Which of the following gas should have maximum value for `k_H`?

Options

A. He
B. `H_2`
C. `N_2`
D. `CO_2`

Answer

To determine which gas should have the maximum value for \( k_H \) (Henry's Law constant), we need to understand the relationship between the solubility of a gas in a liquid and its Henry's Law constant.

### Step-by-Step Solution:

1. **Understanding Henry's Law**:
Henry's Law states that the amount of gas that dissolves in a liquid at a given temperature is proportional to the partial pressure of that gas above the liquid. This can be expressed mathematically as:
\[ P = k_H \cdot X_A \]
where \( P \) is the partial pressure of the gas, \( k_H \) is the Henry's Law constant, and \( X_A \) is the mole fraction of the gas in the liquid phase.

2. **Inversely Proportional Relationship**:
From the equation, we can see that if \( k_H \) increases, the mole fraction \( X_A \) (which represents solubility) decreases at the same partial pressure. Therefore, a higher \( k_H \) indicates lower solubility.

3. **Liquefaction of Gases**:
The solubility of a gas is related to how easily it can be liquefied. Gases that are easier to liquefy will have lower \( k_H \) values because they dissolve better in the liquid phase.

4. **Comparison of Gases**:
We need to compare the gases provided: Helium (He), Hydrogen (H2), Nitrogen (N2), and Carbon Dioxide (CO2).

- **Helium (He)**: A monatomic gas with very weak Van der Waals forces due to its small size.
- **Hydrogen (H2)**: A diatomic gas that can form weak intermolecular forces but is still relatively small.
- **Nitrogen (N2)**: A diatomic gas with stronger Van der Waals forces than H2 due to its larger size.
- **Carbon Dioxide (CO2)**: A triatomic gas with significant intermolecular forces due to its larger size and polar characteristics.

5. **Conclusion**:
Since solubility is inversely related to \( k_H \), the gas that is least soluble (i.e., the one that is hardest to liquefy) will have the highest \( k_H \). Among the gases listed, Helium has the least ability to be liquefied due to its small size and weak intermolecular forces. Thus, it will have the maximum value for \( k_H \).

### Final Answer:
**Helium (He) should have the maximum value for \( k_H \).**