Question

Part 2: Avogadro’s number estimation
Although Avogadro’s number is a huge number, it is possible to estimate it by a simple
experiment. In the experiment a monolayer of stearic acid (SA) molecules is formed on the
surface of water. Based on the amount of SA necessary to cover the surface and the given cross-
sectional area of one SA molecule, Avogadro’s number can be calculated.
A group of students performed the following
experiment using a glass container with the
diameter of 14.5 cm. They started by filling up
the container with water to the rim. Then they
were adding drop by drop stearic acid (SA) on
the surface of water. One drop of SA solution
was measured to contain approximately 1.4 x
10-6 g of SA. In their experiment students
found that 27 drops were enough to create a monolayer of SA on the water surface. In another
experiment the cross-section area of one SA molecule in a monolayer was found to be 0.21 nm2.
The molecular formula of stearic acid is C18H36O2.
a) Discuss with your group how you can use the results of this experiment to estimate
Avogadro’s number. List all the steps in the proposed calculation.
b) Follow the steps to complete the calculation and answer the following question: Do you
think the students performed a successful experiment? Explain.
Hint: use the following formula to calculate surface area of water:
??????? ???? ?? ????? = ??
2

Answer 1

In this experiment we will find avogadro number by forming a monolayer of stearic acid on the surface of water. As we know stearic acid has both polar and non-polar portion, the larger non-polar portion makes it immiscible with the water that's why it creates a layer on the water.

To calculate avogadro number we have to calculate the mass of stearic acid in grams.

We are using 27 drops to make a monolayer and one drop of SA solution contain 1.4 X 10^-6 g of SA.

Mass of stearic acid = 27 drops X 1.4 X 10^-6 g / 1ml = 37.8 X 10^-6 g

Now we have to find the no of moles of stearic acid = 37.8 X 10^-6 g / 284g = 0.133 X 10^-6

Molar mass of stearic acid = 284g

Now we have to calculate the area of dish from its diameter and then divided by 0.21 nm² because each drop of stearic acid or any other fatty acid occupies this much area.

Convert 0.21 nm² to cm² = 2.1 X 10^-15 cm²

Diameter of container = 14.5 cm

Area of container = 3.14 X 7.25 X 7.25 / 2.1 X 10^-15 = 165.05/2.1 X 10^-15 = 78.6 X 10¹⁵ molecules of SA

Now calculate avogadro number = 78.6 X 10¹⁵ / 0.133 X 10^-6 = 590.9 X 10²¹ = 5.91 X 10²³

Avogadro number = 5.91 X 10²³

This result is successful for such type of experiment.THis result is very close to avogadro actual value so we can consider this experiment to be accurate.