The rate of diffusion of a gas X is `sqrt(2)` times that of Y. If the molecular mass X is 16, what is the molecular mass of gas y?

Explanation

To solve the problem, we will 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. The formula can be expressed as:

\[ \frac{R_X}{R_Y} = \sqrt{\frac{M_Y}{M_X}} \]

Where:
- \( R_X \) and \( R_Y \) are the rates of diffusion of gases X and Y, respectively.
- \( M_X \) and \( M_Y \) are the molar masses of gases X and Y, respectively.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The rate of diffusion of gas X is \( \sqrt{2} \) times that of gas Y.
- The molar mass of gas X (\( M_X \)) is 16 g/mol.

2. **Set Up the Equation**:
- According to the problem, we can express the relationship as:
\[ \frac{R_X}{R_Y} = \sqrt{2} \]
- Substituting into Graham's law:
\[ \sqrt{2} = \sqrt{\frac{M_Y}{M_X}} \]

3. **Substitute the Known Values**:
- We know \( M_X = 16 \), so we can substitute this value into the equation:
\[ \sqrt{2} = \sqrt{\frac{M_Y}{16}} \]

4. **Square Both Sides**:
- To eliminate the square root, we square both sides:
\[ 2 = \frac{M_Y}{16} \]

5. **Solve for \( M_Y \)**:
- Multiply both sides by 16 to find \( M_Y \):
\[ M_Y = 2 \times 16 = 32 \]

6. **Conclusion**:
- The molar mass of gas Y is 32 g/mol.

### Final Answer:
The molecular mass of gas Y is **32 g/mol**.