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 the highest value of the hydrolysis constant \( K_h \) for the given salts, we need to analyze the hydrolysis of the ions produced by each salt. Hydrolysis is the reaction of ions with water, and it can lead to the formation of either acidic or basic solutions depending on whether the ions come from strong or weak acids/bases.

### Step-by-Step Solution:

1. **Identify the salts and their ions**: We need to consider the salts provided in the options and identify the cation and anion for each salt. For example:
- KCl: \( K^+ \) (from strong base KOH) and \( Cl^- \) (from strong acid HCl)
- KCN: \( K^+ \) (from strong base KOH) and \( CN^- \) (from weak acid HCN)
- NH4Cl: \( NH_4^+ \) (from weak base NH4OH) and \( Cl^- \) (from strong acid HCl)
- NH4CN: \( NH_4^+ \) (from weak base NH4OH) and \( CN^- \) (from weak acid HCN)

2. **Analyze the hydrolysis of each ion**:
- **KCl**: Both \( K^+ \) and \( Cl^- \) do not undergo hydrolysis as they come from strong acids/bases. Thus, \( K_h \) is negligible.
- **KCN**: \( CN^- \) can hydrolyze to form \( OH^- \) and \( HCN \), while \( K^+ \) does not hydrolyze. This gives a moderate \( K_h \).
- **NH4Cl**: \( NH_4^+ \) can hydrolyze to form \( NH4OH \) and \( H^+ \), while \( Cl^- \) does not hydrolyze. This results in a moderate \( K_h \).
- **NH4CN**: Both \( NH_4^+ \) and \( CN^- \) can hydrolyze. \( NH_4^+ \) produces \( NH4OH \) and \( H^+ \), while \( CN^- \) produces \( OH^- \) and \( HCN \). This leads to a significant hydrolysis effect.

3. **Compare the hydrolysis constants**:
- \( K_h \) for KCl is very low (negligible).
- \( K_h \) for KCN is moderate.
- \( K_h \) for NH4Cl is moderate.
- \( K_h \) for NH4CN is the highest because both ions undergo hydrolysis.

4. **Conclusion**: The salt with the highest value of \( K_h \) is **NH4CN** because both ions contribute to hydrolysis, leading to a greater degree of ionization and thus a higher hydrolysis constant.

### Final Answer:
The highest value of \( K_h \) will be for the salt **NH4CN**.