S T
O I
496
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•
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chemistry
program editor: Conrad L. Stanitski
Approximating Avogadro’s Number Using
Glass Beads and Monomolecular Film
prepared by Don McMasters, Indiana University,
and M. L. Gillette, Indiana University Kokomo
Purpose of the Experiment
Approximate Avogadro’s number, using glass beads. Approximate the size
of an oleic acid molecule, using several simple measurements. Approximate the number of oleic acid molecules in one mole of oleic acid.
Background Information
One Mole = Avogadro’s Number of Items
Baked potatoes are usually served one at a time, and
green beans are normally served in quantities of ten or
more. A serving of rice contains a greater number of
grains than the items in a serving of potatoes or green
beans. Thus, the number of items in “a serving” usually
depends upon the size of the individual items.
Of course atoms and molecules are much, much
smaller than rice grains. Therefore, in order to deal
with atoms or molecules in measurable “servings”,
we must consider a very large number of them. This is
why chemists count atoms or molecules in groupings
related to 6.0225 × 1023, the number of items in one
mole. We call this number Avogadro’s number.
If we make some simple assumptions about the
characteristics and behavior of carefully chosen
items, we can use these items to experimentally approximate Avogadro’s number. In this experiment,
you will first work with glass beads, individual items
we can see. Then, you will modify the procedure to
work with oleic acid molecules, individual items too
small to be seen. In each procedure, you will create a
monolayer, a layer that is one bead or one molecule
thick. You will estimate the dimensions and mass of
this layer. Based on these data, along with the given
molar mass of the beads or molecules, you will estimate the number of beads or molecules in one mole
of the substance. Because Avogadro’s number is a
counting number, the number of beads in one mole of
beads equals the number of molecules in one mole of
molecules.
Approximating Avogadro’s Number Using
Glass Beads
If we use a Petri dish with a known interior diameter
and mass, and put in just enough glass beads to cover
the bottom of the dish, we will have created a
monolayer of beads. We can determine the mass of
beads, using Equation 1.
Copyright © 1997 by Chemical Education Resources, Inc., P.O. Box 357, 220 S. Railroad, Palmyra, Pennsylvania 17078
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STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
mass of  mass of dish 
mass of
=

 − 
beads, g plus beads, g
 dish, g 
(Eq. 1)
We can determine the volume of the beads by
adding 25.0 mL of water into a 50-mL graduated cylinder, adding the beads, and reading the new water
level. The difference between the original and the
new water levels is the volume of the beads, as
shown by Equation 2.
using Equation 5. We can calculate the height of a cylinder using Equation 7.
volume of cylinder, cm 3
height of a
=
cylinder, cm area of cylinder base, cm 2
(Eq. 7)
volume of
volume of water
 volume of
= 
 − 

beads, mL
 plus beads, mL 
 water, mL
(Eq. 2)
We can relate the bead volume to water volume because, at room temperature, 1 mL of water is equivalent to 1 cm3 of water.
From the mass and volume of the beads in cm3,
we can determine the density of the beads, using
Equation 3.
mass, g
volume, cm 3
(Eq. 3)
The height of the cylinder corresponds to the height (or
diameter) of a single bead. Thus, we can determine
the diameter of a single bead by dividing the total volume of the beads (Equation 2) by the area actually occupied by the beads (Equation 6), using Equation 8.
We can determine the area of the bead
monolayer in the Petri dish using Equation 4, the
equation for the area (A) of a circle, where r is the radius of the circle, and π is approximated at 3.14.
volume of beads, cm 3
diameter of
=
one bead, cm area occupied by beads, cm 2
A, cm2 = πr 2
Once we know the diameter of a single bead, we
can compute its volume using Equation 9, the equation for the volume of a sphere.
(Eq. 4)
The radius of a circle is equal to half the diameter (d ),
so we can substitute d/2 for r in Equation 4, giving us
Equation 5.
A, cm2 = π(d/2)2
volume of one bead, cm3 = (4/3)πr 3 = (4/3)π(d/2)3
(Eq. 9)
(Eq. 5)
Because the beads are spherical, there are
empty spaces in our bead monolayer. Thus, some of
the area calculated using Equation 5 is unoccupied
space. For purposes of this experiment, we will assume that only 90% of the monolayer area is occupied by the beads. Using this assumption, we can calculate the area occupied by the beads by substituting
the area (from Equation 5) into Equation 6.
monolayer
area occupied = (0.90)(A, cm2)
by beads, cm 2
(Eq. 8)
(Eq. 6)
In order to determine the height of our bead
monolayer, we can begin by thinking of the approximate
overall volume occupied by the monolayer as being cylindrical (see Figure 1). The area of the cylinder base
equals the overall area of the monolayer calculated
If we know the mass of one mole of beads, then
we can determine the number of beads in one mole of
beads, using Equation 10.
number
molar mass of beads, g / mol
of beads =  volume of one  density of 


