Consider the equation `Z=(PV)/(nRT)`, which of the following statements is correct?

Options

A. When Z > 1, real gases are easier to compress than the ideal gas.
B. When Z = 1, real gases get compressed easily
C. When Z > 1, real gases are difficult to compress.
D. When Z = 1, real gases are difficult to compress

Answer

To solve the question regarding the compressibility factor \( Z \) in the equation \( Z = \frac{PV}{nRT} \), we need to analyze the statements provided and determine which one is correct.

### Step-by-Step Solution:

1. **Understand the Compressibility Factor \( Z \)**:
- The compressibility factor \( Z \) is a measure of how much a real gas deviates from ideal gas behavior. For an ideal gas, \( Z = 1 \).

2. **Analyze the Statements**:
- We have four statements to evaluate regarding the behavior of real gases in relation to the compressibility factor \( Z \).

3. **Evaluate Statement A**:
- **Statement A**: "When \( Z > 1 \), real gases are easier to compress than ideal gases."
- **Analysis**: This statement is incorrect. When \( Z > 1 \), it indicates that the real gas is less compressible than an ideal gas. Therefore, real gases are actually more difficult to compress.

4. **Evaluate Statement B**:
- **Statement B**: "When \( Z = 1 \), real gases get compressed easily."
- **Analysis**: This statement is also incorrect. When \( Z = 1 \), it indicates ideal gas behavior, not real gas behavior. Real gases do not necessarily compress easily under this condition.

5. **Evaluate Statement C**:
- **Statement C**: "If \( Z > 1 \), real gases are difficult to compress."
- **Analysis**: This statement is correct. When \( Z > 1 \), it indicates that the volume of the real gas is greater than that predicted by the ideal gas law, suggesting that it is indeed more difficult to compress.

6. **Evaluate Statement D**:
- **Statement D**: "When \( Z = 1 \), real gases are difficult to compress."
- **Analysis**: This statement is incorrect. When \( Z = 1 \), it reflects ideal gas behavior, which does not imply difficulty in compression.

7. **Conclusion**:
- Among the given statements, only **Statement C** is correct: "If \( Z > 1 \), real gases are difficult to compress."

### Final Answer:
The correct statement is **C**: "If \( Z > 1 \), real gases are difficult to compress."