The ratio of density of a gas A and gas B is three. If the molecular mass of A is M, then molecular mass of B is

Options

A. `sqrt(3)M`
B. `M//sqrt(3)`
C. `M//3`
D. 3M

Answer

To solve the problem, we will use the relationship between the density of gases and their molecular masses. The key principle to remember is that the density of a gas is directly proportional to its molecular mass when the temperature and pressure are constant.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- The ratio of the densities of gas A and gas B is given as:
\[ \frac{D_A}{D_B} = 3 \]
- The molecular mass of gas A is given as \( M \).

2. **Using the Relationship Between Density and Molecular Mass**:
- The density of a gas is directly proportional to its molecular mass. Therefore, we can express this relationship as:
\[ \frac{D_A}{D_B} = \frac{M_A}{M_B} \]
- Here, \( M_A \) is the molecular mass of gas A and \( M_B \) is the molecular mass of gas B.

3. **Substituting Known Values**:
- We know that \( M_A = M \) (the molecular mass of gas A).
- Substituting this into the equation gives:
\[ \frac{D_A}{D_B} = \frac{M}{M_B} \]

4. **Setting Up the Equation**:
- From the density ratio, we can write:
\[ 3 = \frac{M}{M_B} \]

5. **Solving for Molecular Mass of Gas B**:
- Rearranging the equation to find \( M_B \):
\[ M_B = \frac{M}{3} \]

6. **Conclusion**:
- Thus, the molecular mass of gas B is \( \frac{M}{3} \).

### Final Answer:
The molecular mass of gas B is \( \frac{M}{3} \).

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