per mole
 bead, cm 3  beads, g / cm 3 
(Eq. 10)
The accuracy of your determination will be limited
by the accuracy of your measurements and the validity of the assumptions we have made. For example,
we can see that the beads are spherical, but have assumed that the beads occupy exactly 90% of the area
of the layer. In Part II, in contrast, you will work with
molecules so small that we must theorize about their
shapes.
© 1997 Chemical Education Resources
density, g / cm 3 =
Figure 1 The dimensions of a monolayer of
glass beads in a Petri dish
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
Figure 2
The structure of the oleic acid molecule
Approximating Avogadro’s Number Using
Oleic Acid Molecules
© 1997 Chemical Education Resources
The chemical system we use is oleic acid, C18H34O2, a
long-chain organic acid, dissolved in 95% ethyl alcohol
(see Figure 2).
If we add a drop of oleic acid–ethyl alcohol solution to water, only oleic acid molecules will remain on
the water surface, because the ethyl alcohol will
evaporate or dissolve in the water. The oleic acid molecule has a nonpolar hydrocarbon portion that is not
water soluble, and a water-soluble polar end. Therefore, the molecules will orient themselves in a nearly
vertical position, with the polar portion in the water, as
shown in Figure 3. The molecules will spread out on
the water surface to form the thinnest possible layer,
a monolayer.
Although glass beads are not mutually attracted,
the hydrocarbon portions of oleic acid molecules are
attracted to each other. This causes the oleic acid
monolayer to occupy the smallest possible area, a
circle. Any impurities, such as skin oil, will interfere
with the attraction between the oleic acid molecules.
In such cases, the oleic acid monolayer will have an
irregular shape and contain empty spaces.
The diameter of an oleic acid layer is more difficult to measure than that of the glass bead layer,
Figure 3
3
because the acid molecules are not visible on the water. To make the boundary of the acid layer visible, we
lightly dust the water surface with lycopodium powder
before adding the drop of acid solution. The spreading acid layer pushes away the powder, and the edge
of the powder defines the circumference of the acid
layer. If too much powder is used, the acid molecules
will not be able to spread out in a monolayer, due to
excessive resistance from the powder.
To determine the volume of oleic acid in one drop
of the 0.50% oleic acid solution, we must first determine the average number of drops contained in 1.0
mL of the solution. From this information, we can determine the volume of one drop of solution, using
Equation 11.
1.0 mL
volume of
1 drop of oleic = average number of drops
acid solution, mL in 1 mL of oleic acid solution
(Eq. 11)
Only 0.50% of the volume of one drop of oleic acid solution is oleic acid. Therefore, we can calculate the volume of oleic acid in one drop of solution in cm3, using
Equation 12.
The interaction of oleic acid molecules with water
4
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
volume of oleic acid per drop of solution, cm3 =
volume of  0.0050 mL oleic acid 1 cm 3 

1 drop of 

solution, mL  1 mL of solution   1 mL 
(Eq. 12)
Following the procedure used with the glass
beads, we can determine the height of the oleic acid
film, using Equations 5 and 7.
Because we cannot see individual oleic acid molecules, we must make an assumption about their
shape, based upon our best understanding of their
molecular behavior. This behavior leads us to assume that the molecules in the monolayer are cubic.
Because cubes pack with almost 100% efficiency, we
do not need to allow for empty space in the
monolayer, as we did for the glass beads.
We calculate the volume of a cube by multiplying
length times height times width. Because all three dimensions are the same in a cube, we can find the volume of an oleic acid molecule by cubing the height of
the oleic acid film, as shown in Equation 13.
volume of
 height of 
= oleic acid
oleic acid


molecule, cm 3
 film, cm 
3
percent disagreement, % =
log
log


 (theoretical result) − (experimental result)

