Weak acid/base systems exist within broader systems, usually aqueous phase. Sometimes the weak acid/base pair dominates the system and controls the pH of that solution. Other times, there are other constituents or characteristics of the system that control the pH to a certain condition. In the latter, we can use the Henderson-Hasselbach equation, or just the Ka equation, to determine the partitioning between the weak acid and weak base pair(s).
In the former case, we may not know the pH of the solution or the partitioning of the acid/base forms. In those cases, we can use equilibrium chemistry to predict or model what the expected pH and partitioning will be. We will use a four step process to set up these problems and will find exact solutions by solving what usually ends up being a 2nd or 3rd order polynomial. The four-step process is described below. We will illustrate the process using an example of a solution.
6.3.1 Write all reactions; list all unknowns:
6.3.2 Write all equations of equiliubrium
6.3.3 Write a mass balance for the primary acid/base species of interest
6.3.4 Write a charge balance assuming electroneutrality