Proton balance equation for weak monoprotic acids.

Every proton donated by an acting acid has to be accepted by an acting base in solution. Therefore,  a proton balance equation accounts for a balance (equality) between sum of concentrations of compounds produced after donating protons and sum of concentrations of compounds produced after accepting the protons in solution. For example, if acetic acid (HA) is added to water (H₂O) then it partially ionizes according to the following formula:

HA + H₂O ↔ A^- + H₃O⁺

Ka = [A^-][H₃O⁺]/ [HA]             equation (1)

Accordingly, compounds (species) added to solution that donate protons are HA, and H₂O to produce A^- and OH^-. On the other hand, H₂O can accept protons to produce H₃O⁺. Therefore, the proton balance equation for a monoprotice weak acid (e.g. acetic acid) is written as the following:

[H₃O⁺] = [A^-] + [OH^-]              equation (2)

The following diagram further explains how the proton balance equation can be written:

The mass balance equation for a weak monoprotic acid in solution is written as the following:

c = [HA] + [A^-]               equation (3)

Where c is the molar concentration of the added acid. 

Equations 1-3 can be used to derive a general equation for calculation of [H₃O⁺] after addition of a certain concentration of the acid to solution. 

Note: Assumptions can be made to simplify the derivation.

Related posts:

What is pH ?

Ionization constants for weak acids (acid dissociation constant), Ka.

Relations between pH, pOH, pKa, pKb, and pKw.