Henderson–Hasselbalch equation

What is this for?

The Henderson–Hasselbalch equation is the working tool of buffer formulation. It states that the pH of a buffer sits at its pKa when the two conjugate species are present in equal amounts, and shifts one pH unit for every ten-fold change in their ratio.

How to use it

1. Select whether the system is a weak acid or a weak base — this determines which species goes in the numerator.
2. Choose whether you are solving for the pH from known concentrations, or for the ratio required to reach a target pH.
3. Enter the pKa and the relevant concentrations. Any consistent concentration unit works, since only the ratio matters.

Worked example

An acetate buffer contains 0.1 M sodium acetate and 0.05 M acetic acid. Acetic acid has a pKa of 4.76. What is the pH?

Answer: pH = 4.76 + log(0.1 ÷ 0.05) = 4.76 + log(2) = 4.76 + 0.30 = 5.06.

Clinical pearls & pitfalls

• When the two species are equal, the log term is zero and the pH equals the pKa exactly. This is both the point of maximum buffer capacity and a useful arithmetic check.
• A buffer works effectively only within about one pH unit either side of its pKa. Outside that window, small acid or base additions swing the pH substantially.
• Only the ratio matters for pH; the absolute concentrations determine capacity. A 0.001 M buffer and a 0.1 M buffer at the same ratio have the same pH but wildly different resistance to change.
• Buffer choice in formulation is driven by pKa proximity to the target pH, but also by compatibility, toxicity by route, and effect on drug stability — the equation alone does not select the buffer.

Assumptions & limitations

• Uses concentrations rather than activities, so it becomes inaccurate at high ionic strength.
• Assumes the system is a simple monoprotic conjugate pair. Polyprotic acids such as phosphate have multiple pKa values and require the relevant one for the pH region of interest.
• Does not account for temperature, which shifts pKa values, or for the effect of the drug itself on the buffer.
• Predicts equilibrium pH only — it says nothing about buffer capacity, which depends on absolute concentration.

References

• Po HN, Senozan NM. The Henderson–Hasselbalch equation: its history and limitations. J Chem Educ. 2001;78(11):1499-1503.
• Sinko PJ. Martin's Physical Pharmacy and Pharmaceutical Sciences. 7th ed. Wolters Kluwer.
• United States Pharmacopeia. General Chapter <1225> Validation of Compendial Procedures (buffer preparation guidance).

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