Question

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

Answer 1

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 `"Rate"_1` and `"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

∴ `"Rate"_2/"Rate"_1= sqrt(70.91/2.0162) = sqrt35.17 = 5.931`

Hydrogen effuses approximately 6 times as fast as chlorine.