Question

The rate of diffusion of two gases are in the ratio of 2:3 then their corresponding densities are ?

Answer 1

less the density more is the diffusion
so the required ratio of the corresponding densities is reverse of the rate of diffusion that Is 3:2

Answer 2

Explanation:

According to Grahams law, the rate of effusion or diffusion of a gas is inversely proportional to the square root of the mass of its particles.

Mathematically, $\frac{R_{1}}{R_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}$   ....(1)

where       $R_{1}$ = rate of effusion of first gas

                $R_{2}$ = rate of effusion of second gas

                $M_{1}$ = molar mass of first gas

                $M_{2}$ = molar mass of second gas

Also, it is known that density is mass per unit volume.

Therefore,    density = $\frac{mass}{volume}$

or              $mass = density \times volume$     .......... (2)

Putting the values of equation (2) in equation (1) as follows.

            $\frac{R_{1}}{R_{2}} = \sqrt{\frac{d_{2}V}{d_{1}V}}$    

Cancel out V as volume will remain the same, therefore, the equation will be as follows.

          $\frac{R_{1}}{R_{2}} = \sqrt{\frac{d_{2}}{d_{1}}}$    

Now, place the rate of diffusion in the formula as follows.

          $\frac{R_{1}}{R_{2}} = \sqrt{\frac{d_{2}}{d_{1}}}$    

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

Squaring on both the sides as follows.

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

or,        $\frac{d_{1}}{d_{2}} = \frac{4}{9}$

Thus, we can conclude that ration of densities is 4:9.