# A-level Chemistry/OCR (Salters)/Weak acids

## Calculating the pH of a weak acid solution

editThe pH of a weak acid solution can be calculated approximately using the following formula:

### Derivation

editFor 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

Two assumptions are required:

**1** The concentrations of H^{+}(aq) and A^{−}(aq) are equal, or in symbols:

- The reason this is an approximation is that a very slightly higher concentration of H
^{+}(aq) exists in reality, due to the autodissociation of water, H_{2}O(l) ⇌ H^{+}(aq) + A^{−}(aq). We neglect this effect since water produces a far lower concentration of H^{+}(aq) than most weak acids. If you were studying an exceptionally weak acid (you won't at A-level), this assumption might begin to cause big problems.

**2** The amount of HA at equilibrium is the same as the amount originally added to the solution.

- This cannot be quite true, otherwise HA wouldn't be an
*acid*. It is, however, a close numerical approximation to experimental observations of the concentration of HA in most cases.

The effect of assumption **1** is that

becomes

The effect of assumption **2** is that

becomes

which can be rearranged to give

and therefore

By definition,

so