Question

The relative rate of effusion of CH4, to so2, through
the container containing CH4, and so2, in 3 : 2
mass ratio will be
(1) 3:1
(2) 12:1
(3) 1:3
(4) 4:3​

Answer 1

Answer : The correct option is, (1) 3 : 1

Explanation :

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.

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

And the relation between the rate of effusion and volume is :

$R=\frac{V}{t}$

And the relation between the rate of effusion and number of moles is :

$R=\frac{n}{t}$

and moles is also directly proportional to the mass.

From this we conclude that,

$\frac{R_{CH_4}}{R_{SO_2}}=\frac{n_{CH_4}}{n_{SO_2}}\times \sqrt{\frac{M_{SO_2}}{M_{CH_4}}}$

$\frac{R_{CH_4}}{R_{SO_2}}=\frac{3}{2}\times \sqrt{\frac{64}{16}}$

$\frac{R_{CH_4}}{R_{SO_2}}=\frac{3}{1}$

Therefore, the relative rate of effusion of $CH_4$ to $SO_2$ will be, 3 : 1