Question 6.15: Comparing Amounts of Gases Effusing Through an Orifice If 2....
Comparing Amounts of Gases Effusing Through an Orifice
If 2.2 \times 10^{-4} mol N_{2}(g) effuses through a tiny hole in 105 s, then how much H_{2}(g) would effuse through the same orifice in 105 s?
Analyze
Let us reason qualitatively: H_2 molecules are lighter than N_2 molecules, so H_{2}(g) should effuse faster than N_{2}(g) when the gases are compared at the same temperature. Before we set the ratio
\frac{\text{mol} H_2 \text{ effused}}{\text{mol} N_2 \text{ effused}}
equal to \sqrt{\text{ratio of molar masses}} , we must ensure that the ratio of molar masses is greater than 1.
\frac{? mol H_2 }{2.2 \times 10^{-4} mol N_2} = \sqrt{\frac{M_{ N _2}}{M_{ H _2}}} = \sqrt{\frac{28.014}{2.016}} = 3.728
? mol H_2 = 3.728 \times 2.2 \times 10^{-4} = 8.2 \times 10^{-4} mol H_2
Assess
We could have estimated the result before calculating it. Because the ratio of molar masses is approximately 14, the ratio of effusion rates is approximately \sqrt{14}, which is slightly smaller than 4. Therefore, H_2 will effuse almost 4 times as fast as N_2 and almost 4 times as much H_2 will effuse in the same period.