Question 6.12: Calculating the Partial Pressures in a Gaseous Mixture What ...
Calculating the Partial Pressures in a Gaseous Mixture
What are the partial pressures of H_2 and He in the gaseous mixture described in Example 6-11?
Analyze
The ideal gas equation can be applied to each gas individually to obtain the partial pressure of each gas.
One approach involves a direct application of Dalton’s law in which we calculate the pressure that each gas would exert if it were alone in the container.
P_{H_{2}} = \frac{n_{ H _2} \times R T}{V}=\frac{0.50 mol \times 0.0821 atm L mol ^{-1} K ^{-1} \times 293 K }{5.0 L } = 2.4 atm
P_{He} = \frac{n_{ He} \times R T}{V}=\frac{1.25 mol \times 0.0821 atm L mol ^{-1} K ^{-1} \times 293 K }{5.0 L } = 6.0 atm
Expression (6.17) gives us a simpler way to answer the question because we already know the number of moles of each gas and the total pressure from Example 6-11 (P_{tot} = 8.4 atm).
\frac{n_{ A }}{n_{\text {tot }}} = \frac{P_{ A }}{P_{\text {tot }}} = \frac{V_{ A }}{V_{\text {tot }}} = x_{ A } (6.17)
P_{ H _2}=\frac{n_{ H _2}}{n_{\text {tot }}} \times P_{\text {tot }}=\frac{0.50}{1.75} \times 8.4 atm = 2.4 atm
P_{ He} = \frac{n_{ He}}{n_{\text {tot }}} \times P_{\text {tot }} = \frac{1.25}{1.75} \times 8.4 atm = 6.0 atm
Assess
An effective way of checking an answer is to obtain the same answer when the problem is done in different ways, as was the case here.