What assumption is made when calculating the pH of a weak acid?

When calculating the pH of a weak acid, the assumption that the concentration of hydronium ions ([H₃O^+]) is equal to the concentration of the conjugate base ([A^-]) is based on the dissociation equilibrium of the weak acid in water. A weak acid partially ionizes in solution, meaning that not all of the acid molecules dissociate. At equilibrium, the concentration of hydronium ions produced from the dissociation of the weak acid (represented as ([H₃O^+])) will indeed be equal to the concentration of the conjugate base formed (([A^-])). This relationship is a result of the equilibrium expression derived from the dissociation constant (K_a) for the weak acid:

[ K_a = \frac{[H₃O^+][A^-]}{[HA]} ]

Here, since the dissociation is limited, the concentration of the undissociated acid ([HA]) will not change significantly compared to its initial concentration. Hence, it is common to simplify the calculations by making the assumption that ([H₃O^+] = [A^-]) at equilibrium.

This simplification allows for easier calculations