Question

Which is true about the effusion rates of helium and sulphur dioxide when the molar mass of helium is 4 grams/mole and the molar mass of sulphur dioxide is 64 grams?

A. Sulphur dioxide effuses 4 times faster than helium.
B. Sulphur dioxide effuses 0.25 times faster than helium.
C. Helium effuses 0.25 times faster than sulphur dioxide.
D. Helium effuses 4 times faster than sulphur dioxide.
E. Molar mass is not related to effusion.

Answer 1

Helium effuses four times as fast as sulfur dioxide.

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

If you have two different gases, the law becomes

`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 effusion of the two gases
`M_1` and `M_2` are their molecular masses

In this problem, let Gas 1 be sulfur dioxide and Gas 2 be helium.

Then

`"Rate"_2/"Rate"_1 = sqrt(64/4) = sqrt(16) = 4`

Thus, helium effuses four times as fast as sulfur dioxide.