Why is it that water dissociation can contribute to the pH of a weak acid solution if the acid is very dilute, very weak, or dilute and weak?

The [H⁺] due to acid dissociation ([H⁺]_a) is determined primarily by two quantities: the concentration of the acid (C_a) and the strength of the acid (given by K_a).

For strong acids, K_a is so large that the acid completely dissociates, making the actual numerical value of K_a unimportant, so [H⁺]_a depends only on C_a.

However, for weak acids, the exact value of K_a is important, so [H⁺]_a depends on both C_a and K_a. Thus, water will contribute significantly to the pH if the combination of C_a and K_a gives a [H⁺] due to acid dissociation that is comparable to the [H⁺] due to water dissociation ([H⁺]_w).

There are actually an unlimited number of C_a and K_a combinations that will give a certain [H⁺]_a. These include:

• Very dilute weak acid of moderately high strength (Very low C_a, moderately high K_a): Although a moderate proportion of the acid dissociates, the initial concentration of the acid is so low that very little acid is there to dissociate, giving a [H⁺]_a comparable to [H⁺]_w.

• Moderately concentrated, very weak acid (Moderately high C_a, very low K_a): Although the initial concentration of acid is moderately high, so little of that acid dissociates that [H⁺]_a is comparable to [H⁺]_w.

• Dilute, weak acid (Low C_a, low K_a): In between the extremes above is the case where fairly little acid is present in solution, and fairly little of that acid dissociates. The two effects compound to give a [H⁺]_a comparable to [H⁺]_w.
  
  Note that this is not the same as combining the two extremes. A very dilute, very weak acid may actually dissociate so little that [H⁺]_a is negligible compared to [H⁺]_w!