The dissociation constant of acetic acid is `x ×10^(–5)`. When 25 mL of `0.2 M CH_3COONa` solution is mixed with 25 mL of 0.02 M `CH_3COOH` solution, the pH of the resultant solution is found to be equal to 5. The value of x is

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the components of the solution
We have a mixture of acetic acid (CH₃COOH) and sodium acetate (CH₃COONa). This combination forms a buffer solution, which is a mixture of a weak acid and its conjugate base.

### Step 2: Use the Henderson-Hasselbalch equation
The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \]
where:
- \([\text{A}^-]\) is the concentration of the conjugate base (sodium acetate),
- \([\text{HA}]\) is the concentration of the weak acid (acetic acid).

### Step 3: Calculate the concentrations of the components
1. **Volume of each solution**: 25 mL of CH₃COONa and 25 mL of CH₃COOH gives a total volume of 50 mL.
2. **Concentration of sodium acetate**:
- Initial concentration = 0.2 M
- After mixing:
\[ [\text{CH}_3\text{COO}^-] = \frac{0.2 \, \text{mol/L} \times 0.025 \, \text{L}}{0.050 \, \text{L}} = 0.1 \, \text{M} \]
3. **Concentration of acetic acid**:
- Initial concentration = 0.02 M
- After mixing:
\[ [\text{CH}_3\text{COOH}] = \frac{0.02 \, \text{mol/L} \times 0.025 \, \text{L}}{0.050 \, \text{L}} = 0.01 \, \text{M} \]

### Step 4: Substitute values into the Henderson-Hasselbalch equation
Given that the pH of the resultant solution is 5:
\[ 5 = \text{pK}_a + \log \left( \frac{0.1}{0.01} \right) \]
\[ 5 = \text{pK}_a + \log(10) \]
\[ 5 = \text{pK}_a + 1 \]
\[ \text{pK}_a = 5 - 1 = 4 \]

### Step 5: Calculate the dissociation constant \(K_a\)
The relationship between \(K_a\) and \(\text{pK}_a\) is given by:
\[ \text{pK}_a = -\log(K_a) \]
Thus,
\[ K_a = 10^{-\text{pK}_a} = 10^{-4} \]

### Step 6: Express \(K_a\) in terms of \(x\)
Given that \(K_a = x \times 10^{-5}\), we can set up the equation:
\[ 10^{-4} = x \times 10^{-5} \]
Dividing both sides by \(10^{-5}\):
\[ x = 10 \]

### Final Answer
The value of \(x\) is **10**.

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