`pH` for the solution of salt undergoing anionic hydrolysis (say `CH_(3)COONa`) is given by:

Options

A. `pH=1//2[pK_(w)+pK_(a)+log C]`
B. `pH=1//2[pK_(w)+pK_(a)-log C]`
C. `pH=1//2[pK_(w)+pK_(b)-log C]`
D. None of these

Explanation

To find the pH of a solution of a salt undergoing anionic hydrolysis, such as CH₃COONa (sodium acetate), we can follow these steps:

### Step 1: Identify the components of the salt
The salt CH₃COONa is composed of the acetate ion (CH₃COO⁻) and sodium ion (Na⁺). The acetate ion is the conjugate base of acetic acid (CH₃COOH).

### Step 2: Understand the hydrolysis process
When CH₃COONa is dissolved in water, the acetate ion (CH₃COO⁻) undergoes hydrolysis:
\[ \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^- \]
This reaction produces hydroxide ions (OH⁻), which will affect the pH of the solution.

### Step 3: Write the expression for the hydrolysis constant (K_H)
The hydrolysis constant (K_H) can be related to the base dissociation constant (K_B) of the acetate ion and the ion product of water (K_W):
\[ K_H = \frac{K_W}{K_B} \]
Where:
- \( K_W \) is the ion product of water (1.0 x 10⁻¹⁴ at 25°C)
- \( K_B \) is the base dissociation constant for the acetate ion.

### Step 4: Calculate the concentration of OH⁻
The concentration of hydroxide ions produced during hydrolysis can be expressed as:
\[ [\text{OH}^-] = \sqrt{K_H \cdot C} \]
Where \( C \) is the initial concentration of the salt solution.

### Step 5: Calculate pOH
To find the pOH, we use the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the expression for [OH⁻]:
\[ \text{pOH} = -\log\left(\sqrt{K_H \cdot C}\right) \]
Using logarithmic properties, this can be simplified to:
\[ \text{pOH} = \frac{1}{2}(-\log(K_H) - \log(C)) \]

### Step 6: Calculate pH
Finally, we can find the pH using the relationship between pH and pOH:
\[ \text{pH} = 14 - \text{pOH} \]

### Summary of the Steps
1. Identify the components of the salt.
2. Understand the hydrolysis reaction.
3. Write the expression for the hydrolysis constant.
4. Calculate the concentration of hydroxide ions.
5. Calculate pOH.
6. Calculate pH.