When a salt of a weak acid and a weak base is dissolved in water at `25^@C,` the pH of the resulting solution will always

Options

A. be 7
B. be greater than 7
C. be less than 7
D. depend upon `K_a and K_b` values

Answer

To solve the question regarding the pH of a solution when a salt of a weak acid and a weak base is dissolved in water, we can follow these steps:

### Step 1: Understand the Components
When a salt formed from a weak acid (HA) and a weak base (B) is dissolved in water, it undergoes hydrolysis. This means that the salt will dissociate into its ions, which can react with water.

**Hint:** Identify the weak acid and weak base involved in the salt formation.

### Step 2: Hydrolysis Reaction
The hydrolysis of the salt can be represented as:
- The cation from the weak base (B⁺) can react with water to form the weak base (B) and H⁺ ions.
- The anion from the weak acid (A⁻) can react with water to form the weak acid (HA) and OH⁻ ions.

**Hint:** Write down the hydrolysis reactions for both the cation and anion.

### Step 3: Determine the pH Formula
The pH of the solution can be calculated using the formula:
\[ \text{pH} = 7 + \frac{1}{2}(\text{p}K_a - \text{p}K_b) \]
Where:
- \(K_a\) is the acid dissociation constant of the weak acid.
- \(K_b\) is the base dissociation constant of the weak base.

**Hint:** Remember that \(pK = -\log K\) and understand how to convert between \(K\) and \(pK\).

### Step 4: Analyze the pH Value
The resulting pH will depend on the difference between \(pK_a\) and \(pK_b\):
- If \(pK_a > pK_b\), then the pH will be greater than 7 (the solution is basic).
- If \(pK_a < pK_b\), then the pH will be less than 7 (the solution is acidic).
- If \(pK_a = pK_b\), then the pH will be equal to 7 (the solution is neutral).

**Hint:** Compare the values of \(pK_a\) and \(pK_b\) to determine the nature of the solution.

### Step 5: Conclusion
Thus, the pH of the resulting solution when a salt of a weak acid and a weak base is dissolved in water will depend on the values of \(K_a\) and \(K_b\) of the respective weak acid and weak base.

**Final Answer:** The pH of the resulting solution will depend on \(K_a\) and \(K_b\).