Question

Question #8e8f6

Answer 1

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

`color(blue)(bar(ul(|color(white)(a/a) r_2/r_1 = sqrt(M_1/M_2)color(white)(a/a)|)))" "`

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((32.00 color(red)(cancel(color(black)("g/mol"))))/(2.016 color(red)(cancel(color(black)("g/mol"))))) = sqrt15.87 = 3.984`

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

`"3.984 × 50 mL = 200 mL"`