A 1.0 L buffer solution contains 0.100 mol HC2H3O2 and 0.100 mol NaC2H3O2. The value of Ka for HC2H3O2 is 1.8 × 10⁻⁵. Calculate the pH of the solution upon the addition of 0.015 mol of NaOH to the original buffer.

• A. 5.00
• B. 4.74
• C. 4.59
• D. 4.89

Answer: (D)

Verified step by step guidance

1. Identify the components of the buffer solution: acetic acid (HC2H3O2) and its conjugate base, sodium acetate (NaC2H3O2). The buffer solution initially contains 0.100 mol of each component in 1.0 L of solution.
2. Understand that the addition of NaOH will react with the acetic acid (HC2H3O2) in the buffer. The reaction is: \( \text{HC}_2\text{H}_3\text{O}_2 + \text{OH}^- \rightarrow \text{C}_2\text{H}_3\text{O}_2^- + \text{H}_2\text{O} \). This will decrease the amount of acetic acid and increase the amount of acetate ion.
3. Calculate the change in moles of acetic acid and acetate ion due to the addition of NaOH. Since 0.015 mol of NaOH is added, it will react with 0.015 mol of HC2H3O2, reducing its concentration to 0.085 mol and increasing the concentration of NaC2H3O2 to 0.115 mol.
4. 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, \( \text{pK}_a = -\log(1.8 \times 10^{-5}) \), \([\text{A}^-] = 0.115 \text{ mol/L}\), and \([\text{HA}] = 0.085 \text{ mol/L}\).
5. Substitute the values into the Henderson-Hasselbalch equation to find the pH: \( \text{pH} = \text{pK}_a + \log \left( \frac{0.115}{0.085} \right) \). Calculate \( \text{pK}_a \) and the logarithmic term to determine the pH.