Which of the following represents a plot of compressibility factor (Z) versus P at room temperature for helium?

Options

A.
B.
C.
D.

Answer

To solve the question regarding the plot of compressibility factor (Z) versus pressure (P) at room temperature for helium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Compressibility Factor (Z)**:
- The compressibility factor \( Z \) is defined as the ratio of the molar volume of a real gas (\( V_{\text{real}} \)) to the molar volume of an ideal gas (\( V_{\text{ideal}} \)):
\[ Z = \frac{V_{\text{real}}}{V_{\text{ideal}}} \]
- For ideal gases, \( Z = 1 \). For real gases, \( Z \) can be greater than or less than 1 depending on the conditions.

2. **Behavior of Helium as a Real Gas**:
- Helium, while a noble gas and often close to ideal behavior, does exhibit real gas characteristics under certain conditions.
- As pressure increases, the interactions between gas molecules become more significant, leading to deviations from ideal behavior.

3. **Effect of Pressure on Z**:
- For real gases, as pressure increases, the compressibility factor \( Z \) typically increases. This is because the volume occupied by the gas molecules becomes more significant compared to the volume predicted by the ideal gas law.

4. **Effect of Temperature on Z**:
- Conversely, as temperature increases, the compressibility factor \( Z \) tends to decrease. This is due to increased kinetic energy of the gas molecules, which reduces the effects of intermolecular forces.

5. **Analyzing the Graphs**:
- Now, we need to analyze the given options for the plot of \( Z \) versus \( P \):
- **Option 1**: Shows \( Z \) increasing with increasing \( P \) - This is consistent with the behavior of real gases.
- **Option 2**: Shows \( Z \) constant (equal to 1) - This represents ideal gas behavior, which is incorrect for helium at higher pressures.
- **Option 3**: Shows \( Z \) decreasing initially and then increasing with \( P \) - This is incorrect for real gases.
- **Option 4**: Shows \( Z \) increasing initially and then decreasing - This is also incorrect as \( Z \) should not decrease with increasing pressure for real gases.

6. **Conclusion**:
- The correct representation of the plot of compressibility factor \( Z \) versus pressure \( P \) at room temperature for helium is **Option 1**, where \( Z \) increases with increasing pressure.

### Final Answer:
The correct option is **Option 1**.