`HX` is a weak acid `(K_(a) = 10^(-5))`. If forms a salt `NaX(0.1M)` on reacting with caustic soda. The degree of hydrlysis of `NaX` in % is

Options

A. 0.01
B. 0.0001
C. 0.1
D. 0.5

Explanation

To find the degree of hydrolysis of the salt `NaX` formed from the weak acid `HX` (with \( K_a = 10^{-5} \)), we can follow these steps:

### Step 1: Determine the Hydrolysis Constant \( K_h \)

For a salt formed from a weak acid and a strong base, the hydrolysis constant \( K_h \) can be calculated using the formula:

\[ K_h = \frac{K_w}{K_a} \]

Where:
- \( K_w = 10^{-14} \) (the ion product of water)
- \( K_a = 10^{-5} \) (the dissociation constant of the weak acid)

Substituting the values:

\[ K_h = \frac{10^{-14}}{10^{-5}} = 10^{-9} \]

### Step 2: Calculate the Degree of Hydrolysis \( h \)

The degree of hydrolysis \( h \) can be calculated using the formula:

\[ h = \sqrt{\frac{K_h}{C}} \]

Where:
- \( K_h = 10^{-9} \)
- \( C = 0.1 \, \text{M} \) (the concentration of the salt \( NaX \))

Substituting the values:

\[ h = \sqrt{\frac{10^{-9}}{0.1}} = \sqrt{10^{-8}} = 10^{-4} \]

### Step 3: Convert Degree of Hydrolysis to Percentage

To express \( h \) as a percentage, we multiply by 100:

\[ \text{Degree of Hydrolysis in \%} = h \times 100 = 10^{-4} \times 100 = 10^{-2} = 0.01\% \]

### Final Answer

The degree of hydrolysis of \( NaX \) in percentage is **0.01%**.

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