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 need to use the relationship between the density of gases and their molecular masses. The formula for the density of a gas can be expressed as:

\[ \text{Density} (\rho) = \frac{P \cdot M}{R \cdot T} \]

where:
- \( P \) = pressure of the gas,
- \( M \) = molecular mass of the gas,
- \( R \) = universal gas constant,
- \( T \) = temperature of the gas.

Given that the ratio of the densities of gas A and gas B is 3, we can write:

\[ \frac{\rho_A}{\rho_B} = 3 \]

Substituting the density formula into this ratio gives:

\[ \frac{\frac{P \cdot M_A}{R \cdot T}}{\frac{P \cdot M_B}{R \cdot T}} = 3 \]

Since the pressure \( P \), the universal gas constant \( R \), and the temperature \( T \) are the same for both gases, they cancel out:

\[ \frac{M_A}{M_B} = 3 \]

From this equation, we can express the molecular mass of gas B in terms of the molecular mass of gas A:

\[ M_B = \frac{M_A}{3} \]

Now, if we denote the molecular mass of gas A as \( M \), we can substitute this into the equation:

\[ M_B = \frac{M}{3} \]

Thus, the molecular mass of gas B is:

\[ M_B = \frac{M}{3} \]

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

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