The molar volume of `CO_(2)` is maximum at

Options

A. NTP
B. `0^(@)C` and 2.0 atm
C. `127^(@)C` and 1 atm.
D. `273^(@)C` and 2 atm

Explanation

To determine the conditions under which the molar volume of \( CO_2 \) is maximum, we can use the ideal gas law, which is expressed as:

\[ PV = nRT \]

Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature in Kelvin

### Step-by-Step Solution:

1. **Rearranging the Ideal Gas Equation**:
Since we want to find the volume \( V \), we can rearrange the ideal gas equation to solve for \( V \):
\[ V = \frac{nRT}{P} \]
Given that we are considering one mole of gas (\( n = 1 \)):
\[ V = \frac{RT}{P} \]

2. **Understanding Molar Volume**:
The molar volume \( V_m \) is directly proportional to the temperature \( T \) and inversely proportional to the pressure \( P \):
\[ V_m \propto \frac{T}{P} \]

3. **Finding Conditions for Maximum Volume**:
To maximize the molar volume, we need to maximize \( \frac{T}{P} \). This means we should look for high temperatures and low pressures.

4. **Calculating Molar Volume at Given Conditions**:
We will calculate the molar volume for different conditions provided in the question:

- **Condition 1**: Normal temperature (273 K) and pressure (1 atm):
\[ V = \frac{R \cdot 273}{1} = 273R \text{ (L/mol)} \]

- **Condition 2**: 0 °C (273 K) and 2 atm:
\[ V = \frac{R \cdot 273}{2} = 136.5R \text{ (L/mol)} \]

- **Condition 3**: 127 °C (400 K) and 1 atm:
\[ V = \frac{R \cdot 400}{1} = 400R \text{ (L/mol)} \]

- **Condition 4**: 273 °C (546 K) and 2 atm:
\[ V = \frac{R \cdot 546}{2} = 273R \text{ (L/mol)} \]

5. **Comparing the Volumes**:
Now, we compare the calculated volumes:
- At 273 K and 1 atm: \( 273R \)
- At 273 K and 2 atm: \( 136.5R \)
- At 400 K and 1 atm: \( 400R \)
- At 546 K and 2 atm: \( 273R \)

The maximum molar volume occurs at 127 °C (400 K) and 1 atm pressure, which gives us \( 400R \).

### Conclusion:
The molar volume of \( CO_2 \) is maximum at **127 °C and 1 atm pressure**.