`pK_(a)` of a weak acid `(HA)` and `pB_(b)` of a weak base `(BOH)` are 3.2 and 3.4 respectively. The `pH` of their salt (AB) solution is

Options

A. (a) 7.1
B. (b) 6.9
C. (c) 3.4
D. (d) 6.5

Answer

To find the pH of the salt solution formed from a weak acid (HA) and a weak base (BOH), we can use the following steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- \( pK_a \) of the weak acid (HA) = 3.2
- \( pK_b \) of the weak base (BOH) = 3.4

2. **Use the Relationship for pK_w**:
- The relationship between \( pK_a \), \( pK_b \), and \( pK_w \) is given by:
\[ pK_w = pK_a + pK_b \]
- At 25°C, \( pK_w \) is typically 14.

3. **Calculate pK_w**:
- Using the values of \( pK_a \) and \( pK_b \):
\[ pK_w = 3.2 + 3.4 = 6.6 \]
- However, we know \( pK_w \) is actually 14, so we will use this value in our calculations.

4. **Calculate pH of the Salt Solution**:
- The formula for calculating the pH of a salt solution formed from a weak acid and a weak base is:
\[ pH = \frac{1}{2} \left( pK_a + pK_w - pK_b \right) \]
- Substitute the known values into the formula:
\[ pH = \frac{1}{2} \left( 3.2 + 14 - 3.4 \right) \]

5. **Perform the Calculation**:
- Simplifying inside the parentheses:
\[ pH = \frac{1}{2} \left( 3.2 + 14 - 3.4 \right) = \frac{1}{2} \left( 13.8 \right) \]
- Now divide by 2:
\[ pH = 6.9 \]

6. **Conclusion**:
- The pH of the salt solution (AB) is **6.9**.