One of the most fundamental reactions in chemistry is the acid/base neutralization reaction. Perfectly equivalent amounts of acid and base are allowed to react. If done stoichiometrically, both the acid and the base are neutralized to yield two new chemical species. In general we say "an acid plus a base makes water and a salt". The most over used reaction in academia to show this is...
HCl(aq) + NaOH(aq) → H2O(ℓ) + NaCl(aq)
Notice that this a strong acid (HCl) reacting with a strong base (NaOH). In this situation, the products are always water (H2O) and a salt, which in this case is sodium chloride (NaCl). If we actually write this in total ionic form where we show all the separated, dissolved ions, we get
H+(aq) + Cl–(aq) + Na+(aq) + OH–(aq) → H2O(ℓ) + Na+(aq) + Cl–(aq)
And now we can cancel any species that is unchanged on each side of the equation. These types of ions are called spectator ions because they aren't taking part in the reaction (a player or playa as some would say), they are "spectating". The aqueous Na+ and Cl– are both spectator ions and are removed to go the total net ionic equation here
H+(aq) + OH–(aq) → H2O(ℓ)
This net reaction is the same for pretty much every strong acid that reacts with a strong base. Why? Because every ion that is not H+ or OH– is a spectator and will be cancelled out on each side of the reaction.
Stoichiometry is very much in play here. Realize that this could very well be a limiting reactant type of problem and there could be left over acid or base. It is only a true neutralization when the two species are matched in a perfect stoichiometric ratio, which in this case is 1:1. The next section is about matching these amounts in a purposeful and analytical way - a titration.
Once a neutralization (titration) is complete, the original acid or base you started with has now been converted to the opposite type of compound. Specifically, each is converted into their conjugates. The strengths of conjugates are the opposite of the strength of the parent compound. Also remember that we can sort by strength via the size of the Ka or Kb (the bigger, the stronger). Let me point out what I mean by "opposite in strength".
Before you read this, you might first jump ahead to section 6.10 on Weak Acids and Weak Bases. Then come back.
The fact is that all conjugate pairs have the same type of relationship as does H+ and OH– for water. As you know:
Kw = [H+][OH–]
Well, as it turns out, any set of conjugate pairs (the acid form and the base form) have the following relationship for their respective Ka's and Kb's:
Kw = KaKb
So when any chemist says the conjugate is "opposite in strength" what they really mean is that the conjugate is inversely proportional in strength. The only special case where the two conjugates have identical strengths, is when each of the K's equals 1.0 × 10–7. All other values differ in strength. For example: if your weak acid, HA, has a Ka of 2.5 × 10–5, then the conjugate base, A–, has a Kb of 4.0 × 10–10. Notice how those two numbers multiply to give 1.0 × 10–14, AND how Ka >> Kb. BOTH species (HA and A–) are by definition "weak", but the base here is much much weaker than the acid.
Also remember, that even if you have a very very weak acid or base, dissolving them into water WILL move the pH in the acidic (lower than pH 7) direction or basic (higher than pH 7) direction. The weaker they are, the closer to 7 you will be.
What does this mean for a neutralization of a weak acid or base? It means after you completely neutralize a weak acid (HA) with a strong base (NaOH), you will have the conjugate base (A–)solely in solution and that means the pH is above 7 or basic. The opposite must follow the same logic - if you neutralize a weak base (B) with a strong acid (HCl), you will have the conjugate acid (BH+) solely in solution and that means the pH is below 7 or acidic.
Realize that a strong acid which we just pretend to have Ka's equal to infinity (say 10∞) would have conjugates with strengths of 10–∞ or ZERO strength. So what this means is that any strong acid with strong base titration will have an equivalence point pH of 7.00. Why? because no species in solution after the neutralization is an acid or base with any strength. All the conjugates are ZERO for K which means they do not effect the pH of water in any way whatsoever. Now lets summarize all this: