Physical Chemistry of Foods

pressure are constant, it is convenient to use the activity. The activity rather
than the concentration enters in relations on the solubility, the distribution
of a component over various phases, the adsorption of a component onto a
surface, and so on. If for some reason—say, the addition of another
component—the activity coefficient becomes smaller without the concentra-
tion altering, the reactivity of the solute thus has become smaller and its
solubility increased.

Note Equations like (2.6) and (2.8) can also be put in a form

where molarity, molality, or some other concentrative unit is used

rather than mole fraction. This means thatm^7 has another value,

but—more important—it also affects the value of the (apparent)

activity coefficient. For a very dilute solution, the differences tend

to be negligible, but in other cases, the concentrative unit to which

the activity coefficient relates should be stated. Naturally, the

various kinds of concentration can be recalculated into each other;

see Appendix A.7.

2.2.2 Solubility and Partitioning

For amixtureof components that behaves ideally, it can be derived that
there is no change in enthalpy when the components are mixed, i.e., no heat
is released nor consumed. The decrease in free energy due to mixing then is
purely due to an increase in entropy. Such a situation may occur for two
components of very similar properties, for instance for a mixture of closely
related triglycerides. However, if one of the components is a solid at the
temperature of mixing, it has to melt, and this means an increase in
enthalpy, equal to the enthalpy of fusionDHf(the enthalpy of mixing is still
assumed to be zero). This implies that there is a limitedsolubilityðxsÞ, given
by the Hildebrand equation,

lnxs¼

DHf

R

1

Tf

1

T



ð 2 : 9 Þ

where the solubility is expressed as a mole fraction and where the subscript f
refers to fusion. Most solutions are far from ideal, and especially at high
concentrations the activity coefficient may differ greatly from unity (often
being larger). Even the introduction of activity rather than mole fraction in
Eq. (2.9) is insufficient, since the change in enthalpy will generally include
some enthalpy of mixing, which may be large. Nevertheless, a relation like
Eq. (2.9) often holds, viz. a linear relation between log solubility and 1/T.
Examples are given in Chapter 15.