Question

The correct representation of Graham’s law of diffusion is:
a) $\dfrac{{{r}_{1}}}{{{r}_{2}}}\,=\,\dfrac{{{{v}_{1}}}/{{{t}_{1}}}\;}{{{{v}_{2}}}/{{{t}_{2}}}\;}$
b) $\dfrac{{{r}_{1}}}{{{r}_{2}}}=\dfrac{\sqrt{{{d}_{2}}}}{\sqrt{{{d}_{1}}}}$
c) $\dfrac{{{r}_{1}}}{{{r}_{2}}}=\dfrac{\sqrt{{{M}_{2}}}}{\sqrt{{{M}_{1}}}}$
d) $\dfrac{{{r}_{1}}}{{{r}_{2}}}=\dfrac{{{P}_{2}}}{{{P}_{1}}}\dfrac{\sqrt{{{M}_{2}}}}{\sqrt{{{M}_{1}}}}$

Answer 1

Hint:
Diffusion is the movement of molecules of gas from a region of its higher concentration to a region of its lower concentration. According to Graham’s law of diffusion, the rate of diffusion of a gas depends upon the mass of the molecule of gas. If the mass is more than the rate of diffusion will be less. The rate is inversely proportional to the square root of the mass.
This means
rate = $\dfrac{1}{\sqrt{mass\text{ of gas}}}$

Complete step by step answer:
We will derive the result step by step.
First, let’s understand what is Graham’s law of diffusion.
Graham’s law of diffusion says that the rate of diffusion of a gas is inversely proportional to the square root of the mass.
This can be written as -
Rate = $\dfrac{1}{\sqrt{Mass}}$
We have been given rates of two gases. Thus, for these two gases, we can write the equation as –
$\dfrac{Rat{{e}_{1}}}{Rat{{e}_{2}}} = \dfrac{\sqrt{Mas{{s}_{2}}}}{\sqrt{Mas{{s}_{1}}}}$
Where Rate (1) is the rate of the first gas
Rate (2) is the rate of the second gas
Mass (1) is the mass of the first gas
And Mass (2) is the mass of the second gas.
Thus, $\dfrac{{{r}_{1}}}{{{r}_{2}}} = \dfrac{\sqrt{{{M}_{2}}}}{\sqrt{{{M}_{1}}}}$
So, the correct answer is “Option C”.

Additional Information”.
Graham's law of diffusion provides a base for separating isotopes by the method of diffusion. This law is most accurate for molecular effusion which involves the movement of one gas at a time through the hole. The molar mass is proportional to the mass density in the same conditions of temperature and pressure. Thus, the rates of diffusion of different gases are inversely proportional to the square roots of their mass densities even under the same conditions of temperature and pressure.

Note: Whenever there is an equation or some mathematical form; try to do step by step. It decreases the chances of mistakes.