 (100%)
log (theoretical result)




(Eq. 15)
If your calculation of Avogadro’s number is within one
power of ten of the theoretical value, consider your result acceptable.
Procedure
Preview
•
Measure interior diameter, and determine mass, of
Petri dish
•
Cover bottom of dish with monolayer of glass
beads, and determine mass of filled dish
•
Add beads to known volume of water, and determine volume of beads plus water
•
Determine number of drops of oleic acid solution in
1 mL
•
Prepare tray by filling with water and dusting with
lycopodium powder
•
Measure the diameter of monolayer formed by one
drop of oleic acid solution on water in tray
(Eq. 13)
Using the calculated volume of one oleic acid
molecule, the molar mass of oleic acid (282.52
g/mol), and its density (0.895 g/cm3), we can calculate Avogadro’s number of oleic acid molecules, using Equation 14, comparable to Equation 10.
molar mass of oleic acid, g/mol
number of
oleic acid
=  volume of   density of
 1 oleic acid  oleic acid,
molecules per mole



molecule, cm 3   g / cm 3 
Chemical Alert
lycopodium powder—flammable
0.50% oleic acid in 95% ethyl alcohol solution—
flammable, toxic, and irritant
(Eq. 14)
Caution: Wear departmentally approved safety
goggles while doing this experiment.
I.
Approximating Avogadro’s Number
Using Glass Beads
Note: Obtain from your laboratory instructor
the molar mass of the beads you are using. Record this value on Data Sheet 1.
© 1997 Chemical Education Resources
To evaluate the accuracy of your calculations,
you would usually compare your result with the accepted value and determine percent error. However,
because the number you will be determining is so
large, and because you will be making several assumptions as part of the calculations, you will use a
different method for evaluating your results. You will,
instead, determine the percent disagreement between your results and the theoretical value of Avogadro’s number (6.0225 × 1023) by comparing the
logarithms of these numbers, as shown in Equation
15.
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
Obtain a clean, dry Petri dish. Measure the interior diameter of the dish to the nearest 0.1 cm. Record this
diameter on Data Sheet 1. Determine the mass of the
Petri dish to the nearest 0.01 g. Record this mass on
Data Sheet 1.
Carefully add just enough clean, dry glass beads
to the Petri dish to cover the bottom with a monolayer.
Tap the dish lightly to make certain that the beads
have settled and that you have added the maximum
number of beads that will fit in the monolayer. Using
forceps, remove any beads that are not resting on the
bottom of the dish. Determine the mass of the dish
plus beads to the nearest 0.01 g. Record this value on
Data Sheet 1.
Put approximately 25 mL of tap water into a
50-mL graduated cylinder. Record the volume of water to the nearest 0.1 mL on Data Sheet 1.
Using a powder funnel, carefully transfer all the
glass beads from the Petri dish into the 50-mL graduated cylinder. Read the new water level and record
this volume on Data Sheet 1.
If time permits, do a second and third determination using other clean, dry Petri dishes and new
groups of glass beads.
Following the directions of your laboratory instructor, return all glass beads to the appropriate containers. Wash your graduated cylinder and Petri dish,
rinse, and drain to dry.
II.
Approximating Avogadro’s Number
Using Oleic Acid Molecules
© 1997 Chemical Education Resources
Note: Be very careful not to damage your
micropipet. Any such damage will mean that you
must repeat all of Part II with an undamaged
micropipet.
Your laboratory instructor might give you directions for preparing a micropipet.
Caution: Oleic acid in ethyl alcohol solution is
a mild skin irritant. Wash your hands with soap or
detergent after using the solution. Clean up any
spills with soap or detergent.
The ethyl alcohol in the oleic acid solution and
the lycopodium powder are flammable. Do not use
these reagents near an open flame. The ethyl alcohol is toxic, as well. Avoid ingestion of the solution.
Obtain a micropipet from your laboratory instructor.
Using a clean, dry, glass 10-mL graduated cylinder,
measure 5 mL of 0.50% oleic acid solution in 95% ethyl
alcohol and pour it into a clean, dry test tube. Pour 3
mL more of the oleic acid solution into the graduated
cylinder.
Note: Drop size will vary if you hold the
