Question

The rate of diffusion of two gases are in ratio 2:3 and their corresponding densities are

A) 4:9 B) 2:3 C) 9:4 D) 3:2

Answer 1

from grahams law of diffusion of gases,

Answer 2

Answer: Option (C) is the correct answer.

Explanation:

According to Graham's law, rate of diffusion of a gas is inversely proportional to the square root of mass of its particles.

Mathematically,    $\frac{rate_{1}}{rate{2}} = \sqrt{\frac{M_{2}}{M_{1}}}$

whereas   $Rate_{1}$ = rate of diffusion or effusion of gas 1

                $Rate_{2}$ = rate of diffusion or effusion of gas 2

                $M_{1}$ = mass of gas 1

                $M_{2}$ = mass of gas 2

It is known that density is mass per unit.

Mathematically,  $Density = \frac{mass}{volume}$

or,                   $Mass= Density \times volume$    ..........(1)

Keeping the volume equal for both the gases put equation (1) in the Graham's equation as follows.

          $\frac{rate_{1}}{rate{2}} = \sqrt{\frac{Density_{2}}{Density_{1}}}$          

          $\frac{2}{3} = \sqrt{\frac{Density_{2}}{Density_{1}}}$

Squaring on both the  sides, the equation will be as follows.

           $\frac{4}{9} = \frac{Density_{2}}{Density_{1}}$

           $4 Density_{1} = 9 Density_{2}$

           $\frac{Density_{1}}{Density_{2}} = \frac{9}{4}$

Thus, we can conclude that the rate of diffusion of two gases are in ratio 2:3 and their corresponding densities are 9:4.