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

Options

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

Answer

To solve the problem, we will use Graham's law of effusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We know that hydrogen diffuses 6 times faster than gas A.
- Let the rate of diffusion of hydrogen be \( r_H \) and the rate of diffusion of gas A be \( r_A \).
- Thus, we can express this relationship as:
\[ \frac{r_H}{r_A} = 6 \]

2. **Using Graham's Law**:
- According to Graham's law:
\[ \frac{r_H}{r_A} = \sqrt{\frac{M_A}{M_H}} \]
- Where \( M_A \) is the molar mass of gas A and \( M_H \) is the molar mass of hydrogen.
- The molar mass of hydrogen (\( H_2 \)) is known to be 2 g/mol.

3. **Setting Up the Equation**:
- We can substitute the known values into Graham's law:
\[ 6 = \sqrt{\frac{M_A}{2}} \]

4. **Squaring 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. **Solving for Molar Mass of Gas A**:
- To find \( M_A \), we multiply both sides by 2:
\[ M_A = 36 \times 2 \]
- Thus:
\[ M_A = 72 \text{ g/mol} \]

6. **Conclusion**:
- The molar mass of gas A is 72 g/mol.

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

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