The essential conditions for liquefaction of gases were discovered by Andrews in 1869 as a result of his study of pressure-volume-temperature relationship for `CO_(2)` . It was found that above a certain temperature, it was impossible to liquefy a gas whatever the pressure was applied. The temperature below which the gas can be liquefied by the application of pressure alone is called critical temperature (Tc). The pressure required to liquefy a gas at this temperature is called the critical pressure (Pc). The volume occupied by one mole of the substance at the critical temperature and pressure is called critical volume. Critical constants are related with van der waals' constant as follows:
`V_( c) = 3b, P_( c) =a/(27b^(2)), T_( c) =(8a)/(27 Rb)`
The values of critical volumes of four gases A, B, C and D are 0.025L, 0.312L, 0.245L and 0.432L respectively. The gas with larger molecular diameter will be :

Options

A. A
B. D
C. B
D. C

Answer

To determine which gas has the larger molecular diameter based on the given critical volumes, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Critical Volume and Molecular Diameter:**
- The critical volume (Vc) is related to the molecular volume of the gas. The relationship is given by the equation:
\[ V_c = 3b \]
- Here, \(b\) is a measure of the molecular volume of the gas molecules. Therefore, a larger critical volume indicates a larger value of \(b\), which in turn suggests a larger molecular diameter.

2. **List the Critical Volumes of the Gases:**
- The critical volumes provided for gases A, B, C, and D are:
- Gas A: \(0.025 \, \text{L}\)
- Gas B: \(0.312 \, \text{L}\)
- Gas C: \(0.245 \, \text{L}\)
- Gas D: \(0.432 \, \text{L}\)

3. **Identify the Gas with the Largest Critical Volume:**
- Among the given critical volumes, we compare them:
- \(0.025 \, \text{L}\) (A)
- \(0.312 \, \text{L}\) (B)
- \(0.245 \, \text{L}\) (C)
- \(0.432 \, \text{L}\) (D)
- The largest critical volume is \(0.432 \, \text{L}\) for gas D.

4. **Conclude Which Gas Has the Largest Molecular Diameter:**
- Since gas D has the largest critical volume, it will also have the largest molecular volume \(b\) and consequently the largest molecular diameter.

### Final Answer:
The gas with the larger molecular diameter is **Gas D**.

---