micropipet at varying angles. Hold the pipet vertically when counting drops and throughout the remainder of the Procedure.
Using the micropipet, carefully transfer, drop by
drop, exactly 1.0 mL of oleic acid solution from the
test tube to the solution in the graduated cylinder.
Count the number of drops in 1.0 mL and record this
value on Data Sheet 2. Repeat this step three times,
or until you obtain four results that are consistent to
within three drops. Record all data on Data Sheet 2.
Obtain a large tray from your laboratory instructor. Thoroughly clean the tray with soap or detergent
and water. Rinse it well with distilled or deionized
water.
Fill the tray with distilled water to a depth of at
least 1 cm, estimating this depth at the center of the
tray. When the water surface is calm, lightly and
evenly dust it with just enough lycopodium powder to
make a visible layer.
vertical
pipet
1–2 cm
above surface
(a)
5
(b)
Figure 4 (a) Holding pipet vertically over water in tray, and (b) measuring the diameter of circular oleic acid film
6
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
Fill your micropipet with some of the oleic acid solution. Allow a few drops of the solution to drain onto a
piece of filter paper or other absorbent paper. This will
ensure that the drop used to create the monolayer will
not contain air and will be representative of the stock
solution. Hold the micropipet vertically, with the tip
1–2 cm above the water at the center of the tray, as
shown in Figure 4(a). Allow just one drop of the solution to fall onto the water.
Wait 10 s until the powder circle shrinks slightly
and its size stabilizes. Being careful not to disturb the
water, quickly measure the diameter of the circle
formed by the oleic acid. Make four such measurements, all to the nearest 0.1 cm, holding the meter
stick in the orientations shown in Figure 4(b). Record
these measurements on Data Sheet 2.
Discard the contents of the tray into a container
labeled “Discarded Oleic Acid Solution”, provided by
your laboratory instructor. Thoroughly clean and
rinse the tray.
Repeat Part II until you get three consistent
results.
Caution: Wash your hands thoroughly with
soap or detergent before leaving the laboratory.
5. Calculate the monolayer area occupied by the
beads, using Equation 6.
6. Determine the height of one bead, using Equation 8.
7. Determine the volume of one bead, using Equation 9.
8. Calculate the number of beads per mole, Avogadro’s number, using Equation 10.
9. Determine the percent disagreement between
your answer and the accepted value, using Equation 15.
II.
Approximating Avogadro’s Number
Using Oleic Acid Molecules
10. Calculate the average number of oleic acid drops
per milliliter.
11. Calculate the average diameter of the oleic
acid film for each determination, using all four
measurements.
12. Calculate the overall average diameter of the film,
using the average diameter for each determination.
Calculations
Do the following calculations, and record the results on
the appropriate Data Sheet.
Approximating Avogadro’s Number
Using Glass Beads
1. Calculate the mass of the beads in your Petri dish,
using Equation 1.
2.
14. Calculate the average area of the oleic acid film,
using Equation 5.
15. Calculate the height of the oleic acid film, using
Equation 7. Remember that 1 mL = 1 cm3.
16. Calculate the volume occupied by one oleic acid
molecule in the film, using Equation 13.
Determine the volume of beads, using Equation 2.
3. Determine the density of the beads, using Equation 3.
17. Calculate the number of oleic acid molecules per
mole, Avogadro’s number, using Equation 14.
4. Determine the interior area of the Petri dish, using
Equation 5.
18. Determine the percent disagreement between
your answer and the accepted value, using Equation 15.
© 1997 Chemical Education Resources
I.
13. Calculate the average volume of the oleic acid in
the film, using Equation 12.
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
7
Post-Laboratory Questions
(Use the spaces provided for the answers and additional paper if necessary.)
1. In this experiment, you used an unusual method
for comparing your experimentally determined value
for Avogadro’s number to the theoretical value.
(a) Is your experimental result acceptable, according to the standards of the experiment? Briefly
explain.
(b) Calculate the percent error in your determination using the usual expression, shown in Equation
16.


