Volume of a molecule is related to Vander Waal's constant 'b' and Avagadro Number '`N_(0)`' by the equation :

Options

A. `V=b/N_(0)`
B. `V=4bN_(0)`
C. `V=(4b)/N_(0)`
D. `V=b/(4N_(0))`

Answer

To solve the problem of how the volume of a molecule is related to Van der Waals constant 'b' and Avogadro's number 'N₀', we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Volume of a Molecule**:
The volume of a single molecule can be expressed in terms of its radius (R). The formula for the volume (V) of a sphere is given by:
\[ V = \frac{4}{3} \pi R^3 \]

2. **Volume per Mole of Gas**:
To find the volume excluded per mole of gas, we multiply the volume of a single molecule by Avogadro's number (N₀):
\[ V_{\text{mole}} = N₀ \cdot V = N₀ \cdot \left(\frac{4}{3} \pi R^3\right) \]

3. **Relating to Van der Waals Constant 'b'**:
The Van der Waals constant 'b' represents the volume occupied by one mole of molecules, which includes the volume excluded due to the finite size of the molecules. Therefore, we can set:
\[ b = N₀ \cdot \left(\frac{4}{3} \pi R^3\right) \]

4. **Solving for Volume of a Single Molecule**:
Rearranging the equation to solve for the volume of a single molecule (V):
\[ V = \frac{b}{N₀} \cdot \frac{3}{4 \pi} \]

5. **Final Expression**:
Thus, the volume of a molecule can be expressed as:
\[ V = \frac{b}{N₀} \cdot \frac{3}{4 \pi} \]

### Conclusion:
The relationship between the volume of a molecule (V), Van der Waals constant (b), and Avogadro's number (N₀) is given by:
\[ V = \frac{b}{N₀} \cdot \frac{3}{4 \pi} \]