0.1 M solution of a salt of a weak acid a strong base hydrolysis. If `K_(a)` of the weak acid is `1 xx 10^(-5)`, the percent hydrolysis of the salt is

Options

A. 0.01
B. 0.0001
C. 0.001
D. 0.1

Answer

To find the percent hydrolysis of a salt formed from a weak acid and a strong base, we can use the following steps:

### Step 1: Identify the given values
- Concentration of the salt solution (C) = 0.1 M
- \( K_a \) of the weak acid = \( 1 \times 10^{-5} \)
- \( K_w \) (the ion product of water) = \( 1 \times 10^{-14} \)

### Step 2: Use the hydrolysis formula
The formula for hydrolysis (H) of the salt is given by:
\[ H = \sqrt{\frac{K_w}{K_a \cdot C}} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the hydrolysis formula:
\[ H = \sqrt{\frac{1 \times 10^{-14}}{(1 \times 10^{-5}) \cdot (0.1)}} \]

### Step 4: Calculate the denominator
Calculate \( K_a \cdot C \):
\[ K_a \cdot C = (1 \times 10^{-5}) \cdot (0.1) = 1 \times 10^{-6} \]

### Step 5: Substitute back into the hydrolysis formula
Now substitute this value back into the hydrolysis formula:
\[ H = \sqrt{\frac{1 \times 10^{-14}}{1 \times 10^{-6}}} \]

### Step 6: Simplify the fraction
\[ H = \sqrt{1 \times 10^{-8}} = 1 \times 10^{-4} \]

### Step 7: Calculate percent hydrolysis
To find the percent hydrolysis, we multiply by 100:
\[ \text{Percent Hydrolysis} = H \times 100 = (1 \times 10^{-4}) \times 100 = 1 \times 10^{-2} = 0.01\% \]

### Final Answer
The percent hydrolysis of the salt is **0.01%**.

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