ionic equilibrium 2

Calculation of pH
Proton Balance Equations
According to the Br?nsted–Lowry theory, every proton donated by an acid must be accepted by a base. Thus, an equation accounting for the total proton transfers occurring in a system is of fundamental importance in describing any acid–base equilibria in that system. This can be accomplished by establishing a proton balance equation (PBE) for each system. In the PBE, the sum of the concentration terms for species that form by proton consumption is equated to the sum of the concentration terms for species that are formed by the release of a proton.
For example, when HCl is added to water, it dissociates completely into H3O+ and Cl- ions. The H3O+ is a species that is formed by the consumption of a proton (by water acting as a base), and the Cl- is formed by the release of a proton from HCl. In all aqueous solutions, H3O+ and OH- result from the dissociation of two water molecules according to equation (7-28). Thus, OH- is a species formed from the release of a proton. The PBE for the system of HCl in water is



Although H3O+ is formed from two reactions, it is included only once in the PBE. The same would be true for OH- if it came from more than one source.
The general method for obtaining the PBE is as follows:
a. Always start with the species added to water.
b. On the left side of the equation, place all species that can form when protons are consumed by the starting species.
c. On the right side of the equation, place all species that can form when protons are released from the starting species.
d. Each species in the PBE should be multiplied by the number of protons lost or gained when it is formed from the starting species.
e. Add [H3O+] to the left side of the equation and [OH-] to the right side of the equation. These result from the interaction of two molecules of water, as shown previously.