Henderson Hasselbalch and how buffers hold pH steady
Where the buffer equation comes from, how to design a buffer at a target pH, and the assumptions that limit it.
Where the equation comes from
A weak acid HA sits in equilibrium with its conjugate base A- and a proton, governed by the dissociation constant Ka. Taking the negative base-10 logarithm of the Ka expression and rearranging turns it into pH = pKa + log10([A-] / [HA]). That single step is the whole trick: it swaps a hard equilibrium in hydrogen ion concentration for an easy sum built from a constant and a ratio. The log term is what lets a buffer glide smoothly in pH as its two forms shift.
Designing a buffer at a target pH
To build a buffer at a chosen pH, first pick an acid whose pKa is close to that pH, ideally within one unit. Then set the base to acid ratio from 10^(pH - pKa). For a blood-like pH of 7.4 using the carbonic acid system with a pKa of 6.1, the ratio works out to about 20 to 1 bicarbonate over carbonic acid, which is exactly what the body maintains. Choosing an acid with a nearby pKa keeps that ratio moderate, so neither component runs vanishingly small.
Buffer capacity and why pKa matters
A buffer resists pH change best when its two forms are present in comparable amounts, which happens at pH equal to pKa where the ratio is 1. Move more than about one pH unit away and one form dominates, so the buffer has little of the other left to neutralise an incoming acid or base, and capacity falls off. That is why lab recipes pair a target pH with an acid of matching pKa rather than stretching a convenient acid far from its sweet spot.
Assumptions and limits
The equation is an approximation built on a few simplifications. It uses formal, as-mixed concentrations rather than thermodynamic activities, so it grows less accurate in concentrated or high ionic strength solutions. It also assumes the added acid and base fully form the buffer pair and that water's self-ionisation is negligible, which breaks down in very dilute buffers or at extreme pH. For most bench work near the pKa it is accurate to a few hundredths of a pH unit, which is why it remains the everyday tool of choice.