The degree of hydrolysis of a salt of weak acid and strong base is = 0.5. The equation to be used to calculate the accurate value of the degree of hydrolysis (h) is

Options

A. `h=sqrt(K_(w)/(K_(a)*K_(b)))`
B. `h=sqrt(K_(w)/(K_(a)*C))`
C. `h=sqrt(K_(w)/(K_(b)*C))`
D. none of these

Answer

To solve the problem regarding the degree of hydrolysis of a salt formed from a weak acid and a strong base, we need to derive the appropriate equation. The degree of hydrolysis (h) can be calculated using a specific formula.

### Step-by-Step Solution:

1. **Understanding Hydrolysis**:
- Hydrolysis refers to the reaction of a salt with water, which results in the formation of an acid and a base. For a salt derived from a weak acid and a strong base, only the weak acid part undergoes hydrolysis.

2. **Identifying the Components**:
- Let’s denote:
- \( K_w \) = Ion product of water (1.0 x 10^-14 at 25°C)
- \( K_a \) = Acid dissociation constant of the weak acid
- \( C \) = Concentration of the salt solution

3. **Using the Degree of Hydrolysis Formula**:
- The degree of hydrolysis (h) can be calculated using the formula:
\[ h = \sqrt{\frac{K_w}{K_a \cdot C}} \]
- This formula is derived from the equilibrium expressions related to the hydrolysis of the salt.

4. **Substituting Known Values**:
- In this case, we know that the degree of hydrolysis (h) is given as 0.5. We can use this information to analyze the relationship between \( K_w \), \( K_a \), and \( C \).

5. **Conclusion**:
- Therefore, the equation to be used to calculate the accurate value of the degree of hydrolysis (h) is:
\[ h = \sqrt{\frac{K_w}{K_a \cdot C}} \]