If a graph is drawn of pH versus mL of NaOH added, there will be a significant change in pH
in the vicinity of the equivalence point. It is important to understand that the equivalence point
will not be at pH 7, but will be slightly higher. The value of the equilibrium constant for the
dissociation of the acid can be obtained from this graph. Since a weak acid is being studied in
Part II, the dissociation can be represented as
HA H O++ 23 +H O+-Awhich results in the equilibrium expression:
[]
K [][]
HAHO A
a=^3+-This can be rearranged to read []HO 3 + =Ka#[][]HAA-
When the acid is half neutralized, half of the number of moles of HA originally present will
be converted to the conjugate base A–. So [HA] = [A–] and Kawill be equal to [H 3 O+] since
[HA] / [A–] = 1. Therefore, when the acid is half-neutralized, pH = pKa. The point at which the
pH is equal to pKacan be seen in Figure 1.
Figure 1If one were to titrate a weak diprotic acid such as maleic acid with the known NaOH solution,
the graph would show two separate inflections — representing the neutralization of each hy-
drogen — assuming the pKavalues differ by 4 or more pK units (see Figure 2). The dissocia-
tion of a diprotic acid occurs in two separate steps:
HA HO HO HA22 3+++ +-
HA-+-++H O 23 +H O A^20 25 503pH^7Volume of NaOH added (mL)pH = pKaLaboratory Experiments