Critical density of a gas having molecular mass `39 g mol^(-1)` is `0.1 g cm^(3-)`. Its critical volume in `L mol^(-1)` is

Options

A. `0.390`
B. `3.90`
C. `0.039`
D. `39.0`

Explanation

To find the critical volume of a gas given its critical density and molecular mass, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Molecular Mass (M) = 39 g/mol
- Critical Density (ρ_c) = 0.1 g/cm³

2. **Convert Critical Density to g/L:**
- Since 1 cm³ = 1 mL and there are 1000 mL in 1 L, we convert the critical density from g/cm³ to g/L:
\[ \text{Critical Density in g/L} = 0.1 \, \text{g/cm}^3 \times 1000 \, \text{cm}^3/\text{L} = 100 \, \text{g/L} \]

3. **Use the Formula for Volume:**
- The formula relating density, mass, and volume is:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Rearranging this gives us:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

4. **Calculate Critical Volume (V_c):**
- The critical volume (V_c) can be calculated using the molar mass and the critical density:
\[ V_c = \frac{M}{\rho_c} \]
Substituting the values we have:
\[ V_c = \frac{39 \, \text{g/mol}}{100 \, \text{g/L}} = 0.39 \, \text{L/mol} \]

5. **Final Result:**
- The critical volume of the gas is:
\[ V_c = 0.39 \, \text{L/mol} \]