Question

Methane (CH4) effuses through a small opening in the side of a container at the rate of 1.30 × 10 8 mol s 1. An unknown gas effuses through the same opening at the rate of 5.42 × 10 9 mol s 1 when maintained at the same tem- perature and pressure as the methane. Determine the molar mass of the unknown gas.

Answer 1

Answer : The molar mass of unknown gas is 92.0 g/mol

Solution :

According to the Graham's law, the rate of effusion of gas is inversely proportional to the square root of the molar mass of gas.

$R\propto \sqrt{\frac{1}{M}}$

or,

$(\frac{R_1}{R_2})=\sqrt{\frac{M_2}{M_1}}$       ..........(1)

where,

$R_1$ = rate of effusion of methane gas = $1.30\times 10^{-8}mol/s$

$R_2$ = rate of effusion of unknown gas = $5.42\times 10^{-9}mol/s$

$M_1$ = molar mass of methane gas  = 16 g/mole

$M_2$ = molar mass of unknown gas = ?

Now put all the given values in the above formula 1, we get:

$(\frac{1.30\times 10^{-8}mol/s}{5.42\times 10^{-9}mol/s})=\sqrt{\frac{M_2}{16g/mole}}$

$M_2=92.0g/mol$

Therefore, the molar mass of unknown gas is 92.0 g/mol