Answer:
B
Explanation:
Recall the law of effusion:
[tex]\displaystyle \frac{r_1}{r_2} = \sqrt{ \frac{\mathcal{M}_2}{\mathcal{M}_1} }[/tex]
Because 5 mol of oxygen was effused in 10 seconds, the rate is 0.5 mol/s.
Let the rate of oxygen be r₁ and the rate of hydrogen be r₂.
The molecular weight of oxygen gas is 32.00 g/mol and the molecular weight of hydrogen gas is 2.02 g/mol.
Substitute and solve for r₂:
[tex]\displaystyle \begin{aligned} \frac{(0.5\text{ mol/s})}{r_2} & = \sqrt{\frac{(2.02\text{ g/mol})}{(32.00\text{ g/mol})}} \\ \\ r_2 & = \frac{0.5\text{ mol/s}}{\sqrt{\dfrac{(2.02\text{ g/mol})}{(32.00\text{ g/mol})}}} \\ \\ & = 2.0\text{ mol/s}\end{aligned}[/tex]
Because there are 5 moles of hydrogen gas:
[tex]\displaystyle 5.0\text{ mol} \cdot \frac{1\text{ s}}{2.0\text{ mol}} = 2.5\text{ s}[/tex]
In conclusion, it will take about 2.5 seconds for the hydrogen gas to effuse.
Check: Because hydrogen gas is lighter than oxygen gas, we expect that hydrogen gas will effuse quicker than oxygen gas.
