The vapour density of gas A is four times that of B. If molecular mass of B is M, then molecular mass of A is

1. Break Down the Problem

We know that vapor density (VD) is related to molecular mass (MM) by the formula: $\text{VD} = \frac{\text{MM}}{2}$ Given that the vapor density of gas A (VD_A) is four times that of gas B (VD_B), we can express this relationship as: $VD_A = 4 \cdot VD_B$

2. Relevant Concepts

Using the vapor density relationship, we can write: $VD_A = \frac{MM_A}{2} \quad \text{and} \quad VD_B = \frac{MM_B}{2}$ From the problem, we also have: $VD_A = 4 \cdot VD_B$

3. Analysis and Detail

Now substituting the molecular mass of B (MM_B = M) into the equation for VD_B, we get: $VD_B = \frac{M}{2}$ Now substituting this expression into the first equation gives us: $VD_A = 4 \cdot \frac{M}{2} = 2M$ Using the relationship for VD_A, we replace it: $VD_A = \frac{MM_A}{2}$ Thus, setting the two expressions for VD_A equal to each other: $\frac{MM_A}{2} = 2M$

4. Verify and Summarize

Now, we can solve for MM_A: $MM_A = 2 \cdot 2M = 4M$ Therefore, the molecular mass of gas A is four times the molecular mass of gas B.

Final Answer

The molecular mass of gas A is $4M$.