| FIGURE 9.11 The total pressure of a mixture of gases equals the sum of the individual gas pressures. |
We have already noted that the composition of a gas does not affect the validity of the gas laws. It follows then that mixtures of gases must follow those laws in the same way that a single gas does. They do and, when Boyle's Law is applied to a mixture of gases, there is a relationship between the composition of a gas sample and its total pressure. This relationship is known as Dalton's Law of Partial Pressures (the same Dalton who proposed the atomic theory described in Section 3.1. Dalton's Law of Partial Pressures states: (1) Each gas in a mixture of gases exerts a pressure, known as its partial pressure, that is equal to the pressure the gas would exert if it were the only gas present; (2) the total pressure of the mixture is the sum of the partial pressures of all the gases present. This law is based on the postulate of the kinetic molecular theory (Section 9.3), which states that a gas sample is mostly empty space. The gas molecules are so far apart from one another that each acts independently. A mathematical expression of the Law of Partial Pressures is:
PTotal = P1 + P2 + P3 + · · ·
where PTotal equals the total pressure of the mixture, and P1, P2, P3, . . . . are the partial pressures of the gases present in the mixture.
Suppose we have 1 L oxygen at 1 atm pressure in one container, 1 L nitrogen at 0.5 atm pressure in a second container, and 1 L hydrogen at 3 atm pressure in a third container (Figure 9.11). If we combine the samples in a single 1-L container, the total pressure is 4.5 atm (1 atm + 0.5 atm + 3 atm).
| FIGURE 9.11 The total pressure of a mixture of gases equals the sum of the individual gas pressures. |
A corollary of this law is that, in a mixture of gases, the percent of each gas in the total volume is the same as the percent of each partial pressure in the total pressure. From the total pressure of a mixture of gases and its percent composition, we can calculate the partial pressure of the individual gases.
| Vgas VTotal |
= | Pgas PTotal |
|
Example: Dry air contains 78.08% nitrogen, 20.095% oxygen, and 0.93% argon. Calculate the partial pressure of each gas in a sample of dry air at 760 torr. Calculate also the total pressure exerted by the three gases combined. 1. The equation is:
2. Calculate the partial pressure of each gas by using the corollary of Dalton's Law, which states that each partial pressure is the same percent of the total pressure as the percent each gas is of the total volume.
3. The total pressure is: The difference between the total pressure of the three gases and thetotal pressure of the air sample is due to the partial pressure of other gases such as carbon dioxide, present in dry air. |
|
Example: Gases insoluble in water can be purified by bubbling them through water. This process removes impurities that are soluble in water; but at the same time, water vapor is picked up the the sample. A sample of nitrogen that was purified by this method had a volume of 6.523 L at 26 °C and a total pressure of 747 torr. In any gas sample saturated with water vapor at 26 °C, the partial pressure of the water is 25.2 torr. How many moles of nitrogen did the sample contain? Solution The solution to this problem requires the use of the ideal gas equation in the form:
To use the gas constant R = 0.821 L-atm/mol-K, we must first convert the values for each parameter in the equation to those of the gas constant:
The total pressure of the gas sample is the sum of the partial pressure of the nitrogen and the partial pressure of the water vapor:
Rearranging this equation gives
Converting to atmospheres to mathc the units of R,
Substituting these values into the equation gives:
|
