`pK_(a)` value for acetic acid at an experimental temperature is 5. The percentage hydrolysis of `0.1` M sodium acetate solution will be

Options

A. `1.0 xx 10^(-4)`
B. `1.0 xx 10^(-2)`
C. `1.0xx 10^(-3)`
D. `1.0 xx 10^(-5)`

Answer

To solve the problem of finding the percentage hydrolysis of a 0.1 M sodium acetate solution given that the pK_a value for acetic acid is 5, we will follow these steps:

### Step 1: Understand the nature of sodium acetate
Sodium acetate (CH₃COONa) is a salt derived from a weak acid (acetic acid) and a strong base (sodium hydroxide). When dissolved in water, it hydrolyzes to produce acetate ions (CH₃COO⁻) and sodium ions (Na⁺). The hydrolysis of the acetate ion can be represented as follows:

\[ \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^- \]

### Step 2: Calculate the ionization constant (K_a) of acetic acid
Given that the pK_a of acetic acid is 5, we can calculate the K_a using the formula:

\[ K_a = 10^{-pK_a} \]

Substituting the given value:

\[ K_a = 10^{-5} \]

### Step 3: Calculate the hydrolysis constant (K_h)
The hydrolysis constant (K_h) for a salt derived from a weak acid and a strong base can be calculated using the relation:

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

Where \( K_w \) is the ionization constant of water, which is \( 1 \times 10^{-14} \) at 25°C. Thus:

\[ K_h = \frac{1 \times 10^{-14}}{10^{-5}} = 1 \times 10^{-9} \]

### Step 4: Calculate the degree of hydrolysis (H)
The degree of hydrolysis (H) can be calculated using the formula:

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

Where \( C \) is the concentration of the sodium acetate solution, which is 0.1 M. Substituting the values:

\[ H = \sqrt{\frac{1 \times 10^{-9}}{0.1}} = \sqrt{1 \times 10^{-8}} = 1 \times 10^{-4} \]

### Step 5: Calculate the percentage hydrolysis
To find the percentage hydrolysis, we multiply the degree of hydrolysis by 100:

\[ \text{Percentage Hydrolysis} = H \times 100 = 1 \times 10^{-4} \times 100 = 1 \times 10^{-2} \% = 0.01 \% \]

### Final Answer
The percentage hydrolysis of the 0.1 M sodium acetate solution is **0.01%**.

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