How To Calculate Percent Dissociation

When strong acids are placed in water, they completely dissociate. That is, all of the acid (HA) separates into protons (H⁺) and their companion anions (A¯).

In contrast, weak acids placed in aqueous solution do not completely dissociate. The extent to which they do separate is described by the dissociation constant K_a:

**K_a = ([H⁺] [A¯]) ÷ [HA]**

The quantities in square brackets are the concentrations of the protons, anions and intact acid (HA) in solution.

K_a is useful for calculating the percent of a given weak acid that is dissociated in a solution with a known acidity, or pH.

Recall that pH is defined as the negative logarithm of the proton concentration in solution, which is the same as 10 raised to the negative power of the proton concentration:

pH = -log₁₀[H⁺] = 10^-[H+]

[H⁺] = 10^-pH

K_a and pK_a are related in a similar way:

pK_a = -log₁₀K_a = 10^-Ka

K_a = 10^-pKa

If given the pK_a and pH of an acid solution, calculating the percent of the acid that is dissociated is straightforward.

A weak acid, HA, has a pK_a of 4.756. If the solution pH is 3.85, what percentage of the acid is dissociated?

First, convert pK_a to K_a and pH to [H+]:

K_a = 10^-4.756 = 1.754 x 10^-5

[H⁺] = 10^-3.85 = 1.413 x 10^-4

Now use the equation K_a = ([H⁺] [A¯]) ÷ [HA], with [H⁺] = [A¯]:

1.754 x 10^-5 = [(1.413 x 10^-4 M)(1.413 x 10^-4 M)] ÷ [HA]

[HA] = 0.0011375 M

Percent dissociation is therefore given by 1.413 x 10^-4 ÷ 0.0011375 = 0.1242 = 12.42%.