Calculate the pH value for a buffer solution prepared by adding 1.0 mL of a 0.10M acetic acid solution to 20 mL of a 0.10M sodium acetate solution. (Ka = 1.7 × 10⁻⁵)

• A. 4.74
• B. 3.74
• C. 5.74
• D. 6.74

Answer: (A)

Verified step by step guidance

1. First, understand that a buffer solution consists of a weak acid and its conjugate base. In this case, acetic acid (CH₃COOH) is the weak acid, and sodium acetate (CH₃COONa) provides the conjugate base, acetate ion (CH₃COO⁻).
2. Use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \). Here, \( \text{pK}_a \) is the negative logarithm of the acid dissociation constant \( K_a \).
3. Calculate \( \text{pK}_a \) using the given \( K_a \) value: \( \text{pK}_a = -\log(1.7 \times 10^{-5}) \).
4. Determine the concentrations of acetic acid \([\text{HA}]\) and acetate ion \([\text{A}^-]\) in the buffer solution. Since the volumes are additive, calculate the final concentrations after mixing: \([\text{HA}] = \frac{0.10 \text{ M} \times 1.0 \text{ mL}}{21.0 \text{ mL}}\) and \([\text{A}^-] = \frac{0.10 \text{ M} \times 20.0 \text{ mL}}{21.0 \text{ mL}}\).
5. Substitute the values of \( \text{pK}_a \), \([\text{A}^-]\), and \([\text{HA}]\) into the Henderson-Hasselbalch equation to find the pH: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \).