Determining the Avogadro Constant

One of the most important concepts in the study of chemistry is the mole concept. The mole is a counting unit. One mole of any substance contains 6.02 X 10²³ atoms, molecules, or formula units.

The value 6.02 X 10²³, called the Avogadro constant, has been determined by precise experiments. This laboratory activity will allow you to explore one way of finding the Avogadro constant. The experiment is not precise and the value it gives is only an approximation. Your value, therefore, may be close to the correct value, or it may be quite different.

At a given temperature, molecules of any gas have the same average kinetic energy. The result is that, at the same temperature and pressure, one mole of gas occupies the same amount of space as any other gas.

The Avogadro constant can be determined by dividing the volume occupied by one mole of gas by the volume occupied by one molecule of gas.

The volume occupied by a measured mass of butane gas is found experimentally in this activity. This volume is proportionally converted to the volume that would be occupied by one mole. The volume occupied by one molecule is estimated as the space occupied by an imaginary cylinder containing one moving molecule of the gas. The diameter of the cylinder equals the estimated diameter of a butane molecule, 4.5 X 10^–8 cm. The height of the cylinder equals the mean free path of the molecule. The mean free path is the average distance traveled by a molecule before it collides with another molecule and is approximately 1 X 10^–4 cm.

In this activity, the butane gas will be collected by the displacement of water. When you collect a gas by displacing water in a container, some of the water evaporates and mixes with the collected gas. The total pressure of the gases is the sum of the vapor pressure of the water and the pressure of the collected gas. The warmer the water, the greater its vapor pressure will be. To account for the presence of the water vapor, you must subtract its vapor pressure from the total pressure of the gases in the container. Obtain the value for water vapor pressure (Pwater) from the following table

In this laboratory activity, you will measure the volume occupied by a quantity of butane gas and use this information to calculate the Avogadro constant.

OBJECTIVES

• Determine the molar volume of butane.

• Calculate a value for the Avogadro constant.

HYPOTHESIS:

MATERIALS

apron

goggles

barometer

thermometer

100-mL graduated cylinder

large beaker,

trough, or dish pan

butane lighter

balance

paper towel

PROCEDURE

1. You will collect a sample of butane gas and determine its molar volume. Before you proceed, think about what properties of the gas you must measure and what equation you must use to convert the volume of butane to a form that you can use in your calculations. Record your thoughts in the Data and Observations section.

2. Find the atmospheric pressure by reading a barometer, or obtain the value from your teacher. Record the value.

3. Determine the mass of a butane lighter to the nearest 0.01 g. Record the mass.

4. Fill the 100-mL graduated cylinder all the way to the top with tap water.

5. Add water to the large beaker, trough, or dish pan until it is half full.

6. Measure the temperature of the water in the beaker or trough and record it.

7. Invert the water-filled graduated cylinder in the trough or beaker so that the top is under water. Hold it in place as shown in Figure A. Make certain there is no air trapped in the cylinder.

8. Hold the butane lighter under the water with the valve in the position shown in Figure A so that you can release gas from the lighter into the cylinder.

9. Press the valve and release gas until the cylinder is filled with a little less than 100 mL of the gas.

10. Remove the lighter from the water.

11. Adjust the cylinder in the trough until the water levels inside and outside the cylinder are equal. This assures that the pressure of the gas inside the cylinder is the same as atmospheric pressure. Hold the cylinder in that position and read the volume of the trapped gas to the nearest milliliter. Record the volume in liters.

12. Release the gas from the graduated cylinder as your teacher instructs.

13. Dry the lighter very thoroughly. Use a paper towel or tissue to get rid of any water trapped in the valve area of the lighter. Do this very carefully; even a little trapped water will affect results.

14. Determine the mass of the dried lighter and record it.

15. Rinse the graduated cylinder, and pour the water in the beaker or trough down the drain.

DATA AND OBSERVATIONS

What properties of the gas must you measure?

What equation must you use to convert the volume of butane to a form that you can use in your calculations?

1. Barometric pressure ________ mm Hg

2. Initial mass of lighter _____________ g

3. Temperature of water _____________ °C

4. Volume of gas _____________ L

5. Final mass of lighter _____________ g

ANALYSIS

3. How does your result compare with the correct value of 6.02 X 10²³?

EXTENSION AND APPLICATION (pick one and answer)

1. A super computer can count at the rate of one billion (l X 10⁹) per second. To the nearest million, how many years would it take for this computer to count up to the Avogadro constant?

2. The accepted value of the Avogadro constant is 6.022 013 67 X 102³. How many more significant digits does this value have than the one you found experimentally?

3. In your calculation of the volume of one mole of butane at STP, which quantity limited the number of significant digits in your answer? What could you have done in the experiment to increase the number of significant digits in your answer?