Physical Chemistry of Foods

It may further be noted that the volume of a mixture of two
components is generally not equal to the sum of the volumes of each. For
many aqueous mixtures, the volume is decreased; one then speaks of
contraction. For example, when mixing 10 ml (15.8 g) of ethanol with 80 ml
of water, the mixture has a volume of 98.3 ml, which implies a contraction
by 1.7%.

Partitioning. A substance may have limited solubility in two mutually
immiscible solvents, for instance water and oil. This often happens in foods,
for example with many flavoring and bactericidal substances. It then is
important to know the concentration (or rather activity) in each phase. For
low concentration, the partitioning ordistribution law of Nernstusually
holds:

ca

cb

¼constant ð 2 : 10 Þ*

wherecis concentration andaandbrefer to the two phases.
This law is readily derived from thermodynamics, assuming both
solutions to be ideally dilute. At equilibrium we must have for the solute (2)
thatm 2 ;a¼m 2 ;b. Although the standard chemical potential of the pure solute
mis, of course, the same, the apparent standard chemical potentialm^7 (see
Fig. 2.2) will generally be different. We thus have

m^72 ;aþRTlna 2 ;a¼m^72 ;bþRTlna 2 ;b

from which follows

a 2 ;a

a 2 ;b

¼exp

m^72 ;b
m^72 ;a

RT

!

ð 2 : 11 Þ

which is constant at constant temperature. Since for dilute solutions the
(apparent) activities mostly are proportional to the concentrations, Eq.
(2.11) comes down to Nernst’s law. Note that the partition ratioðca=cbÞwill
decrease with increasing temperature if the ratio is larger than unity and vice
versa.

2.2.3 Determination of Activity

When preparing a solution, one usually knows the concentration of the
solute. Most analytical methods also yield concentrations rather than
activities. Often, the solute is allowed to react in some way, and although the
reaction rate will be determined by the activity rather than the concentra-