# Question #8e8f6

Feb 8, 2017

The volume of hydrogen is 200 mL.

#### Explanation:

Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of the mass of its molecules.

We can write the formula as

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} {r}_{2} / {r}_{1} = \sqrt{{M}_{1} / {M}_{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

where

${r}_{1}$ and ${r}_{2}$ are the rates of effusion of the two gases and

${M}_{1}$ and ${M}_{2}$ are their molar masses.

If gas 2 is hydrogen and gas 1 is oxygen, then

${r}_{2} / {r}_{1} = \sqrt{\left(32.00 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g/mol"))))/(2.016 color(red)(cancel(color(black)("g/mol}}}}\right)} = \sqrt{15.87} = 3.984$

Hydrogen diffuses 3.984 times as fast as oxygen, so the original volume of oxygen must be

$\text{3.984 × 50 mL = 200 mL}$