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
lab balance
peas
beans
other beans
large paper clips
small paper clips
weighing boats
lab notebook
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.
Weigh an empty weighing boat.
Find the mass of 20 dried beans.
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.
Add enough beans to the pan to balance the beam.
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.
Repeat these same steps using the other items provided.
Data Table
1
2
3
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
Twelve peas have a mass of 48 g.
Find the mass of 6 peas.
Find the mass of 100 grains of
rice if 250 grains have a mass of 7.5 g.
A mass of 60 g of beans contains
how many beans, if each one has a mass of 0.3 g?
The mass of 1 grain of rice is
0.020 g. How many grains are in 1 lb (0.454 kg)?
The mass of 6.02 x 10^{23}
atoms of copper is 63.5 g. Find the mass of one atom in g.
The mass of 6.02 x 10^{23}
molecules of water is 18.0 g. Find the mass of one molecule
in g.
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)%
Determine the percentage error
for each sample in your chart.
Which was the least accurate?
Suggest factors that might
result in this being the least accurate.
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.
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.
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 Actual Average Atomic Mass.
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) for
the large paper clips by the mass of one large paper
clip.
Multiply the percent abundance for the small paper
clips by the mass of one small paperclip.
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
How close are your predictions to
the actual average mass of each setup (each
‘element’)? Explain any discrepancies and/or
fix any calculation errors.
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.
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 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?
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.