Question

The rate of effusion of a particular gas was measured to be 24.0 mL /min. Under the same conditions the rate of effusion of pure methane gas, CH4 is 47.8 mL/min. What is the molar mass of the unknown gas?

Answer 1

The rate of effusion of two gases is inversely proportional to the square root of their masses:

$\frac{Rate1}{Rate2}=\frac{\sqrt {M2}}{\sqrt {M1}}$

The molecular weight of M1,CH4, is 16.04g/mol

Squaring both sides, you get:

$\frac{M2}{M1}=[\frac{Rate 1}{Rate2}]^2$

$M2=M1×[\frac{Rate1}{Rate2}]^2=16.04×[\frac{47.8}{24.0}]^2 = 63.63g/mol$

Molecular weight of unknown gas =63.63g/mol