At a high pressure, the compressibility factor (Z) of a real gas is usually greater than one. This can be explained from van der Waals equation by neglecting the value of:

Options

A. b
B. a
C. Both a and b
D. V

Explanation

To solve the question regarding the compressibility factor (Z) of a real gas at high pressure using the van der Waals equation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Compressibility Factor (Z)**:
The compressibility factor (Z) is defined as \( Z = \frac{PV}{nRT} \). For an ideal gas, Z is equal to 1. However, for real gases, especially at high pressures, Z can be greater than 1.

2. **Recall the van der Waals Equation**:
The van der Waals equation for one mole of a gas is given by:
\[ \left(P + \frac{a}{V^2}\right)(V - b) = RT \]
where \( a \) and \( b \) are constants specific to the gas, representing intermolecular forces and the volume occupied by gas molecules, respectively.

3. **Analyze Conditions at High Pressure**:
At high pressure, the volume (V) of the gas decreases significantly because pressure and volume are inversely related (Boyle's Law). Therefore, we can conclude that V becomes very small.

4. **Neglecting Terms in the van der Waals Equation**:
Since V is small at high pressure, the term \( \frac{a}{V^2} \) becomes very large. However, we are interested in what we can neglect. As V decreases, the term \( \frac{a}{V^2} \) becomes significant, but the volume correction term \( b \) (which accounts for the volume occupied by the gas molecules) becomes less significant compared to the pressure correction term \( \frac{a}{V^2} \).

5. **Final Form of the Equation**:
Thus, we can neglect the term \( \frac{a}{V^2} \) in the van der Waals equation when considering high pressures. The modified equation simplifies to:
\[ P(V - b) = RT \]

6. **Conclusion**:
Therefore, the value that we neglect in the van der Waals equation at high pressure is \( \frac{a}{V^2} \) or simply \( a \).

### Answer:
The correct answer is that we neglect the value of \( \frac{a}{V^2} \) in the van der Waals equation.

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