass of 30 paper clips of one size.
3. Calculate the average mass of that paper clip.
4. Repeat this procedure with the other size of paper clip.
5. In order to check your accuracy, and if necessary update your average mass, follow this procedure:
   1. Multiply your average mass for one size of paper clip by 100.
   2. Set the 3-beam balance equal to this mass.
   3. Add paper clips to the balance pan until it balances.
   4. Remove them from the pan and count them. There should be exactly 100 paper clips. If not, then update your average mass by weighing exactly 100 and dividing by 100 this time.

Data Table

Part II, Average Atomic Mass

Procedure

In this section of the lab activity you will set up several ‘elements’ which have two ‘isotopes’ each. You will mathematically predict the average atomic mass of each ‘element’. Finally you will weigh out the correct number of ‘isotopes’ to calculate the true average atomic mass.

1. Record the corrected mass of one large and one small paperclip in the space provided.
2. The large paper clips represent a heavier isotope. The small paper clips represent a lighter isotope. Think of the small ones like carbon-12 and the large like carbon-13. In the table are several setups. The setups are like ‘elements’ because each one has different abundances of the isotopes of that element. Each differs by the number of large and small paper clips. Calculate the Percent Abundance for each ‘isotope’ and enter it in the table.
   1. Add up the total number of small and large paper clips.
   2. Divide the number of small paper clips by the total from the previous step. Multiply by 100% to get the percent abundance of this ‘isotope’. Enter it in the data table.
   3. Divide the number of large paper clips by the total from the previous step. Multiply by 100% to get the percent abundance of this ‘isotope’. Enter it in the data table.
3. To calculate the predicted average atomic mass for each ‘element’ set-up perform the following steps:
   1. Multiply the percent abundance (as a decimal so 50% is 0.50, etc.) for the large paper clips by the mass of one large paper clip.
   2. Multiply the percent abundance (again, as a decimal) for the small paper clips by the mass of one small paper clip.
   3. Add these two results together and enter your final answer in the table under Predicted Average Atomic Mass. This is the calculated average atomic mass for each setup or ‘element’. Record your result to the nearest 0.01 g.
4. To find the actual average atomic mass for each setup you will count out the number of paper clips of each kind and weigh them all as a group. Then, by dividing by 40, you will calculate an experimental average mass. Make your measurements carefully by estimating to the nearest 0.01 g. You are doing this to demonstrate to yourself that whether you calculate the weighted average atomic mass using percent abundances or weigh out samples with those abundances you will get the same average atomic mass. This is analagous to how the average atomic mass works for the elements in the periodic table. This activity is an analogy to that idea.
   1. Count out the number of large paper clips and small paper clips in each setup (element) and weigh them all together.
   2. Divide the total mass from the previous step by the total number of paper clips on the balance pan. Enter the result under Experimental Average Atomic Mass in the data table on the next page.

Data Tables

Questions

1. Your answers for the predicted average atomic masses for each element setup should be the same as the answers for the experimental average atomic masses. Both answers required calculations so what made them different?
2. Look at setup number one in the data table. For this element the lighter isotope is much more abundant. Is the final average mass of the element closer in size to the mass of the lighter or the heavier isotope? Why?
3. Look at setup number two in the data table. Compare the average for this setup to setup number one. Why the average for this setup a larger number than for setup number one?
4. Look at setup number three in the data table. For this element the lighter isotope has the same abundance as the heavier isotope. Calculate the average mass if you have exactly one of each size of paper clip by adding up the two masses in the first data table on the previous page and dividing by two. How is this result related to the average mass for setup number three?
5. Look at setup number four in the data table. For this element the heavier isotope is much more abundant. Is the final average mass of the element closer in size to the mass of the lighter or the heavier isotope? Why?
6. The abundance of isotopes on the earth provides valuable information to paleontologists, who are interested in the history of life on the planet. On average planet-wide, carbon-12 has a relative abundance of 98.90% and carbon-13 has a relative abundance of 1.10%. Living things prefer to use the lighter isotope because—although the chemical reactions of carbon-13 are identical to those of carbon-12—carbon-12 reacts just a bit faster. This means that living things leave behind traces with a higher-than-normal carbon-12 content. In the analysis of a particular type of rock scientists found that for every 5,000 carbon atoms 4,960 were carbon-12 and 40 were carbon-13. Does the rock show traces of ancient life? Show whether it does by calculating the relative abundances of the two isotopes in the rock analyzed by the scientist.