Question

During an effusion experiment, it took 75 seconds for a certain number of moles of an unknown gas to pass through a tiny hole. Under the same conditions, the same number of moles of oxygen gas passed through the hole in 30 seconds. What is the molar mass of the unknown gas?

Answer 1

$t_u = 75 \;s \\ t_{O_2} = 30 \;s \\ M(O_2) = 32.0 \;g/mol \\ \sqrt{\frac{M_2}{M_1}} = \frac{t_2}{t_1} \\ \sqrt{\frac{32.0}{M_u}} = \frac{30.0}{75.0} \\ \sqrt{\frac{32.0}{M_u}} = 0.4 \\ \frac{32.0}{M_u} = 0.4^2 = 0.16 \\ M_u = \frac{32.0}{0.16} = 200 \;g/mol$

Answer: 200 g/mol