# Which gas effuses faster: hydrogen or chlorine? How much faster?

Feb 18, 2016

Hydrogen effuses about 5.9 times as fast as chlorine.

#### Explanation:

Graham's law of effusion states that the rates of effusion of two different gases vary INVERSELY as the SQUARE roots of the mass of their particles.

color(blue)(bar(ul(|color(white)(a/a)"Rate"_2/"Rate"_1= sqrt(M_1/M_2)color(white)(a/a)|)))" "

where ${\text{Rate}}_{1}$ and ${\text{Rate}}_{2}$ are the rates of the two gases and

${M}_{1}$ amd ${M}_{2}$ are their respective relative molar masses.

In this problem, we can say

Chlorine gas has ${M}_{1}$ of 70.91
Hydrogen gas has ${M}_{2}$ of 2.016

${\text{Rate"_2/"Rate}}_{1} = \sqrt{\frac{70.91}{2.0162}} = \sqrt{35.17} = 5.931$

Hydrogen effuses approximately 6 times as fast as chlorine.