Calculate the pH of a buffer solution that is 0.04 M `CH_3COONa` and 0.08 M `CH_3COOH` at `25^@C`. `pK_a` =4.74

Explanation

To calculate the pH of the buffer solution containing 0.04 M `CH₃COONa` (sodium acetate) and 0.08 M `CH₃COOH` (acetic acid) at 25°C, we can use the Henderson-Hasselbalch equation:

### Step-by-Step Solution:

1. **Identify the components of the buffer solution:**
- The weak acid is acetic acid (`CH₃COOH`).
- The conjugate base is sodium acetate (`CH₃COONa`).

2. **Write down the Henderson-Hasselbalch equation:**
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{Base}]}{[\text{Acid}]}\right) \]

3. **Substitute the values into the equation:**
- Given:
- \(\text{pK}_a = 4.74\)
- \([\text{Base}] = 0.04 \, \text{M}\) (sodium acetate)
- \([\text{Acid}] = 0.08 \, \text{M}\) (acetic acid)
\[ \text{pH} = 4.74 + \log\left(\frac{0.04}{0.08}\right) \]

4. **Calculate the ratio of the concentrations:**
\[ \frac{0.04}{0.08} = 0.5 \]

5. **Calculate the logarithm:**
\[ \log(0.5) \approx -0.3010 \]

6. **Substitute the logarithm back into the equation:**
\[ \text{pH} = 4.74 + (-0.3010) \]

7. **Perform the final calculation:**
\[ \text{pH} = 4.74 - 0.3010 = 4.439 \]

### Final Answer:
The pH of the buffer solution is approximately **4.44**.