a and b are van der Waals' constants for gases. Chlorine is more easily liquefied than ethane because

Options

A. `a " and b for " Cl_2 gt a " and b for " C_2 H_6`
B. `a " and b for " Cl_2 lt a " and b for " C_2 H_6`
C. `a " for " Cl_2 lt a " for " C_2 H_6 " but b for " Cl_2 gt " b for " C_2 H_6`
D. `a " for " Cl_2 gt a " for " C_2 H_6 " but b for " Cl_2 lt " b for " C_2 H_6`.

Explanation

To explain why chlorine is more easily liquefied than ethane, we need to analyze the Van der Waals constants A and B, which are crucial in understanding the behavior of real gases.

### Step-by-Step Solution:

1. **Understanding Van der Waals Constants**:
- The Van der Waals equation is a modified ideal gas equation that accounts for the volume occupied by gas molecules and the intermolecular forces between them.
- The equation is given as:
\[ \left( P + \frac{a n^2}{V^2} \right) (V - nb) = nRT \]
- Here, **A (a)** represents the strength of intermolecular attractions, and **B (b)** represents the volume occupied by the gas molecules.

2. **Liquefaction of Gases**:
- Gases can be liquefied by increasing pressure or decreasing temperature.
- The ease of liquefaction depends on the values of A and B. For a gas to be easily liquefied:
- The value of A should be **high** (indicating strong intermolecular forces).
- The value of B should be **low** (indicating smaller molecular size).

3. **Comparing Chlorine and Ethane**:
- Chlorine (Cl₂) and ethane (C₂H₆) are both gases, but they have different molecular structures and properties.
- For chlorine to be more easily liquefied than ethane, it must have:
- A higher value of A (indicating stronger intermolecular forces).
- A lower value of B (indicating a smaller effective volume per molecule).

4. **Conclusion**:
- Since chlorine is more easily liquefied than ethane, we conclude that:
- The Van der Waals constant A for chlorine is greater than that for ethane.
- The Van der Waals constant B for chlorine is less than that for ethane.
- Therefore, the correct answer is that chlorine has a higher A value and a lower B value compared to ethane.

### Final Answer:
Chlorine is more easily liquefied than ethane because its Van der Waals constant A is greater and constant B is lesser than those of ethane.