At high pressure , the van der Waals equation is reduced to

Options

A. `(P + (n^(2)a)/(V^(2))) = nRT`
B. `P(V-B) = nRT`
C. `P(V-nb) = nRT`
D. PV = nRT

Explanation

To solve the problem, we need to analyze the Van der Waals equation for real gases and see how it behaves under high pressure conditions.

### Step-by-Step Solution:

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

2. **Consider High Pressure**:
At high pressure, the pressure \( P \) becomes significantly larger than the term \( \frac{a n^2}{V^2} \). This means:
\[ P \gg \frac{a n^2}{V^2} \]

3. **Simplify the Equation**:
Given that \( P \) is much greater than \( \frac{a n^2}{V^2} \), we can approximate the equation:
\[ P + \frac{a n^2}{V^2} \approx P \]
Thus, the Van der Waals equation simplifies to:
\[ P(V - n b) = nRT \]

4. **Final Form of the Equation**:
Therefore, at high pressure, the Van der Waals equation reduces to:
\[ PV = nRT + P n b \]
or rearranging gives:
\[ P(V - n b) = nRT \]

### Conclusion:
At high pressure, the Van der Waals equation is reduced to:
\[ P(V - n b) = nRT \]