The buffer equations

Henderson-Hasselbalchbuffer pHpKabuffer calculationhow to make a buffer

Henderson–Hasselbalch in both its acid and base forms, plus the pKa and pKb conversions that feed them — buffer pH from a ratio.

Henderson–Hasselbalch Equation (Weak Acid Buffer)

\mathrm{pH} = \mathrm{p}K_a + \log_{10}\!\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}

Gives the pH of a buffer from the acid's pKa and the ratio of conjugate base to undissociated acid, the master equation of buffer preparation.

Henderson–Hasselbalch Equation (Weak Base Buffer)

\mathrm{pOH} = \mathrm{p}K_b + \log_{10}\!\frac{[\mathrm{BH^+}]}{[\mathrm{B}]}

Gives the pOH of a weak base buffer from the base's pKb and the ratio of conjugate acid to free base, the mirror image of the acid form.

pKa from Acid Dissociation Constant

\mathrm{p}K_a = -\log_{10} K_a

Converts an acid dissociation constant into its logarithmic pKa form and back, compressing a huge range of acid strengths onto one readable scale.

pKb from Base Dissociation Constant

\mathrm{p}K_b = -\log_{10} K_b

Converts a base dissociation constant into its logarithmic pKb form and back, the basic-side counterpart of the pKa scale.

How they fit together

Henderson–Hasselbalch is nothing more than the Ka expression with a logarithm taken of both sides, but rearranging it that way exposes the useful truth: a buffer's pH depends on the ratio of conjugate base to acid, not on their absolute amounts. Dilute a buffer tenfold and the ratio is unchanged, so the pH barely moves — which is precisely the behaviour you bought it for. When the ratio is 1:1 the log term vanishes and pH = pKa exactly.

Pick the acid form when you know Ka or pKa for the acidic member of the pair, and the base form when your tables give Kb — or convert with Ka·Kb = Kw and use the acid form throughout, which is what most people do. Choose the buffer whose pKa sits within about one unit of your target pH; outside that window the ratio has to run past 10:1 and capacity collapses on one side. The classic error is treating the equation as valid everywhere: it assumes both species are present in comparable, non-trivial amounts, so it says nothing sensible about a solution of the acid alone, and it breaks down once added strong acid or base has consumed one member of the pair entirely.