Answer

🧪 Measurement of the pKa of Acetic Acid

Using the Half-Neutralization Method

Objective: Determine the pKa and Ka of acetic acid using titration data, and calculate the following at the half-equivalence point:

• [H₃O⁺] — Hydronium ion concentration
• [HA] — Acetic acid concentration
• [A⁻] — Acetate ion concentration

⚗️ Key Concept: Half-Equivalence Point

• At the half-equivalence point, half of the acetic acid has been neutralized.
• This means: [HA] = [A⁻]
• From the Henderson-Hasselbalch equation:
  pH = pKa + log([A−] / [HA])
  Thus, when [A⁻] = [HA], then pH = pKa.

🧮 Step-by-Step Calculations

1. Calculate pKa

Given pH values: 5.01 and 4.79

Average pKa = (5.01 + 4.79) / 2 = 4.90

2. Calculate Ka

pKa = −log(Ka) ⇒ Ka = 10−4.90 = 1.26 × 10−5

3. Calculate [H₃O⁺]

[H3O+] = 10−pH = 1.26 × 10−5 M

4. Moles of NaOH at Half-Equivalence

Average volume of NaOH: (4.25 + 4.15) / 2 = 4.20 mL = 0.00420 L

Molarity of NaOH = 0.1503 mol/L

moles = M × V = 0.1503 × 0.00420 = 0.00063 mol

5. Moles of Acetic Acid

At half-neutralization: total acid moles = 2 × 0.00063 = 0.00126 mol

6. Volume of Acetic Acid Solution

Mass = 30 g, Density = 1.05 g/mL

Volume = mass / density = 30 / 1.05 = 28.57 mL

7. Total Solution Volume

Total volume = 28.57 + 4.20 = 32.77 mL = 0.03277 L

8. Concentration of [HA] and [A⁻]

[HA] = [A−] = 0.00063 mol / 0.03277 L ≈ 0.038 M