Compressibility factor of a gas is given by the equation `Z=(PV)/(nRT)`. On this basis , mark the correct statement.

Options

A. (a) When `Z gt 1` , real gases get compressed easily .
B. (b) When `Z = 1` real gases get compressed easily .
C. (c) When `Z gt 1` , real gases are difficult to compress .
D. (d) When `Z = 1` , real gases are difficult to compress .

Explanation

To solve the question regarding the compressibility factor \( Z \) of a gas, we will analyze the equation provided and the implications of different values of \( Z \).

### Step-by-Step Solution:

1. **Understanding the Compressibility Factor**:
The compressibility factor \( Z \) is defined by the equation:
\[ Z = \frac{PV}{nRT} \]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature.

2. **Identifying Ideal vs. Real Gases**:
- For **ideal gases**, \( Z = 1 \). This means that the behavior of the gas follows the ideal gas law perfectly.
- For **real gases**, \( Z \) can be greater than or less than 1:
- If \( Z > 1 \): The gas shows a **positive deviation** from ideal behavior, indicating that the repulsive forces dominate.
- If \( Z < 1 \): The gas shows a **negative deviation**, indicating that the attractive forces dominate.

3. **Analyzing the Implications of \( Z \)**:
- When \( Z > 1 \): The gas is **difficult to compress** because the repulsive forces between gas molecules are stronger than the attractive forces.
- When \( Z < 1 \): The gas is **easier to compress** because the attractive forces are stronger, allowing the gas to be compressed more readily.
- When \( Z = 1 \): The gas behaves ideally, and while it can be compressed, it does not exhibit the same behavior as real gases under non-ideal conditions.

4. **Evaluating the Statements**:
- **Statement 1**: If \( Z > 1 \), gases get compressed easily. **(Incorrect)**
- **Statement 2**: If \( Z = 1 \), real gases get compressed easily. **(Incorrect)**
- **Statement 3**: If \( Z > 1 \), gases are difficult to compress. **(Correct)**
- **Statement 4**: If \( Z = 1 \), real gases are difficult to compress. **(Incorrect)**

5. **Conclusion**:
The correct statement based on the analysis is:
- **If \( Z > 1 \), the gases are difficult to compress.**