Experiment #6 / Unit 2
Counting with Counting Units
Objectives:
1. To develop a system for counting small objects using a "counting unit".
2. To determine the relative mass of different small objects by comparing
them with an arbitrarily chosen standard mass.
3. Compare the model system for beans to the mole system for atoms.
(A) Model System:
In counting a large number of objects, it is often easier to use a counting unit.
One counting unit that you are all familiar with is the dozen. If I told you I had a
dozen eggs, you would immediately be able to associate a number with the word
dozen. Eggs are counted and sold in dozens. We might buy a dozen donuts. Yet
a counting unit can be used in any context because it is just a word that
represents a number. "Johnny scored a dozen points." Of course there are other
counting units besides the dozen. Many are only used with certain products. A
paper salesman sells paper by the ream. If the school buys five reams of paper
they will know that they have 2500 sheets without counting. In chemistry, we
have a system for counting atoms which greatly simplifies their study. However,
before we consider the chemical counting unit, we will develop are own counting
unit using different varieties of beans. Yes, beans. We will count beans in groups
called "________" (your choice). You will determine the number of beans in your
counting unit by choosing an arbitrary standard of mass and relating each bean
to the standard. By using your counting unit in terms of mass you will avoid
having to count large numbers of beans. In part II, we will relate your "________"
counting unit for beans to the mole counting unit for atoms.
Procedure (A):
1. Tare an empty styrofoam cup. Count out exactly 100 beans of one type, but
discard any beans which differ greatly from the average bean. Record the
mass of the 100 beans. Repeat for each type of beans.
2. Calculate the average mass of each type of bean and record it in the data table.
3. Choose one of the types of beans as your standard bean. Choose an arbitrary
relative mass for your standard bean. Determine the relative mass of the
other beans by comparison to the standard. Record these values.
Hint: your standard should have a value of at least 5.00 to avoid having a
really small counting unit
4. Now create a second relative scale where the unit is grams. Keep the same
values except use grams instead of your arbitrary mass unit so that we can
use the balances to measure. Exchange the units…..switch them…..replace
arbitrary with grams. Got it? Yes, this is somewhat contrived but will be good
training for where we’re headed (moles!).
5. Find out how many beans (approx.) make up a relative mass (in grams) for
each type of bean by counting them into a tared cup and recording the nearest
whole number of beans.
6. Calculate how many beans (exactly) are in a relative mass (in grams) by using
the average mass.
Chemistry I
Cary Academy
W.G. Rushin
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Data (A):
 mass of 100 beans for each type
 avg. mass of each type
 relative mass of each type (circle arbitrary standard) with your new unit of mass
 relative mass scale in grams
 approx. number of beans in a relative mass of each type (by counting)
 exact number of beans in a relative mass of each type (by calculation)
Calculations and Questions (A):
 Calculations must be solved by the factor-label method and you can not use
the average mass of 1 object in your calculations.
1. Your counting unit " _____________" is now defined as ____ number of
beans (use whole number).
2. If you were given a new type of bean with a relative mass of 54, how
many beans are in this relative mass?
3. Calculate the number of counting units in 5000 beans.
4. If you wanted 1000 of the heaviest bean, explain how you would quickly
measure out that number without counting (using the counting unit!).
5. Calculate the number of beans in 20 counting units of navy beans.
6. Calculate the number of beans if you had 8.5 g of a bean whose relative mass is 1.85.
7. What would be the mass of 22 counting units of the smallest bean?
8. How many hockey pucks would be in a “___________” of hockey pucks?
Explain why this must be true.
(B) Mole System:
In our model system, we saw that by knowing the relative mass of the beans
and the number of beans in a counting unit, we could more easily measure out
given amounts or numbers of beans. Chemists use a similar system for
measuring out numbers of atoms.
The periodic table already contains the relative masses of all the atoms.
These relative masses are based on an arbitrary standard just as in your model
system. Chemists chose the carbon-12 isotope to be the standard and the
relative masses of the other atoms are based on it. By looking at the table we
can quickly see that an oxygen atom is four times as heavy as a helium atom and
both are much lighter than a lead atom.
As in our model system, a relative mass of any of the atoms contains the
same number of atoms. This number represents our counting unit and is called
the mole. The word mole represents the number 6 x 10 23. This number is
extremely large (just try writing it on the page). This number is so large because
atoms are so small and it takes a lot of them piled up together to give us the
relative mass in grams. We need to work with these large quantities just to be
able to see and measure them with ordinary balances. The beans were so large
that it only took a small number to represent a relative mass.
Knowing the relative masses and that the mole represents 6 x 10 23, we can
now mass and "count" atoms with ease. This ability to quantitate atoms will serve
as the backbone to many of our future experiments.
Chemistry I
Cary Academy
W.G. Rushin
2
Calculations and Questions (B):
1. What is the relative mass (in grams) of carbon?
2. How many atoms are in a relative mass (in g) of carbon? a relative mass (in g)
of silver?
3. What is this counting unit called?
4. How many grams will be represented by a mole of phosphorus atoms? A
mole of krypton atoms?
5. How many moles are represented by 1.2 x 1024 gold atoms?
6. What would be the mass of 15 moles of sulfur atoms?
7. If you wanted a sample containing 8.2 x 1024 iron atoms, how could you
measure out this number without counting?
8. Calculate the mass of one mole of the lightest bean used in the model
system. Compare this with the mass of the earth (6 x 1027 g).
9. Determine the new value of Avogadro's number if the mole were to be
redefined as "the number of atoms in 10 g of hydrogen." Using this
definition, what would be the mass of one mole of oxygen atoms.
Lab Report #2.6:
 title page
 procedure
 data
 calculations and questions (A)
 calculations and questions (B)
Chemistry I
Cary Academy
W.G. Rushin
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