Van der Waals real gas acts an ideal gas at which conditions?

Options

A. High temperature, low pressure
B. Low temperature, high pressure
C. High temperature, high pressure
D. Low temperature, low pressure

Explanation

To determine the conditions under which a Van der Waals real gas behaves like an ideal gas, we can analyze the Van der Waals equation and compare it with the ideal gas law.

### Step-by-Step Solution:

1. **Understand the Van der Waals Equation**:
The Van der Waals equation for real gases is given by:
\[ \left(P + \frac{n^2 a}{V^2}\right)(V - n b) = nRT \]
Here, \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the universal gas constant, \(T\) is the temperature, \(a\) accounts for intermolecular forces, and \(b\) accounts for the volume occupied by gas molecules.

2. **Compare with Ideal Gas Law**:
The ideal gas law is:
\[ PV = nRT \]
For a real gas to behave like an ideal gas, the effects of \(a\) and \(b\) must be negligible.

3. **Conditions for Negligibility**:
- **High Temperature**: At high temperatures, the kinetic energy of gas molecules increases. This reduces the effect of intermolecular attractive forces (represented by the term \(\frac{n^2 a}{V^2}\)). Thus, the term becomes negligible.
- **Low Pressure**: At low pressures, the volume of the gas increases. This means that the volume occupied by the gas molecules (represented by \(n b\)) becomes less significant compared to the total volume \(V\). Therefore, the term \(V - n b\) approaches \(V\), making the correction for the volume negligible.

4. **Conclusion**:
Combining these observations, we conclude that a Van der Waals real gas behaves like an ideal gas under the conditions of **high temperature and low pressure**.

### Final Answer:
A Van der Waals real gas acts as an ideal gas at **high temperature and low pressure**.

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