Acidity constant

The equilibrium constant for the disassociation of a Bronsted acid:

This constant can be used as a way of comparing acidity. To make comparing acidity simpler, the concentration of water can be assumed to be constant in dilute solutions and removed, because constants won't affect relative sizes. This produces the K_a, called the acidity constant:

Remember [H₃O⁺ is equivalent to [H⁺].

K_a is often expressed in a negative log form as the pK_a:

Note the similarity with the formula for pH (-log[H⁺]), in general the p sign takes the -log of something.

Both the pH and pK_a decrease with the strength of an acid. pH is related to concentration of H⁺ while pK_a is related to an equilibrium constant, so only pH will change with concentration. I suggest to avoid trying to understand them intuitively and to just focus on being able to relate them in equations.

Example: Calculate the pKa of 0.145M CH₃COOH (acetic acid) with a pH of 2.80

First we convert pH to the concentration of hydrogen ions.

Then we substitute this into the equation for K_a

We know that the concentration of [H⁺] is the same as the concentration of the conjugate base. So [H₃O⁺]=[X^-]. Subtracting that concentration from the initial concentration of acetic acid gives us of the concentration of the disassociated molecules, or [HX].

Taking the negative log of the answer gives a pK_a of 4.75