Calculating 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 Ka:

**Ka = ([H+] [A¯]) ÷ [HA]**

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

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

The Dissociation Constant Across Equations

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

Ka and pKa are related in a similar way:

pKa = -log10Ka = 10-Ka

Ka = 10-pKa

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

Sample Dissociation Calculation

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

First, convert pKa to Ka and pH to [H+]:

Ka = 10-4.756 = 1.754 x 10-5

[H+] = 10-3.85 = 1.413 x 10-4

Now use the equation Ka = ([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%.