The vapour densities of two gases are in the ratio of `1 : 3 ` . Their molecular masses are in the ratio of : -

Options

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

Answer

To solve the problem, we need to find the ratio of the molecular masses of two gases given their vapor densities. Here’s the step-by-step solution:

### Step 1: Understand the relationship between vapor density and molecular mass
Vapor density (VD) is defined as half of the molecular mass (M) of a gas. Therefore, we can express this relationship mathematically as:
\[ \text{Vapor Density} = \frac{\text{Molecular Mass}}{2} \]

### Step 2: Set up the ratio of vapor densities
We are given that the vapor densities of two gases (let's call them Gas 1 and Gas 2) are in the ratio:
\[ \frac{VD_1}{VD_2} = \frac{1}{3} \]

### Step 3: Relate vapor densities to molecular masses
Using the relationship from Step 1, we can express the vapor densities in terms of molecular masses:
\[ \frac{VD_1}{VD_2} = \frac{\frac{M_1}{2}}{\frac{M_2}{2}} = \frac{M_1}{M_2} \]

### Step 4: Substitute the given ratio into the equation
From the given ratio of vapor densities:
\[ \frac{M_1}{M_2} = \frac{1}{3} \]

### Step 5: Conclusion
Thus, the molecular masses of the two gases are in the ratio:
\[ M_1 : M_2 = 1 : 3 \]

### Final Answer
The molecular masses are in the ratio of **1 : 3**.

---