Critical temperature `(T_(C))` and critical pressure `(P_(C))` of carbon dioxide gas are `30.98^(@) C` and 73 atm . Carbon dioxide gas cannot be liquified under following conditions

Options

A. `t = 30.98^(@) C` , P = 73 atm
B. `t = 30.98^(@) C , P = 83` atm
C. `t = 32^(@) C , P = 80` atm
D. `t = 30.98^(@) C , P = 85` atm

Explanation

To determine the conditions under which carbon dioxide (CO2) gas cannot be liquefied, we need to analyze the critical temperature (T_C) and critical pressure (P_C) of CO2, which are given as 30.98°C and 73 atm, respectively.

### Step-by-Step Solution:

1. **Understand Critical Temperature and Pressure**:
- The critical temperature (T_C) is the maximum temperature at which a gas can be liquefied, regardless of the pressure applied. For CO2, T_C = 30.98°C.
- The critical pressure (P_C) is the minimum pressure required to liquefy a gas at its critical temperature. For CO2, P_C = 73 atm.

2. **Analyze the Given Conditions**:
- We need to evaluate four different conditions (options) regarding temperature and pressure to determine if CO2 can be liquefied.

3. **Evaluate Each Option**:
- **Option A**: T = 30.98°C, P = 73 atm
- This is equal to both T_C and P_C. CO2 can be liquefied under these conditions.

- **Option B**: T = 30.98°C, P = 83 atm
- The temperature is at T_C, and the pressure is greater than P_C. CO2 can be liquefied under these conditions.

- **Option C**: T = 32°C, P = 80 atm
- The temperature is greater than T_C (32°C > 30.98°C). CO2 cannot be liquefied under these conditions, regardless of the pressure applied.

- **Option D**: T = 30.98°C, P = 85 atm
- The temperature is at T_C, and the pressure is greater than P_C. CO2 can be liquefied under these conditions.

4. **Conclusion**:
- The only condition where CO2 cannot be liquefied is **Option C** (T = 32°C, P = 80 atm).

### Final Answer:
Carbon dioxide gas cannot be liquefied under the conditions of **Option C** (T = 32°C, P = 80 atm).