Hydrogen diffuses six times faster than gas `A`. The molar mass of gas `A` is

Options

A. 72
B. 6
C. 24
D. 36

Explanation

To find the molar mass of gas A, we can use Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Let's go through the steps to solve the problem.

### Step-by-Step Solution:

1. **Understand the relationship**: According to Graham's law, the rates of diffusion of two gases are related to their molar masses. The formula is given by:
\[ \frac{\text{Rate of diffusion of gas 1}}{\text{Rate of diffusion of gas 2}} = \sqrt{\frac{M_2}{M_1}} \]
where \( M_1 \) and \( M_2 \) are the molar masses of gas 1 and gas 2, respectively.

2. **Identify the gases**: In this case, gas 1 is hydrogen (H₂) and gas 2 is gas A. We know that hydrogen diffuses six times faster than gas A. Therefore, we can express this as:
\[ \frac{\text{Rate of diffusion of H₂}}{\text{Rate of diffusion of gas A}} = 6 \]

3. **Set up the equation**: Using Graham's law, we can write:
\[ 6 = \sqrt{\frac{M_A}{M_{H_2}}} \]
where \( M_A \) is the molar mass of gas A and \( M_{H_2} \) is the molar mass of hydrogen, which is 2 g/mol.

4. **Square both sides**: To eliminate the square root, we square both sides of the equation:
\[ 6^2 = \frac{M_A}{2} \]
This simplifies to:
\[ 36 = \frac{M_A}{2} \]

5. **Solve for \( M_A \)**: Multiply both sides by 2 to find the molar mass of gas A:
\[ M_A = 36 \times 2 = 72 \text{ g/mol} \]

### Final Answer:
The molar mass of gas A is **72 g/mol**.