Vander waal's equation of state is obeyed by real gases for n moles of real gas the expression will be

Options

A. `(p/n+(na)/v^2)(V/(n-b))=RT`
B. `(p+a/V^2)(V-b)=Nrt`
C. `(p+na/V^2)(Nv-b)=Nrt`
D. `(p+n^2a/V^2)(V-nb)=Nrt`

Answer

To derive the Van der Waals equation of state for n moles of a real gas, we start with the general form of the equation. The Van der Waals equation accounts for the finite size of molecules and the intermolecular forces that exist between them.

### Step-by-Step Solution:

1. **Understanding the Van der Waals Equation**:
The Van der Waals equation is given by:
\[ \left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT \]
where:
- \( P \) is the pressure of the gas,
- \( V \) is the volume of the gas,
- \( n \) is the number of moles,
- \( R \) is the universal gas constant,
- \( T \) is the temperature,
- \( a \) is a measure of the attraction between particles,
- \( b \) is the volume occupied by one mole of the gas particles.

2. **Rearranging the Equation**:
To express it clearly, we can expand the left-hand side:
\[ P + \frac{a n^2}{V^2} = \frac{nRT}{V - nb} \]
This shows how pressure is adjusted for the volume occupied by the gas particles and the intermolecular forces.

3. **Final Form of the Van der Waals Equation**:
Thus, the complete expression for n moles of a real gas according to the Van der Waals equation is:
\[ P + \frac{a n^2}{V^2} = \frac{nRT}{V - nb} \]

### Conclusion:
The correct expression for the Van der Waals equation for n moles of a real gas is:
\[ \left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT \]