What is Henderson-Hasselbach equation?

The Henderson-Hasselbach equation is the relation of the pH of an aqueous solution of an acid to the acid dissociation constant of that acid. Its equation is the following:

pH=pKa+log([A−]/[HA]) 

It is derived from the definition of the acid dissociation constant, and for instance, one can use the compound HA in water.

HA+H2O⇌A−+H3O+

The acid dissociation constant of HA

Ka=[A−][H3O+]/[HA]

Ka[HA]/[A−]=[H3O+]

Flipping the equation around

[H3O+]=Ka[HA][A−]

log10[H3O+]=log10Ka+log10[HA]/[A−]

Multiplying both sides by -1

−log10[H3O+]=−log10Ka−log10[HA]/[A−]

pH=pKa−log10[HA]/[A−]

pH=pKa+log10[A−]/[HA]

This equation is particularly useful for estimating the pH of a buffer solution and determining the equilibrium pH in an acid-base reaction. It can also be used for determining the amount of acid and conjugate base needed to make a buffer solution of a certain pH. It is important to note that this equation is an approximation and does not account for the self-dissociation of water, which is important in dilute solutions.