# Calculating Avogadro's Number by Use of the Monolayer by hcj

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Determining Avogadro's Number by the use of a Monolayer

Background:
Your purpose in this experiment is to employ a monolayer of oleic acid to determine the
size of a single molecule of an organic acid and from the measurements obtained to
calculate Avogadro's Number. There are several basic assumptions you will have to make,
and your results may be expected to be quite satisfactory if they are within an order of
magnitude of the accepted value. The main point of the experiment is to learn a technique
for obtaining a measurement of something very small and to recognize the limitations of the
method. A second point is to obtain a clearer understanding of what Avogadro's Number is
and how it can be calculated directly.
When you put a drop of oleic acid solution on the water surface, the drop forms a very flat
cylinder of molecules, a monolayer. The volume of a cylinder can be calculated by the
formula V = π r2h where r is the radius and h is the height. You will know the volume of the
cylinder, it is the same as the volume of the drop. We will assume that the drop spreads out
in a layer 1 molecule thick. If you were to compute the area of the circles formed by one
drop, two drops, three drops, etc. You would find the areas approximately double and then
triple with the second and third drops. This supports the idea that the solution spreads out to
a layer just one molecule thick and does not "pile up" in the center of the circle. The only
other explanation would be that the molecules always come in multiples of one drop-a
conclusion not justified by other observations.
Materials Needed:
   Large petri dish or watch glass
   Oleic acid - CH3(CH2)7CH=CH(CH2)7COOH, Density = 0.895 g/cm3
   Denatured ethyl alcohol for dilution
   1 eyedropper
   1 graduated cylinder (10 ml. preferably)
   1 large beaker
   Lycopodium powder or chalk dust (suggested)

Procedures:
Complete steps 1-3 with another group. Do steps 4-8 as individual pairs
1. One drop of pure oleic acid will be too concentrated. It will need to be dissolved to about
a 0.5% solution with ethyl alcohol as the solvent.
2. Add 2 drops of oleic acid to a clean beaker.
3. Measure exactly 10mL of ethyl alcohol in a graduated cylinder. Then add this to the
beaker containing the oleic acid. Stir solution until both liquids are evenly dispersed. You
4. You will need to know the volume of one drop of the oleic acid-alcohol solution. To
measure the volume of a drop, you will count how many drops it takes to make 1mL. To
do this, obtain a 10mL graduated cylinder and an eye dropper. Keep adding drops of your
solution until the liquid has reached the 1mL mark. Then calculate the volume of 1 drop
by dividing 1 by the number of drops and record it in your data.
5. Next obtain a large petri dish. (You may need to clean this before using) Fill the dish ½
to ¾ full of water. Then place the dish on a piece of white paper to increase visibility.
6. Add a very small amount of lycopodium powder to the surface of the water. This will
enhance the visibility of the monolayer of oleic acid. The more you add, the more visible
the results, but the less accurate as well. Try to aim for a happy medium.
7. Using your eye dropper, add 1 drop of the oleic acid solution to the surface of the water.
Immediately, measure the diameter of the monolayer using a ruler.
8. Determine and Record the radius of the monolayer of the solution, repeat this process
(Steps 5-7) three times.
Classroom Copy—Do NOT write on this!

Calculations:
A.     Calculate the average radius of a drop of the solution.
B.     Determine the volume of oleic acid in 1 drop of solution. Use the volume of a drop
and what you know about the solution of oleic acid from step 1 of the procedure.
C.     Using the average radius from problem A, the volume of oleic acid in a drop
determined in problem B, and the formula for the volume of a cylinder, determine the
height of a oleic acid molecule. V = π r2h
D.     Study the model of a molecule of oleic acid and decide a shape that can be used to
calculate the volume of the molecule. Use one of the following formulae:
Volume of a cube = height3
Volume of a cylinder = π x radius2 x height (assume the radius=0.05xheight)
Volume of a sphere = (4π x (0.5xheight)2)/3
Determine the volume of a molecule, using the height of a molecule from problem C.
E.     Calculate the gram molecular mass of oleic acid using your Periodic Table.
F.     Divide gram formula mass (grams per mole) from Step E by density (grams per cubic
centimeter) from the Materials section, to get volume of a mole of oleic acid.
G.     Divide volume of a mole of oleic acid (cubic centimeters per mole) from part F by your
answer in part D (cubic centimeters per molecule) to get N, the number of molecules
% error = (Actual - Experimental)/Actual *100

Conclusion:
You should describe the problem you are attempting, a brief description of your procedure
and materials used, calculations of your data, and the conclusions reached in the experiment.
It should be written clearly enough that an uninformed person could read your report,
understand it, and if necessary be able to repeat the experiment on the basis of your
conclusion alone.

Monolayer:                                        Oleic Acid:

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