Question

The rate of diffusion of a gas A is √5 times more than of gas B. If the molar mass of A is x gmol^-1, the molar mass of B ( in g mole^-1) is

• A. 4x
• B. 5x
• C. 16x
• D. 25x

Answer 1

The Correct Option is B

To solve the problem, we apply Graham’s law of diffusion, which relates the rate of diffusion of two gases to their molar masses.

1. Graham’s Law of Diffusion:
The rate of diffusion of a gas is inversely proportional to the square root of its molar mass:
$ \frac{r_A}{r_B} = \sqrt{\frac{M_B}{M_A}} $
Where:
- $r_A$ and $r_B$ are the rates of diffusion of gases A and B
- $M_A$ and $M_B$ are the molar masses of gases A and B

2. Given:
$ \frac{r_A}{r_B} = \sqrt{5} $, and $M_A = x$

3. Substitute into Graham’s Law:
$ \sqrt{5} = \sqrt{\frac{M_B}{x}} $

4. Square Both Sides:
$ 5 = \frac{M_B}{x} $
$\Rightarrow M_B = 5x$

Final Answer:
The molar mass of gas B is $ 5x \, \text{g mol}^{-1} $.