The hydrolysis constant of a salt of weak acid and weak base is inversely proportional to

Options

A. ionic product constant of water
B. dissociation constant of both acid and weak base
C. dissociation constant of weak acid
D. dissociation constant of weak base

Answer

To solve the question regarding the hydrolysis constant of a salt formed from a weak acid and a weak base, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Hydrolysis**:
- When a salt formed from a weak acid and a weak base dissolves in water, it undergoes hydrolysis. This means that the salt dissociates into its constituent ions, which can react with water.

2. **Identify the Components**:
- Let’s consider a salt formed from acetic acid (CH₃COOH) and ammonium hydroxide (NH₄OH). The salt formed is ammonium acetate (NH₄CH₃COO).

3. **Dissociation of the Salt**:
- The dissociation of ammonium acetate in water can be represented as:
\[ NH₄CH₃COO \rightleftharpoons NH₄^+ + CH₃COO^- \]

4. **Hydrolysis Reactions**:
- The ions produced can undergo hydrolysis:
- For \( NH₄^+ \):
\[ NH₄^+ + H₂O \rightleftharpoons NH₃ + H₃O^+ \]
- For \( CH₃COO^- \):
\[ CH₃COO^- + H₂O \rightleftharpoons CH₃COOH + OH^- \]

5. **Equilibrium Constants**:
- The hydrolysis constant (K_h) for the salt can be expressed in terms of the dissociation constants of the weak acid (K_a) and weak base (K_b):
\[ K_h = \frac{K_w}{K_a \cdot K_b} \]
- Here, \( K_w \) is the ion product of water.

6. **Inversely Proportional Relationship**:
- From the equation \( K_h = \frac{K_w}{K_a \cdot K_b} \), we can see that the hydrolysis constant \( K_h \) is inversely proportional to the product of the dissociation constants \( K_a \) and \( K_b \). This means that as \( K_a \) or \( K_b \) increases, \( K_h \) decreases, and vice versa.

### Conclusion:
The hydrolysis constant of a salt of a weak acid and a weak base is inversely proportional to the product of the dissociation constants of the weak acid and weak base.