Question

The rates of diffusion of two gases A and B are in the ratio 1:4. If the ratio of their masses present in the mixture is 2:3. Calculate the ratio of their mole fraction.
A. 24:1
B. 1:24
C. 32:1
D. 3:17

Answer 1

Diffusion is basically a process of movement of molecules under a concentration process and important in all living beings. This process helps the substances to move out and to move in the cells.

Complete answer:
During the process of diffusion molecules move from the region of higher concentration to the region of lower concentration until the concentration remains equal throughout the process.
Rate of diffusion can be explained by Graham’s law of diffusion. This law states that the rate at which a gas diffuses is inversely proportional to the density of the gas and we know that density is given by the mass by volume.
Rate of diffusion = 1:4
As the rate of diffusion is directly proportional to the $\dfrac{1}{\sqrt{M}}$ , whereas directly proportional means to increase the value with increase of that value. Here M denotes the mass of the gases. Here ${{M}_{1}}$is the mass of gas A and ${{M}_{2}}$is the mass of gas B.
$\dfrac{{{r}_{1}}}{{{r}_{2}}}=\sqrt{\dfrac{{{M}_{2}}}{{{M}_{1}}}}=\dfrac{1}{4}$
$\dfrac{{{M}_{2}}}{{{M}_{1}}}=\dfrac{1}{16}$
${{M}_{1}}=16{{M}_{2}}$
${{X}_{1}}=\dfrac{{{n}_{1}}}{{{n}_{1}}+{{n}_{2}}}=\dfrac{\dfrac{2x}{{{M}_{1}}}}{\dfrac{2x}{{{M}_{1}}}+\dfrac{3x}{{{M}_{2}}}}$
${{X}_{2}}=\dfrac{{{n}_{2}}}{{{n}_{1}}+{{n}_{2}}}=\dfrac{\dfrac{3x}{{{M}_{2}}}}{\dfrac{2x}{{{M}_{1}}}+\dfrac{3x}{{{M}_{2}}}}$
This implies
$\dfrac{{{X}_{1}}}{{{X}_{2}}}=\dfrac{{{n}_{1}}}{{{n}_{2}}}=\dfrac{2{{M}_{2}}}{2{{M}_{1}}}=\dfrac{2{{M}_{2}}}{48{{M}_{2}}}=\dfrac{1}{24}$

This suggests that ratio should be 1:24, option B is the correct answer.

Note:
Only liquids and gases are able to undergo through the process of diffusion as only liquids and gases molecules are free to move. Diffusion is of two types like simple diffusion and facilitated diffusion. And the process which is opposite to diffusion is known as effusion.