A salt is formed when a weak acid of dissociation constant `10^(-4)` and weak base of dissociation constant `10^(-5)` are mixed. The pH and degree of hydrolysis of salt solution are

Options

A. `5.1%`
B. `7.14%`
C. `6.5, 0.3%`
D. `0.3, 6.5%`

Answer

To solve the problem, we need to determine the pH and degree of hydrolysis of a salt formed from a weak acid and a weak base. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Given Values
- Dissociation constant of the weak acid (Ka) = \(10^{-4}\)
- Dissociation constant of the weak base (Kb) = \(10^{-5}\)

### Step 2: Calculate pKa and pKb
- pKa is calculated using the formula:
\[ pKa = -\log(Ka) \]
Substituting the value of Ka:
\[ pKa = -\log(10^{-4}) = 4 \]

- pKb is calculated similarly:
\[ pKb = -\log(Kb) \]
Substituting the value of Kb:
\[ pKb = -\log(10^{-5}) = 5 \]

### Step 3: Calculate pKw
- The value of pKw at 25°C is a constant:
\[ pKw = 14 \]

### Step 4: Calculate pH of the Salt Solution
- For a salt formed from a weak acid and a weak base, the pH can be calculated using the formula:
\[ pH = \frac{1}{2} (pKw + pKa - pKb) \]
Substituting the values:
\[ pH = \frac{1}{2} (14 + 4 - 5) = \frac{1}{2} (13) = 6.5 \]

### Step 5: Calculate Degree of Hydrolysis (αH)
- The degree of hydrolysis can be calculated using the formula:
\[ \alpha_H = \frac{Kw}{Ka \cdot Kb} \]
Where:
- \(Kw = 10^{-14}\)
- \(Ka = 10^{-4}\)
- \(Kb = 10^{-5}\)

Substituting the values:
\[ \alpha_H = \frac{10^{-14}}{10^{-4} \cdot 10^{-5}} = \frac{10^{-14}}{10^{-9}} = 10^{-5} \]

### Step 6: Convert Degree of Hydrolysis to Percentage
- To express the degree of hydrolysis as a percentage:
\[ \alpha_H \text{ (in percentage)} = \alpha_H \times 100 = 10^{-5} \times 100 = 0.01\% \]

### Final Results
- The pH of the salt solution is **6.5**.
- The degree of hydrolysis of the salt solution is **0.01%**.

### Summary
- pH = 6.5
- Degree of Hydrolysis = 0.01%