A one litre solution contains 0.08 mole of acetic acid `(K_(a)=1.75xx10^(-5))`. To the solution, `0.02` mole of `NaOH` is added. Then the `P^(H)` of resulting solution is `[log 1.75=0.273]`

Options

A. `5.234`
B. `5.058`
C. `4.28`
D. `4.456`

Explanation

To find the pH of the solution after adding NaOH to acetic acid, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Moles**:
- We have 0.08 moles of acetic acid (CH₃COOH).
- We have 0.02 moles of sodium hydroxide (NaOH).

2. **Determine the Reaction**:
- NaOH is a strong base and will react with acetic acid (a weak acid) to form sodium acetate (CH₃COONa) and water.
- The reaction can be represented as:
\[ \text{CH}_3\text{COOH} + \text{NaOH} \rightarrow \text{CH}_3\text{COONa} + \text{H}_2\text{O} \]

3. **Calculate Moles After Reaction**:
- After the reaction, the moles of acetic acid and sodium acetate will be:
- Moles of acetic acid remaining: \(0.08 - 0.02 = 0.06\) moles
- Moles of sodium acetate formed: \(0.02\) moles

4. **Determine Concentrations**:
- Since the volume of the solution is 1 litre, the concentrations will be:
- Concentration of acetic acid: \(0.06 \, \text{M}\)
- Concentration of sodium acetate: \(0.02 \, \text{M}\)

5. **Calculate pKa**:
- The dissociation constant \(K_a\) of acetic acid is given as \(1.75 \times 10^{-5}\).
- Calculate \(pK_a\):
\[ pK_a = -\log(K_a) = -\log(1.75 \times 10^{-5}) \approx 4.75 \]

6. **Use the Henderson-Hasselbalch Equation**:
- The pH of a buffer solution can be calculated using the formula:
\[ pH = pK_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
- Substituting the values:
\[ pH = 4.75 + \log\left(\frac{0.02}{0.06}\right) \]

7. **Calculate the Logarithm**:
- Calculate the ratio:
\[ \frac{0.02}{0.06} = \frac{1}{3} \]
- Therefore,
\[ \log\left(\frac{1}{3}\right) \approx -0.477 \]

8. **Final pH Calculation**:
- Substitute back into the pH equation:
\[ pH = 4.75 - 0.477 \approx 4.273 \]
- Rounding gives us \(pH \approx 4.27\).

### Final Answer:
The pH of the resulting solution is approximately **4.27**.