The highest value of `K_(h)` will be for the salt

Options

A. KCI
B. `(NH_(4))_(2) SO_(4)`
C. KCN
D. `NH_(4)CN`

Answer

To determine which salt has the highest value of the hydrolysis constant \( K_H \), we need to analyze the hydrolysis reactions of the given salts: KCl, \( NH_4 \)SO\(_4\), KCN, and \( NH_4 \)CN.

### Step-by-Step Solution:

1. **Understanding Hydrolysis Constant \( K_H \)**:
- The hydrolysis constant \( K_H \) is an equilibrium constant for the hydrolysis reaction of a salt in water. It indicates the extent to which a salt dissociates into its ions and reacts with water.

2. **Analyzing Each Salt**:
- **KCl**:
- Dissociates into \( K^+ \) and \( Cl^- \).
- \( K^+ \) does not hydrolyze (as it comes from a strong base, KOH).
- \( Cl^- \) does not hydrolyze (as it comes from a strong acid, HCl).
- Therefore, \( K_H \) for KCl is very low (essentially negligible).

- **\( NH_4 \)SO\(_4\)**:
- Dissociates into \( NH_4^+ \) and \( SO_4^{2-} \).
- \( NH_4^+ \) hydrolyzes to form \( NH_4OH \) (a weak base).
- \( SO_4^{2-} \) does not hydrolyze (as it comes from a strong acid, \( H_2SO_4 \)).
- Thus, \( K_H \) is positive but not very high.

- **KCN**:
- Dissociates into \( K^+ \) and \( CN^- \).
- \( K^+ \) does not hydrolyze (strong base).
- \( CN^- \) hydrolyzes to form \( HCN \) (a weak acid).
- Therefore, \( K_H \) is positive but limited by the weak acid nature of \( HCN \).

- **\( NH_4 \)CN**:
- Dissociates into \( NH_4^+ \) and \( CN^- \).
- Both ions can hydrolyze:
- \( NH_4^+ \) forms \( NH_4OH \) (weak base).
- \( CN^- \) forms \( HCN \) (weak acid).
- The hydrolysis reaction can be represented as:
\[ NH_4^+ + CN^- + H_2O \rightleftharpoons NH_4OH + HCN \]
- This reaction can proceed significantly because both products are weak, leading to a higher \( K_H \).

3. **Conclusion**:
- Among the salts, \( NH_4 \)CN has the highest hydrolysis constant \( K_H \) because both ions can hydrolyze, leading to a more significant equilibrium shift.

### Final Answer:
The salt with the highest value of \( K_H \) is \( NH_4 \)CN.

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