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 1: Understand Hydrolysis
Hydrolysis refers to the reaction of a salt with water to produce an acid and a base. In this case, we are dealing with a salt formed from a weak acid and a weak base.

### Step 2: Identify the Components
Let’s consider a weak acid (e.g., acetic acid, CH₃COOH) and a weak base (e.g., ammonium hydroxide, NH₄OH). When these react, they form a salt (e.g., ammonium acetate, CH₃COONH₄) and water.

### Step 3: Write the Hydrolysis Reaction
The hydrolysis of the salt can be represented as:
\[ \text{CH}_3\text{COONH}_4 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \]

### Step 4: Define Hydrolysis Constant (Kₕ)
The hydrolysis constant (Kₕ) can be expressed in terms of the concentrations of the products and reactants:
\[ K_h = \frac{[\text{NH}_4^+][\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COONH}_4]} \]

### Step 5: Relate Kₕ to Kₐ and Kₑ
For the weak base (NH₄OH), the dissociation constant (Kₑ) is given by:
\[ K_b = \frac{[\text{NH}_4^+][\text{OH}^-]}{[\text{NH}_4OH]} \]

For the weak acid (CH₃COOH), the dissociation constant (Kₐ) is:
\[ K_a = \frac{[\text{CH}_3\text{COO}^-][\text{H}^+]}{[\text{CH}_3\text{COOH}]} \]

### Step 6: Use the Relationship Between Kₕ, Kₐ, and Kₑ
The relationship between the hydrolysis constant, the dissociation constants of the weak acid and weak base can be expressed as:
\[ K_h \cdot K_a \cdot K_b = K_w \]
where \( K_w \) is the ion product of water.

### Step 7: Determine the Inverse Proportionality
From the equation above, we can rearrange it to show that:
\[ K_h = \frac{K_w}{K_a \cdot K_b} \]

This indicates that the hydrolysis constant (Kₕ) is inversely proportional to both the dissociation constants of the weak acid (Kₐ) and the weak base (Kₑ).

### Conclusion
Thus, the hydrolysis constant of a salt of a weak acid and a weak base is inversely proportional to the dissociation constants of both the acid and the base.

### Final Answer
The hydrolysis constant of a salt of weak acid and weak base is inversely proportional to the dissociation constants of both the weak acid and the weak base.

---