Degree hydrolysis (h) of a salt of weak acid and a strong base is given by

Options

A. `h=sqrt((K_h)/c)`
B. `h=sqrt(K_h)`
C. `h=sqrt(c/(K_h))`
D. `h=sqrt((K_w)/(K_b))`

Answer

To solve the question regarding the degree of hydrolysis (h) of a salt formed from a weak acid and a strong base, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Components**:
- We have a weak acid (e.g., acetic acid, CH₃COOH) and a strong base (e.g., sodium hydroxide, NaOH).
- The salt formed from this reaction is sodium acetate (CH₃COONa).

2. **Dissociation of the Salt**:
- Sodium acetate dissociates in water to give acetate ions (CH₃COO⁻) and sodium ions (Na⁺).
- The dissociation can be represented as:
\[ \text{CH}_3\text{COONa} \rightarrow \text{CH}_3\text{COO}^- + \text{Na}^+ \]

3. **Establish Hydrolysis Reaction**:
- The acetate ion (CH₃COO⁻) can undergo hydrolysis in water:
\[ \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^- \]
- This reaction indicates that the acetate ion acts as a base.

4. **Set Up Initial Concentrations**:
- Let the initial concentration of sodium acetate be \( C \).
- At equilibrium, let the degree of hydrolysis be \( h \). Therefore, the concentrations at equilibrium will be:
- CH₃COO⁻: \( C - h \)
- CH₃COOH: \( h \)
- OH⁻: \( h \)

5. **Write the Hydrolysis Constant Expression**:
- The hydrolysis constant \( K_h \) can be expressed as:
\[ K_h = \frac{[\text{CH}_3\text{COOH}][\text{OH}^-]}{[\text{CH}_3\text{COO}^-]} \]
- Substituting the equilibrium concentrations:
\[ K_h = \frac{h \cdot h}{C - h} = \frac{h^2}{C - h} \]

6. **Assume \( h \) is Small**:
- Since \( h \) is small compared to \( C \), we can approximate \( C - h \approx C \).
- Thus, the equation simplifies to:
\[ K_h \approx \frac{h^2}{C} \]

7. **Solve for Degree of Hydrolysis \( h \)**:
- Rearranging the equation gives:
\[ h^2 = K_h \cdot C \]
- Taking the square root:
\[ h = \sqrt{\frac{K_h}{C}} \]

8. **Conclusion**:
- The degree of hydrolysis \( h \) of the salt of a weak acid and a strong base is given by:
\[ h = \sqrt{\frac{K_h}{C}} \]

### Final Answer:
The degree of hydrolysis \( h \) of a salt of a weak acid and a strong base is given by:
\[ h = \sqrt{\frac{K_h}{C}} \]