Physical Chemistry of Foods

dissociation is greater. Figure 2.9b gives a titration curve for citric acid; here

the degree of neutralization rather than dissociation is given, and only when

using a very strong base for the titration and after extrapolation to zero

ionic strength would the two be identical. Figure 2.9b also gives a titration

curve for phosphoric acid; this has intrinsic pKavalues of 2.1, 7.2, and about

12.7. These differences are far larger than in the case of citric acid, because

the three acid groups are essentially different; the neutralization of the

various groups can now be distinguished on the titration curve.

For bases comparable relations hold.

The relations involving activity coefficients are slightly more

complicated for ions of a valence higher than 1. For instance, for CaCl 2 Ð

Ca^2 þþ2Cl
the dissociation constant is given by

KD¼

aðCa^2 þÞa^2 ðCl
Þ

aðCaCl 2 Þ

¼

½Ca^2 þŠ?½Cl
Š^2

½CaCl 2 Š

6

gþðCa^2 þÞ?g^2 
ðCl
Þ

g 0 ðCaCl 2 Þ

ð 2 : 25 Þ

FIGURE2.9 Dissociation of acids as function of pH. (a) Calculated degree of
dissociationðaÞof a fatty acid (intrinsic pKa¼ 4 : 7 Þat very small ionic strength. (b)
Titration curves, i.e., experimentally determined degree of neutralizationða^0 Þby
KOH of citric acid and phosphoric acid; the intrinsic pKavalues are indicated by
vertical dashes.