Question

Which of the following gases will have the highest rate of diffusion?
(A) ${O_2}$
(B) $C{O_2}$
(C) $N{H_3}$
(D) ${N_2}$

Answer 1

In this question, we will follow Graham's law that is applicable in the case of gases, states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight.

Complete answer:
As we know that the rate of diffusion is inversely proportional to the square of the molecular mass of gases:
$\therefore \text{Rate of diffusion} \propto \,\,\dfrac{1}{{\sqrt {\text{Molecular mass}} }}$
That means, the higher is the rate of diffusion, the lesser is the molecular mass and vice-versa.
For ${O_2}$ : Mass of ${O_2}$ molecule $= 32g.mo{l^{ - 1}}$
For $C{O_2}$ : Mass of $C{O_2}$ molecule $= 44.01\;g.mo{l^{ - 1}}$
For $N{H_3}$ : Mass of $N{H_3}$ molecule $= 17.031\;g.mo{l^{ - 1}}$
For ${N_2}$ : Mass of ${N_2}$ molecule $= 22g.mo{l^{ - 1}}$
As we can see above, the molecular mass of $N{H_3}$ is less than the masses of three other gases.
So, as we can discuss earlier, if the molecular mass of any gas is less in comparison with others, that means its rate of diffusion is highest among them.
Therefore, the rate of diffusion of $N{H_3}$ is higher than the rate of diffusion of ${O_2}$ , $C{O_2}$ and ${N_2}$ .
Hence, the correct option is (C) $N{H_3}$ .

Note:
The slower the rate of diffusion becomes as the material distribution approaches equilibrium. The diffusing molecules' mass is: Because heavier molecules move more slowly, they diffuse more slowly. Lower temperatures reduce the energy of the molecules, slowing the diffusion rate.