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
lab balance
large paper clips
small paper clips
weighing boats
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.
Weigh an empty weighing boat.
Find the mass of 30 paper clips of one size.
Calculate the average mass of that paper clip.
Repeat this procedure with the other size of paper clip.
In order to check your accuracy, and if necessary update your average mass, follow this procedure:
Multiply your average mass for one size of paper clip by 100.
Set the 3-beam balance equal to this mass.
Add paper clips to the balance pan until it balances.
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
Large paper clips
Small paper clips
Mass of boat
Mass of boat + 30 paper clips
Mass of 30 paper clips
Calculated mass of 1 paper clip
Calculated mass of 100
Actual No. in that mass
Corrected mass of one clip
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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.
Record the corrected mass of one large and one small paperclip in the space provided.
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.
Add up the total number of small and large paper
clips.
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.
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.
To calculate the predicted average atomic mass for each
‘element’ set-up perform the following steps:
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.
Multiply the percent abundance (again, as a decimal) for the small paper
clips by the mass of one small paper clip.
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.
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.
Count out the number of large paper clips and small
paper clips in each setup (element) and weigh them all
together.
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
Average Mass of
paper clips—‘Isotopes’
Mass
Small paper clip
Large paper clip
Predicted Average Atomic Mass for Elements with Different
Abundances
Setup
No. Large
(No. of Heavier Isotope)
No. Small
(No. of Lighter Isotope)
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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Experimental Average Atomic Mass for Elements with Different
Abundances
Setup
Percent Abundance Large
Percent Abundance Small
Experimental Average Atomic Mass
Element 1
Element 2
Element 3
Element 4
Questions
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?
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?
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?
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?
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?
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.