van der Waal's equation for a gas is stated as,
`P=(nRT)/(V-nb)-a(n/V)^(2)`
This equation reduces to the perfect gas equation, `P=(nRT)/V` when,

Options

A. temperature is sufficient high and pressure is low.
B. temperature is sufficient low and pressure is high.
C. both temperature and pressure are very high.
D. both temperature and pressure are very low.

Explanation

To determine the conditions under which the Van der Waals equation reduces to the ideal gas equation, we can analyze the equation step by step.

### Step-by-Step Solution:

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

2. **Identifying the Ideal Gas Equation**:
The ideal gas equation is:
\[ P = \frac{nRT}{V} \]
We need to find the conditions under which the Van der Waals equation simplifies to this form.

3. **Conditions for Reduction**:
- **Low Pressure**: When the pressure \(P\) is low, the volume \(V\) becomes very large compared to \(nb\). Thus, \(V - nb \approx V\).
- **High Temperature**: At high temperatures, the kinetic energy of gas molecules increases, which reduces the effect of intermolecular forces. Therefore, the term \(a\left(\frac{n}{V}\right)^2\) becomes negligible.

4. **Substituting Conditions into the Van der Waals Equation**:
Under these conditions (low pressure and high temperature), we can rewrite the Van der Waals equation:
\[ P \approx \frac{nRT}{V} - 0 \]
This simplifies to:
\[ P \approx \frac{nRT}{V} \]
Thus, we see that the Van der Waals equation reduces to the ideal gas equation under these conditions.

### Conclusion:
The Van der Waals equation reduces to the ideal gas equation when the pressure is low and the temperature is high.

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