Biochemistry of buffers — Which equation shows that pKa equals pH when the molar concentrations of a weak acid and its conjugate base are equal?

Introduction / Context:
Buffer chemistry underpins pH control in biology, fermentation, and analytical work. A cornerstone relationship is the Henderson–Hasselbalch equation, which connects pH, pKa, and the ratio of conjugate base to acid. It explains practical rules of thumb used in preparing effective buffers.

Given Data / Assumptions:

• The acid is weak and in equilibrium with its conjugate base.
• We are comparing equations/laws from biochemistry and genetics.
• We seek the one that directly links pH and pKa.

Concept / Approach:
The Henderson–Hasselbalch equation: pH = pKa + log10([A−]/[HA]). When [A−] = [HA], the log term becomes log10(1) = 0, so pH = pKa. This relationship guides buffer selection: buffers work best within about pKa ± 1 pH unit because the ratio of base to acid remains near unity with good capacity.

Step-by-Step Solution:

Verification / Alternative check:
Experimental titration curves show midpoint (half-neutralization) at pH ≈ pKa, confirming the equation.

Why Other Options Are Wrong:

• Michaelis–Menten: relates enzyme rate to substrate concentration (not pH buffering).
• Haldane’s equation: enzyme kinetics/thermodynamics relationships.
• Hardy–Weinberg: population genetics equilibrium, unrelated to acid–base.

Common Pitfalls:
Using Henderson–Hasselbalch beyond its valid assumptions (dilute solutions, weak acids, activity approximations).

Final Answer:
Henderson–Hasselbalch equation