A buffer solution is prepared by mixing 20 ml of 0.1 M `CH_3COOH` and 40 ml of 0.5 M `CH_3COONa` and then diluted by adding 100 ml of distilled water . The pH of resulting buffer solution is (Given `pK_a CH_3COOH=4.76`)

Options

A. 5.76
B. 4.67
C. 3.48
D. 5.9

Answer

To solve the problem, we need to find the pH of the buffer solution prepared by mixing acetic acid (CH₃COOH) and sodium acetate (CH₃COONa) and then diluting it with distilled water. We will use the Henderson-Hasselbalch equation to find the pH.

### Step-by-Step Solution:

1. **Calculate the moles of CH₃COOH and CH₃COONa before dilution:**
- Moles of CH₃COOH = Volume (L) × Concentration (M)
\[ \text{Moles of CH₃COOH} = 0.020 \, \text{L} \times 0.1 \, \text{M} = 0.002 \, \text{mol} \, (2 \, \text{mmol}) \]
- Moles of CH₃COONa = Volume (L) × Concentration (M)
\[ \text{Moles of CH₃COONa} = 0.040 \, \text{L} \times 0.5 \, \text{M} = 0.020 \, \text{mol} \, (20 \, \text{mmol}) \]

2. **Total volume after dilution:**
- Total volume = Volume of CH₃COOH + Volume of CH₃COONa + Volume of water
\[ \text{Total Volume} = 20 \, \text{ml} + 40 \, \text{ml} + 100 \, \text{ml} = 160 \, \text{ml} = 0.160 \, \text{L} \]

3. **Calculate the concentrations after dilution:**
- Concentration of CH₃COOH after dilution:
\[ [\text{CH₃COOH}] = \frac{0.002 \, \text{mol}}{0.160 \, \text{L}} = 0.0125 \, \text{M} \]
- Concentration of CH₃COONa after dilution:
\[ [\text{CH₃COONa}] = \frac{0.020 \, \text{mol}}{0.160 \, \text{L}} = 0.125 \, \text{M} \]

4. **Use the Henderson-Hasselbalch equation to find the pH:**
- The Henderson-Hasselbalch equation is:
\[ \text{pH} = pK_a + \log\left(\frac{[\text{Base}]}{[\text{Acid}]}\right) \]
- Here, \( pK_a = 4.76 \), \( [\text{Base}] = [\text{CH₃COONa}] = 0.125 \, \text{M} \), and \( [\text{Acid}] = [\text{CH₃COOH}] = 0.0125 \, \text{M} \).
- Substitute the values:
\[ \text{pH} = 4.76 + \log\left(\frac{0.125}{0.0125}\right) \]
- Calculate the ratio:
\[ \frac{0.125}{0.0125} = 10 \]
- Now, take the logarithm:
\[ \log(10) = 1 \]
- Finally, calculate the pH:
\[ \text{pH} = 4.76 + 1 = 5.76 \]

### Final Answer:
The pH of the resulting buffer solution is **5.76**.