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 establish the relationship between vapor density and molecular mass. The key points to remember are:

1. **Definition of Vapor Density**: Vapor density (VD) is defined as the mass of a certain volume of gas compared to the mass of an equal volume of hydrogen at the same temperature and pressure.

2. **Relationship**: The molecular mass (MM) of a gas is related to its vapor density by the formula:
\[ \text{Molecular Mass} = 2 \times \text{Vapor Density} \]
This means that the molecular mass is directly proportional to the vapor density.

### Step-by-Step Solution:

1. **Given Ratios**: We are given that the vapor densities of two gases are in the ratio of 2:5. Let's denote the vapor densities as:
\[ VD_1 = 2x \quad \text{and} \quad VD_2 = 5x \]
where \(x\) is a common multiplier.

2. **Calculate Molecular Masses**: Using the relationship between vapor density and molecular mass, we can express the molecular masses of the two gases:
\[ MM_1 = 2 \times VD_1 = 2 \times (2x) = 4x \]
\[ MM_2 = 2 \times VD_2 = 2 \times (5x) = 10x \]

3. **Find the Ratio of Molecular Masses**: Now, we can find the ratio of the molecular masses:
\[ \text{Ratio of Molecular Masses} = \frac{MM_1}{MM_2} = \frac{4x}{10x} = \frac{4}{10} = \frac{2}{5} \]

4. **Conclusion**: Therefore, the ratio of the molecular masses of the two gases is also 2:5.

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