Statement-1: `CH_(4),CO_(2)` has value of Z (compressibility factor) less than one, generally. Statement-2: `Zlt1` is due to repulsive forces among the molecules.

Options

A. If both the statement are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B. If both the statement are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To analyze the statements regarding the compressibility factor (Z) of CH₄ (methane) and CO₂ (carbon dioxide), we can break down the solution step by step:

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

For an ideal gas, the value of Z is equal to 1.

**Hint:** Remember that Z indicates how much a real gas deviates from ideal gas behavior.

### Step 2: Evaluating Statement 1
Statement 1 claims that CH₄ and CO₂ have a compressibility factor (Z) less than 1 generally.

For real gases, Z can be less than, equal to, or greater than 1 depending on the interactions between gas molecules. If Z < 1, it indicates that the gas is more compressible than an ideal gas, which typically occurs when attractive forces between molecules are significant.

- CH₄ and CO₂ are both real gases and exhibit attractive forces due to their molecular interactions.

**Hint:** Consider the nature of intermolecular forces in CH₄ and CO₂ to determine their compressibility.

### Step 3: Evaluating Statement 2
Statement 2 states that Z < 1 is due to repulsive forces among the molecules.

This statement is incorrect. A compressibility factor (Z) less than 1 is primarily due to attractive forces between molecules, not repulsive forces. Repulsive forces would cause Z to be greater than 1, as they would resist compression.

**Hint:** Recall that attractive forces lead to a decrease in volume and thus a lower value of Z.

### Step 4: Conclusion
- **Statement 1** is **True**: CH₄ and CO₂ generally have Z < 1 due to significant attractive forces.
- **Statement 2** is **False**: Z < 1 is due to attractive forces, not repulsive forces.

Thus, the correct answer is that Statement 1 is true and Statement 2 is false.

### Final Answer
- **Correct Option**: Statement 1 is true, Statement 2 is false (Option C).