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Lab: Atomic Mass &
Average Atomic Mass

Background

Individual beans, peas or 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 these small items 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 several types of items too small to weigh individually. 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 20 dried beans.
  3. Set your balance at a mass determined by the formula, mass-of-one-bean × 100. That is, with nothing on the pan, move the weights to read the mass you predicted for 100 beans. If you’re using one don’ forget to add the mass of your weighing boat to the mass you set on the balance.
  4. Add enough beans to the pan to balance the beam.
  5. Count the number of beans on the balance. This is so you can check the accuracy of your earlier measurement of the mass of one bean.
  6. Repeat these same steps using the other items provided.
Data Table
 
Mass of boat      
Mass of boat + 20 items      
Mass of 20 items      
Calculated mass of 1 item      
Calculated mass of 100      
Actual No. in that mass      



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Questions

  1. Twelve peas have a mass of 48 g. Find the mass of 6 peas.
  2. Find the mass of 100 grains of rice if 250 grains have a mass of 7.5 g.
  3. A mass of 60 g of beans contains how many beans, if each one has a mass of 0.3 g?
  4. The mass of 1 grain of rice is 0.020 g. How many grains are in 1 lb (0.454 kg)?
  5. The mass of 6.02 x 1023 atoms of copper is 63.5 g. Find the mass of one atom in g.
  6. The mass of 6.02 x 1023 molecules of water is 18.0 g. Find the mass of one molecule in g.
  7. The percentage error in the predicted number of "seeds" for this experiment is equal to the absolute value of the following expression: (Counted number - 100)%
    1. Determine the percentage error for each sample in your chart.
    2. Which was the least accurate?
    3. Suggest factors that might result in this being the least accurate.
  8. Using your experience with the techniques in this lab so far write how it is that scientists go about finding the average masses of atoms.



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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. Determine the mass of one small paper clip and one large paper clip using the method from Part I of this lab. Do not use fewer than 20 clips in measuring the mass of an average paperclip. Write your final results in the data table below but do your work for this section in your lab notebook. Use the maximum allowed number of significant figures when reporting your result.
  2. Count out the number of large paper clips and small paper clips in each setup (element) and weigh them all together.
  3. Divide the total mass from the previous step by the total number of paper clips on the balance pan. Enter the result under Actual Average Atomic Mass.
  4. 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.
  5. To calculate the predicted average atomic mass for each ‘element’ set-up perform the following steps:
    1. Multiply the percent abundance (as a decimal) for the large paper clips by the mass of one large paper clip.
    2. Multiply the percent abundance for the small paper clips by the mass of one small paperclip.
    3. Add these two results together and enter your final answer in the table under Predicted Average Atomic Mass. This is the average atomic mass for each setup or ‘element’.
Data Tables
Average Mass of Paperclips—‘Isotopes’
  Mass Percent Error in Weighing 100
Small paperclip    
Large paperclip    

Average Atomic Mass for Elements with Different Abundances
Setup No. Large
(No. of Heavier Isotope)
No. Small
(No. of Lighter Isotope)
Actual Average Atomic Mass Percent Abundance Large Percent Abundance Small Predicted Average Atomic Mass
Element 1 5 35        
Element 2 10 30        
Element 3 20 20        
Element 4 35 5        



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Questions

  1. How close are your predictions to the actual average mass of each setup (each ‘element’)? Explain any discrepancies and/or fix any calculation errors.
  2. One small paper clip has a mass of 0.4001 g. One large paperclip has a mass of 1.209 g. An element has two isotopes with abundances of 25% for the lighter isotope and 75% for the heavier isotope. Taking the masses of the paper clips to be the masses of the isotopes, calculate the average atomic mass of the element.
  3. 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?
  4. Look at setup number three in the data table. For this element the lighter isotope has the same abundance as the heavier isotope. Is the final average mass of the element closer in size to the mass of the lighter or the heavier isotope? Why?
  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.


Paper clips used in my classroom had the following masses.
Large, 1.1861 g based on a sample of 20. Small, 0.39903 g based on a sample of 30.

This lab activity belongs in sequence after a group activity on the same topic, which introduces the necessary concepts and mathematical techniques. It can be found here. There is a homework assignment as well which can be used to extend the study of this topic.

The material found in Part I comes from the Doing Chemistry page from the Teacher Resources section at the D.W. Brooks Site. It is based on Experiment 16: Introduction to Atomic Mass.
The material in Part II is original to the author.
Last updated: Dec 09, 2015 Home