Acid-base equilibria

On first encounter, the study of acid-base equilibria is a little like a strange land with seemingly confusing trails that make passage difficult. In fact, there is a road map that, once understood, allows
us to navigate acid-base equilibria with confident precision and so become masters of its domain. Here is an overview of this road map.
Fundamentally, aqueous acid-base equilibria are just a particular example of the ideas and techniques we have already learned in the study of gas phase chemical equilibria. However, there are two aspects that complicate the application of these ideas. First, because the autoionization of water, 2 H 2 OHlL F H 3 O + HaqL + OH - HaqL, K w , is always present in aqueous solution, the analysis of aqueous acid-base equilibria must always take
into account at least two competing equilibria, the acid or base ionization and the water autoionization. Second, because we will be interested in how acid-base equilibria respond to changes in the system (typically by adding additional base or acid), we need also to be able to separate the chemical reactions that take place when things are combined from the subsequent equilibration of the
reaction product. The key idea is to let what are combined react 100% as a limiting reagent problem as a preliminary step done before equilibration.
Our overarching goal, then, is to learn to clearly distinguish and to separately master these two aspects—competing equilibria and limiting reagent reactions. Once this is achieved, we will have a framework in which any problem in aqueous acid-base equilibria can be solved in a straightforward
way.
The approach we take is to distinguish four regimes:
1. pure acid (or base) solution,
2. acid (or base) that has been partially consumed by addition of base (or acid),
3. acid (or base) that has been exactly consumed by addition of base (or acid),
4. acid (or base) that has been consumed by reaction with excess base (or acid).
The details will be different depending on whether the acid (or base) initially present is a weak or
strong acid (or base), that is, whether its ionization constant is large or small compared with 1. In all
cases, the other component will be a strong base (or acid).
The first regime is a straightforward equilibrium problem. The second regime involves reaction of
the acid and base as a limiting reagent problem, followed by straightforward equilibration of the
resulting solution. The third regime is handled differently depending on whether the acid (or base)
initially present is a weak or strong acid (or base). The fourth regime, like the second, involves
reaction of the acid and base as a limiting reagent problem, but then equilibration of the products is
simple since it will always be the excess base (or acid) that is left after the limiting reagent reaction.
You will know that you have mastered this road map of acid-base equilibria when you approach such
an equilibrium as a two step process: First (always!), determine which regime applies. Then,
implement the calculational procedure for that regime to determine the chemical equilibrium. That
really is all there is to it. In this way you can come to find that things will seem simple; not easy, but
simple.