ion activity coefficientof NaCl as
g+ðNaClÞ:½gþðNaþÞ?gðClÞ^1 =^2 ð 2 : 22 ÞNote that the subscripts to the activity coefficient here have the following
meanings:
+of the salt in its dissociated form
0 of the salt in its undissociated form
þof the cation
of the anionThe solubility of a salt is given as thesolubility product Ks, which is to
be compared with the activity productKa. For NaCl this is given by
Ka¼aðNaþÞ?aðClÞ¼f½Naþ?½Clg 6 fgþðNaþÞ?gðClÞgð 2 : 23 ÞThe activity product of the ions in solution thus cannot be higher thanKs.
To be sure, for a very soluble salt like NaCl, it often would make little sense
to use the solubility product, because of the large nonideality at the relevant
concentration; but it is a very useful concept for salts of lower solubility,
especially if the activities of the cations and anions are not equal, as will
often be the case in foods.
For the dissociation of an acidðHAcÐHþþAcÞwe can write,
recalling that pH¼logaðHþÞand that pKa¼logKD,
pHpKa¼log½Acþlogglog½HAcð 2 : 24 ÞThe pKa(subscript a for acid) is the pH at which the dissociation is exactly
50 %ð½Ac¼½HAcÞ, provided thatg¼1; however, the latter mostly is
<1, implying that the stoichiometric pKais smaller than the intrinsic one,
say by 0.1 or 0.2 units. Strong acids have a low pKa(largeKD), often<1;
fatty acids, for instance, are weak acids and have a pKa& 4 :7. At a pH one
unit higher, the acid will be dissociated for 91%according to (2.24), at a pH
one unit lower for 9%, at 2 units lower for 1%, at 3 units lower for 0.1%, etc.
This is illustrated in Figure 2.9a.
Di- and triprotic acids have two and three pKa^0 s, respectively. For
instance, the intrinsic pKa values of citric acid, CH 2 ðCOOHÞ
CHðCOOHÞCH 2 ðCOOHÞ, are 3.1, 4.7, and 5.4. The three acid groups
are almost identical, and the differences in pKare due to the increased
charge if more than one group is dissociated. When increasing the pH, the
second proton to be dissociated must be removed against the electric
potential of two, rather than one negative charge. This needs additional free
energy and will thus happen at a higher pH, where the driving force for