Consider the equation `Z= (PV)/(RT)`. Which of the following statements is correct?

Options

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

Explanation

To solve the question regarding the equation \( Z = \frac{PV}{RT} \) and to determine which statement is correct, we will follow these steps:

### Step 1: Understand the Compressibility Factor (Z)
The compressibility factor \( Z \) is defined as:
\[ Z = \frac{PV}{RT} \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( R \) = universal gas constant
- \( T \) = temperature of the gas

### Step 2: Analyze the Condition for Ideal Gases
For ideal gases, the equation simplifies to:
\[ Z = 1 \]
This means that under ideal conditions, the behavior of the gas follows the ideal gas law perfectly.

### Step 3: Consider Real Gases
Real gases do not always behave ideally. The value of \( Z \) for real gases can be:
- **Less than 1**: Indicates attractive forces dominate (gas is more compressible).
- **Equal to 1**: Indicates ideal behavior.
- **Greater than 1**: Indicates repulsive forces dominate (gas is less compressible).

### Step 4: Evaluate the Statements
Now, we will evaluate the statements provided in the question:

1. **When \( Z > 1 \), real gases are easier to compress**: This is incorrect. When \( Z > 1 \), it indicates that the gas is less compressible due to repulsive forces dominating.

2. **When \( Z = 1 \), real gases get compressed easily**: This is incorrect. \( Z = 1 \) is the condition for ideal gases, not real gases.

3. **When \( Z > 1 \), it is difficult to compress**: This is correct. Since repulsive forces dominate, it becomes difficult to compress the gas.

4. **When \( Z = 1 \), ideal gases are difficult to compress**: This is incorrect. Ideal gases are not difficult to compress at \( Z = 1 \).

### Step 5: Conclusion
The correct statement is:
**When \( Z > 1 \), it is difficult to compress real gases.**

### Final Answer
The correct option is **option 3**.

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