Figure 6.7a gives titration curves of a sample of poly(methacrylic
acid). We will first consider the curve for low ionic strength, wheregis not
much smaller than unity. It is seen that Eq. (6.8) with pKa¼ 4 :7 is not nearly
obeyed: the curve is shifted to higher pH (by almost 2 units), and the slope is
far too small (spanning nearly four pH units rather than two).
The main cause for the discrepancy is that the molecule hasmany
ionizable groups, rather than one. If it is partly charged, any additional
proton to be dissociated has to be removed against the electric potential
caused by several neighboringCOOgroups, rather than just one. See
Section 2.3.1, especially Figure 2.9b. The extent to which the presence of
many ionizable groups affects the titration curve depends on the immediate
chemical environment of these groups, notably on the distance between
them. In practice, one often finds a so-called Henderson–Hasselbalch
relation,
log1 a
a¼
pKavpH
fð 6 : 9 Þwhereais now the fraction ionized (or neutralized) averaged over all groups
FIGURE6.7 Titration curves. (a) The degree of ionizationaas a function of pH for
a single carboxyl group (calculated) and for solutions of poly(methacrylic acid) in
0.01 and 1 normal KCl. (b) The (average) valencezofb-lactoglobulin as a function
of pH. (After various sources.)