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. (a) b
B. (b) a
C. (c) Both a and b
D. (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 1: Understand the van der Waals equation
The van der Waals equation for a real gas is given by:
\[ (P + \frac{a n^2}{V^2})(V - nb) = nRT \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = temperature
- \( a \) = measure of the attractive forces between particles
- \( b \) = volume occupied by the gas particles

### Step 2: Analyze the behavior at high pressure
At high pressure, the volume \( V \) of the gas becomes very small. This means that the term \( \frac{a n^2}{V^2} \) becomes significant because \( V^2 \) in the denominator will be very small, making the entire term larger.

### Step 3: Identify which term can be neglected
In the van der Waals equation, as pressure increases and volume decreases, the term \( b \) (which accounts for the volume occupied by the gas particles) becomes less significant compared to the term \( \frac{a n^2}{V^2} \). Thus, we can neglect the \( b \) term when considering the behavior of the gas at high pressures.

### Step 4: Rewrite the van der Waals equation
Neglecting the \( b \) term, we can simplify the van der Waals equation to:
\[ P(V - nb) \approx nRT \]
This simplification shows that the compressibility factor \( Z \) (defined as \( Z = \frac{PV}{nRT} \)) will be greater than 1, indicating that the gas is less compressible than an ideal gas at high pressures.

### Step 5: Conclusion
From our analysis, we conclude that at high pressures, the compressibility factor \( Z \) of a real gas is greater than 1 because we can neglect the \( b \) term in the van der Waals equation.

### Final Answer
The value that can be neglected from the van der Waals equation at high pressure is the **b value**.

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