For a salt of weak acid and weak base `[pK_a- pK_b]` would be equal to –

Options

A. `2 pH + pK_(W)`
B. `2 pH - log 10^(-14)`
C. `2 pH + pK_(W)`
D. None of these

Answer

To solve the question regarding the value of \( pK_a - pK_b \) for a salt of a weak acid and a weak base, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components**:
- We have a salt formed from a weak acid and a weak base. For example, let's consider acetic acid (weak acid) and ammonium hydroxide (weak base).
- The salt formed from these two is ammonium acetate \((CH_3COONH_4)\).

2. **Understand Hydrolysis**:
- When this salt is dissolved in water, it undergoes hydrolysis. The ammonium ion \((NH_4^+)\) can donate a proton to water, forming \(H_3O^+\) and acetate ion \((CH_3COO^-)\) can accept a proton.

3. **Use the Henderson Equation**:
- The pH of the solution can be calculated using the Henderson-Hasselbalch equation:
\[ pH = \frac{1}{2}pK_w + \frac{1}{2}(pK_a - pK_b) \]
where \(pK_w\) is the ionization constant of water.

4. **Rearranging the Equation**:
- From the equation, we can rearrange it to isolate \(pK_a - pK_b\):
\[ pK_a - pK_b = 2pH - pK_w \]

5. **Understanding \(pK_w\)**:
- The value of \(pK_w\) at 25°C is 14. Therefore, we can substitute this value into our equation:
\[ pK_a - pK_b = 2pH - 14 \]

6. **Conclusion**:
- The expression \(pK_a - pK_b\) can be determined from the pH of the solution. However, the exact numerical value will depend on the pH of the solution formed by the salt of the weak acid and weak base.

### Final Answer:
Thus, for a salt of a weak acid and a weak base, \(pK_a - pK_b\) is equal to \(2pH - 14\).