What will be the `pH` and `% alpha` ( degree of hydrolysis ) respectively for the salt `BA` of `0.1M` concentration ? Given `: K_(a)` for `HA=10^(-6)` and `K_(b)` for `BOH=10^(-6)`
(a)`5,1%`
(b)`7, 10%`
(c)`9, 0.01%`
(d)`7, 0.01%`

Options

A. `5,1%`
B. `7, 10%`
C. `9, 0.01%`
D. `7, 0.01%`

Answer

To solve the problem, we will calculate the pH and the degree of hydrolysis (% alpha) for the salt BA of 0.1 M concentration, given the \( K_a \) for HA and \( K_b \) for BOH.

### Step 1: Understand the Hydrolysis of the Salt
The salt BA is formed from a weak acid (HA) and a weak base (BOH). When BA is dissolved in water, it undergoes hydrolysis:
\[ BA \rightleftharpoons B^+ + A^- \]
Where \( B^+ \) is the cation from the weak base and \( A^- \) is the anion from the weak acid.

### Step 2: Calculate \( pK_a \) and \( pK_b \)
Given:
- \( K_a = 10^{-6} \)
- \( K_b = 10^{-6} \)

We can calculate \( pK_a \) and \( pK_b \):
\[ pK_a = -\log(K_a) = -\log(10^{-6}) = 6 \]
\[ pK_b = -\log(K_b) = -\log(10^{-6}) = 6 \]

### Step 3: Calculate pH using the formula
For a salt formed from a weak acid and a weak base, the pH can be calculated using the formula:
\[ pH = 7 - \frac{1}{2}(pK_a + pK_b) \]
Substituting the values:
\[ pH = 7 - \frac{1}{2}(6 + 6) = 7 - \frac{12}{2} = 7 - 6 = 1 \]
This calculation seems incorrect, as it should yield a neutral pH. Let's correct it:
\[ pH = 7 - \frac{1}{2}(6 + 6) = 7 - 6 = 1 \]
This indicates a mistake in interpreting the formula. The correct interpretation should yield:
\[ pH = 7 + 0 = 7 \]

### Step 4: Calculate the Degree of Hydrolysis (% alpha)
The degree of hydrolysis (alpha) can be calculated using the formula:
\[ \alpha = \sqrt{\frac{K_w}{K_a \cdot K_b}} \times 100 \]
Where:
- \( K_w = 10^{-14} \)

Substituting the values:
\[ \alpha = \sqrt{\frac{10^{-14}}{10^{-6} \cdot 10^{-6}}} \times 100 = \sqrt{\frac{10^{-14}}{10^{-12}}} \times 100 = \sqrt{10^{-2}} \times 100 = 0.1 \times 100 = 10\% \]

### Final Answers
- The pH of the solution is **7**.
- The degree of hydrolysis (% alpha) is **10%**.

### Conclusion
Thus, the correct answer is **(b) 7, 10%**.