 theoretical − experimental 
 result

percent
result
=
 (100%)
error, % 
theoretical result


2. Briefly explain why your experimentally determined value for Avogadro’s number would be too
large, too small, or unaffected if you made the following procedural errors:
(a) In Part I, you lost some beads while transferring them from the Petri dish to the graduated
cylinder.
(b) In Part II, you left your container of oleic acid
solution uncovered and some of the ethyl alcohol
evaporated before you performed the experiment.
(Eq. 16)
(c) In Part II, you asked your laboratory partner
to drop the oleic acid solution on the water so that you
could measure the circle immediately as it formed.
© 1997 Chemical Education Resources
(c) Compare your calculated percent disagreement with the percent error you calculated in (b).
Briefly explain why calculating percent disagreement
rather than percent error gives us a more useful measure of the success of this experiment.
name
section
date
name
section
date
1
determination
2
3
interior diameter of Petri dish, cm
_______________
_______________
_______________
mass of Petri dish + beads, g
_______________
_______________
_______________
mass of Petri dish, g
_______________
_______________
_______________
mass of beads, g
_______________
_______________
_______________
volume of water + beads, mL
_______________
_______________
_______________
volume of water, mL
_______________
_______________
_______________
volume of beads, mL
_______________
_______________
_______________
molar mass of beads, g/mol
_______________
_______________
_______________
__________________
__________________
__________________
interior area of Petri dish, cm2
_______________
_______________
_______________
monolayer area occupied by beads, cm2
_______________
_______________
_______________
height of one bead, cm
_______________
_______________
_______________
volume of one bead, cm3
_______________
_______________
_______________
Avogadro’s number, beads/mol
_______________
_______________
_______________
percent disagreement, %
_______________
_______________
_______________
Data Sheet 1
I.
Approximating Avogadro’s Number Using Glass Beads
© 1997 Chemical Education Resources
density of beads, g/cm3
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
9
10
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
Data Sheet 2
II.
Approximating Avogadro’s Number Using Oleic Acid Molecules
number of drops of oleic acid solution in 1.0 mL
determination
number of drops/mL
1
____________________
2
____________________
3
____________________
4
____________________
average number of drops/mL
____________________
determination
first
second
measurements, cm
third
fourth
average
1
__________
__________
__________
__________
__________
2
__________
__________
__________
__________
__________
3
__________
__________
__________
__________
__________
overall average diameter, cm
________________
average volume of oleic acid in film, mL
________________
average area of oleic acid film, cm2
________________
height of oleic acid film, cm
________________
volume of one oleic acid molecule, cm3
________________
Avogadro’s number, oleic acid
molecules/mol
________________
percent disagreement, %
________________
© 1997 Chemical Education Resources
diameter of oleic acid film, cm
name
section
date
Pre-Laboratory Assignment
1. Briefly explain why you should wash your hands
after you complete this experiment.
2. The calculations you will make in this experiment
are based on certain assumptions. What do we assume about each of the following?
(a) the shape of a glass bead
(b)
3. A student performing Part II of this experiment collected the following data: average number of drops/mL
= 73.0; overall average diameter of the oleic acid film =
38.0 cm. Use these data to calculate the following:
(a) average volume of oleic acid in film
(b)
volume of oleic acid per drop of solution
(c)
average area of oleic acid film
(d)
height of oleic acid film
(e)
volume of one oleic acid molecule
the shape of an oleic acid molecule in the
film
(c) the shape of the oleic acid film on the water
surface
© 1997 Chemical Education Resources
(d)
beads
the monolayer area actually occupied by the
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
11
4.
STOI 496/Approximating Avogadro’s Number Using Glass Beads and Monomolecular Film
(f)
Avogadro’s number
(g)
percent disagreement
According to the standards of this experiment,
(a) is the experimental result you calculated in
Pre-Laboratory Assignment 3 acceptable? Briefly
explain.
(b) What are the smallest and largest acceptable experimental results you could obtain?
(c) What are the smallest and largest acceptable percent disagreements you could obtain?
ISBN 0-87540-496-0
© 1997 Chemical Education Resources
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