Physical Chemistry of Foods

KDis now in mol^2 ?L
^2 rather than moles per liter. Further,

g+ðCaCl 2 Þ¼½gþðCa^2 þÞ?g^2 
ðCl
ފ^1 =^3

or, more generally, for a cation C and an anion A making a salt CxAy,

g+ðCxAyÞ¼½gxþðCÞ?gy
ðAފ^1 =ðxþyÞ ð 2 : 26 Þ

It is generally difficult to determine the ion activity coefficients, and
one commonly makes shift with values calculated with semiempirical
equations: see Section 2.3.2. Anyway,gdecreases with an increase in total
ionic strength. This means that adding any other electrolyte will decrease the
activity coefficients, causing the solubility and the dissociation to increase.
For instance, if KNO 3 is added to a solution of CaCl 2 , this affects the
latter’s dissociation equilibrium.gþandg
decrease andg 0 remains at 1,
and—since the intrinsic dissociation constant remains unaltered—it thus
follows from (2.25) that the concentrations of Ca^2 þand Cl
increase and
that of the undissociated salt decreases.
It should finally be remarked that dissociation constants generally
depend, and often strongly depend, on temperature. The dissociation may
either increase or decrease with temperature, and there are no general rules.
The same holds for solubility products.

Note In principle, the ion activity coefficient of a saltðg+Þcan be

determined, but not those of individual ionsðg
andgþÞ, because

their concentrations cannot be varied independently. Nevertheless,

the activity coefficients of individual ions are very useful, and as

mentioned, one tries to calculate them from theory. Ion-selective

electrodes measure chemical potentials (which depend on activities,

not concentrations), but the standard potential is unknown. For the

measurement of pH, which is the negative logarithm of the

hydrogen ion activity, one has therefore arbitrarily chosen a

reference potential for a certain buffer, which potential is of course

as close to the real one as theory permits it to be calculated.

2.3.2 Debye–Hu ̈ckel Theory

The ion activity coefficients depend on a great number of factors, but for
low ionic strength, electric shielding is by far the main factor. On this basis
the Debye–Hu ̈ckel ‘‘limiting law’’ has been derived. As depicted in Figure
2.10, an ion in solution is, on average, surrounded by more counterions
(opposite charge) than coions (same charge), thereby to some extent