## Calculating the pH of a buffer solutionEdit

### DerivationEdit

For any equilibrium

the equilibrium constant, *K*, is defined as

Therefore, for the dissociation equilibrium of any acid

the acid dissociation constant, *K*_{a}, is defined as

This equation can be rearranged to make [H^{+}(aq)] the subject:

Two assumptions are required:

**1** Every A^{−} ion comes from the salt

- Although this is not quite true, it is a close enough that the pH value we get from the final equation is very close to that found experimentally. It allows us to assume that

**2** Every HA molecule remains undissociated

- Again, despite being slightly inaccurate, this assumption creates the following useful equation

The equations in assumptions **1** and **2** allow us to replace [A^{−}(aq)] with [salt] and [HA(aq)] with [acid] as follows.

The effect of assumption **1** is that

becomes

The effect of assumption **2** is that

becomes

By definition,

so