Which of the following gas/gases show `Zgt1` at all temperature?

Options

A. `H_(2)`
B. `He`
C. `CH_(4)`
D. None of these.

Answer

To solve the question "Which of the following gas/gases show Z > 1 at all temperatures?", we need to understand the concept of the compressibility factor (Z) and how it relates to different gases.

### Step-by-Step Solution:

1. **Understanding Compressibility Factor (Z)**:
- The compressibility factor (Z) is defined as \( Z = \frac{PV}{nRT} \), where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
- For ideal gases, Z = 1. However, real gases can have Z values that are either greater than or less than 1.

**Hint**: Remember that Z = 1 indicates ideal gas behavior.

2. **Identifying Conditions for Z**:
- Z > 1 indicates that the gas shows positive deviation from ideal behavior, which means it is less compressible due to strong repulsive forces between molecules.
- Z < 1 indicates negative deviation, meaning the gas is more compressible due to attractive forces between molecules.

**Hint**: Positive deviation (Z > 1) occurs due to repulsive forces, while negative deviation (Z < 1) occurs due to attractive forces.

3. **Analyzing Real Gases**:
- Common gases like methane (CH4) and carbon dioxide (CO2) exhibit Z < 1 at standard conditions because they have significant attractive forces.
- Gases like hydrogen (H2) and helium (He) can show Z > 1, but this typically occurs at higher temperatures and lower pressures.

**Hint**: Check the behavior of gases at different temperatures and pressures to determine their Z values.

4. **Determining Z Behavior at All Temperatures**:
- The question specifically asks for gases that show Z > 1 at all temperatures.
- Hydrogen and helium do not consistently show Z > 1 at all temperatures; they only do so under certain conditions (usually at higher temperatures).

**Hint**: Consider whether the gases can maintain Z > 1 across the entire temperature range.

5. **Conclusion**:
- Since none of the gases listed consistently show Z > 1 at all temperatures, the correct answer is "none of these."

**Final Answer**: None of these gases show Z > 1 at all temperatures.