Physical Chemistry of Foods

by

m 2 ¼m^72 þRTlnx 2 ð 2 :6aÞ

Note in Figure 2.2a that at high concentration of ethanol the activity of the
solvent (water) is proportional to its mole fraction, hence to 1
x 2 ; here the
solution is ideally dilute for the solvent.
For those cases wherexdoes not equala, one arbitrarily introduces an
activity coefficientg, defined by

ai:xi 6 gi ð 2 : 8 Þ*

To be sure, it is implicitly assumed that the standard chemical potential is
the apparent one (m^7 rather thanm) in the present solvent. Even in dilute
solutions,goften markedly deviates from unity.
The chemical potential determines thereactivityof a component, i.e.,
the composition of a mixture at chemical equilibrium and the driving force
for a reaction, though not its rate. Transfer of a component from one phase
or position to another one will always proceed in the direction of the lowest
chemical potential, whether the transfer is by diffusion, evaporation,
crystallization, dissolution, or some other process. If temperature and

FIGURE2.2 Thermodynamic aspects of mixtures. (a) Activityða 2 Þof ethanol as a
function of its mole fraction in an aqueous mixtureðx 2 Þ. (b) Example of the chemical
potentialðm 2 Þof a substance as a function of its mole fractionðx 2 Þin a mixture of
substances 1 (solvent) and 2 (solute).