The vapour densities of two gases are in the ratio of 2 : 5 Their molecular masses are in the ratio of

Options

A. `5 : 2`
B. `1 : 3`
C. `2 : 5`
D. `3 : 1`

Answer

To solve the problem, we need to find the ratio of the molecular masses of two gases given the ratio of their vapor densities.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between vapor density (VD) and molecular mass (MM) is given by the formula:
\[ \text{Vapor Density} = \frac{\text{Molecular Mass}}{2} \]
This implies that:
\[ \text{Molecular Mass} = 2 \times \text{Vapor Density} \]

2. **Set Up the Ratios**:
According to the problem, the vapor densities of the two gases are in the ratio of 2:5. We can denote:
- Vapor Density of Gas 1 (VD1) = 2
- Vapor Density of Gas 2 (VD2) = 5

3. **Calculate Molecular Masses**:
Using the relationship established in step 1:
- For Gas 1:
\[ \text{Molecular Mass of Gas 1 (MM1)} = 2 \times \text{VD1} = 2 \times 2 = 4 \]
- For Gas 2:
\[ \text{Molecular Mass of Gas 2 (MM2)} = 2 \times \text{VD2} = 2 \times 5 = 10 \]

4. **Find the Ratio of Molecular Masses**:
Now, we can find the ratio of the molecular masses:
\[ \text{Ratio of MM1 to MM2} = \frac{\text{MM1}}{\text{MM2}} = \frac{4}{10} = \frac{2}{5} \]

5. **Conclusion**:
The ratio of the molecular masses of the two gases is 2:5.

### Final Answer:
The molecular masses are in the ratio of **2:5**.