Q.34 In a lactic acid solution at pH 4.8, the concentrations of lactic acid and lactate are
0.01 M and 0.087 M, respectively. The calculated pKa of lactic acid is ________.
(Round off to one decimal place)
🎯 Final Answer
The pKa of lactic acid in this solution is calculated using the Henderson-Hasselbalch equation, yielding 3.9 when rounded to one decimal place.
🔬 Problem Solution
Lactic acid (HA) dissociates as HA ⇌ H⁺ + A⁻ (lactate), where [HA] = 0.01 M and [A⁻] = 0.087 M at pH 4.8.
The Henderson-Hasselbalch equation states: pH = pKa + log([A⁻]/[HA]).
Rearranging gives pKa = pH - log([A⁻]/[HA]) = 4.8 - log(0.087/0.01) = 4.8 - log(8.7) = 4.8 - 0.940 = 3.86, which rounds to 3.9.
📊 Step-by-Step Calculation
- Calculate the ratio
[A⁻]/[HA] = 0.087 / 0.01 = 8.7 - Then
log₁₀(8.7) ≈ 0.940(sincelog₁₀(10) = 1andlog₁₀(8) ≈ 0.903) - Subtract:
4.8 - 0.940 = 3.86, rounded to 3.9 as specified
This matches experimental pKa values near 3.86 for lactic acid.
📚 Article Content
Lactic acid pKa calculation at pH 4.8 with 0.01 M lactic acid and 0.087 M lactate is a key concept for CSIR NET Life Sciences and biochemistry exams. This Henderson-Hasselbalch equation application determines the acid dissociation constant for weak acids like lactic acid (CH₃CH(OH)COOH).
Henderson-Hasselbalch Fundamentals
- The equation
pH = pKa + log([lactate]/[lactic acid])relates pH to the ratio of conjugate base (lactate, A⁻) and acid (HA) - For buffers, when
[A⁻] > [HA],pH > pKa, as seen here where the ratio exceeds 1 - Lactic acid’s standard pKa ≈ 3.86 aligns with biological systems like muscle metabolism
Detailed Calculation Walkthrough
Given: pH = 4.8, [HA] = 0.01 M, [A⁻] = 0.087 M.
- Ratio = 0.087/0.01 = 8.7
- log(8.7) = 0.94
- pKa = 4.8 – 0.94 = 3.86 ≈ 3.9
No options provided; direct computation confirms 3.9 (rounding 3.86 per instruction).
🎓 CSIR NET Exam Relevance
This problem tests buffer equilibrium mastery, vital for enzyme kinetics and pH regulation topics. Similar GATE XL questions verify pKa via concentrations, emphasizing log calculations. Practice verifies lactic acid behaves as a weak acid (pKa 3.8-3.9) in fermentation and glycolysis contexts.
