One of the important approach to the study of real gases involves the analysis of parameter `Z` called the compressibility factor `Z = (PV_(m))/(RT)` where `P` is pressure, `V_(m)` is molar volume, `T` is absolute temperature and `R` is the universal gas constant. such a relation can also be expressed as `Z = ((V_(m)real)/(V_(m)ideal))` (where `V_(m ideal)` and `V_(m real)` are the molar volume for ideal and real gas respectively). Gas corresponding `Z lt 1` have attractive forces amoung constituent particles. As the pressure is lowered or temperature is increased the value of `Z` approaches 1. (reaching the ideal behaviour)
`{:("Observation",,"Conclusion"),(I.Z =1,,I."The gas need not be showing the ideal behaviour"),(II. Zgt1,, II. "On applying pressure the gas will respond by"),(,,"increasing its volume"),(III. Z lt 1,, III. "The gas may be liquefied"),(IV. Z rarr1 "for low" P,, IV. "The gas is approaching the ideal behaviour") :}`

Options

A. All conclusions are true
B. Conclusions I, II & IV ar true
C. Conclusions I, III & IV are true
D. Conclusion III & IV are true

Answer

To solve the problem regarding the compressibility factor \( Z \) and its implications for real gases, we will analyze the observations and conclusions step by step.

### Step-by-Step Solution:

1. **Understanding the Compressibility Factor \( Z \)**:
- The compressibility factor is defined as:
\[ Z = \frac{PV_m}{RT} \]
where \( P \) is the pressure, \( V_m \) is the molar volume, \( T \) is the absolute temperature, and \( R \) is the universal gas constant.
- It can also be expressed as:
\[ Z = \frac{V_{m \, \text{real}}}{V_{m \, \text{ideal}}} \]
- This means \( Z \) compares the molar volume of a real gas to that of an ideal gas.

2. **Analyzing the Conditions for \( Z \)**:
- If \( Z < 1 \): This indicates that the gas has attractive forces among its constituent particles. Under these conditions, the gas is more likely to be liquefied.
- If \( Z = 1 \): This indicates ideal gas behavior, but it does not guarantee that the gas is behaving ideally in all situations.
- If \( Z > 1 \): This suggests that the gas is experiencing repulsive forces, and under pressure, the gas will respond by increasing its volume.

3. **Evaluating the Observations and Conclusions**:
- **Observation I**: \( Z = 1 \) → Conclusion: "The gas need not be showing ideal behavior."
- **Evaluation**: This is incorrect. If \( Z = 1 \), it indicates ideal gas behavior.

- **Observation II**: \( Z > 1 \) → Conclusion: "On applying pressure, the gas will respond by increasing its volume."
- **Evaluation**: This is incorrect. If \( Z > 1 \), applying pressure would typically decrease the volume, not increase it.

- **Observation III**: \( Z < 1 \) → Conclusion: "The gas may be liquefied."
- **Evaluation**: This is correct. Gases with \( Z < 1 \) have attractive forces and can be liquefied.

- **Observation IV**: \( Z \to 1 \) for low \( P \) → Conclusion: "The gas is approaching ideal behavior."
- **Evaluation**: This is correct. As pressure decreases, \( Z \) approaches 1, indicating that the gas behaves more ideally.

4. **Final Conclusion**:
- The correct pairs of observations and conclusions are:
- Observation III is correct.
- Observation IV is correct.
- Observations I and II are incorrect.

### Summary of Correct Conclusions:
- **Correct**: III and IV
- **Incorrect**: I and II