Physical Chemistry of Foods

2.2.1 The Chemical Potential

In a homogeneous mixture each component i has a chemical potentialmi,
defined as the partial molar free energy of that component (i.e., the change
in Gibbs energy per mole of component n 1 added, for addition of an
infinitesimally small amount). It is given by

mi:

qG

qni



T;p;nj

:miþRTlnai ð 2 : 6 Þ

wheremiis the standard chemical potential of the pure substance i and the
subscript j refers to all other components.Ris the universal gas constant,
given by

R¼kBNAV¼ 8 :314 J?K
^1 ?mol
^1 ð 2 : 7 Þ*

where Avogadro’s number NAV¼the number of molecules in a mole
ð 6 : 02? 1023 Þ. It should be noted that Eq. (2.6) only applies at standard
pressure.

Note If the pressure is raised, this increases the chemical potential,

in first approximation by an amount pvi, wherevi is the molar

volume of the component.

aiis theactivityof i; it is sometimes called the thermodynamic or the
effective concentration. The activity is directly related to concentration: for
zero concentrationa¼0; for the pure substancea¼1. For solutions called
ideal, the activity equals concentration, if the latter is expressed as mole
fraction (x). Ideality is, however, not often observed, except for a mixture of
very similar compounds. Figure 2.2a gives an example for the mixture
ethanol (2) and water (1), and it is seen that the deviation from ideality is
large. It is also seen that for small mole fractions of ethanol its activity is
proportional to its mole fraction (or to ethanol concentration expressed in
another way). One then speaks of anideally dilutesystem. This is further
illustrated in Figure 2.2b, where a hypothetical example is given of the
chemical potential of a solute (2) as a function of its mole fraction, for two
components (1 and 2) that can be mixed in all proportions. For smallx 2 ;
the chemical potential is proportional to lnx 2 and the slope is given byRT,
all in agreement with Eq. (2.6), but the line does not extrapolate tomat ln
x 2 ¼0 (i.e.,x 2 ¼1). For smallx 2 ;the solution is thus ideally dilute, and we
now have an apparent standard chemical potentialm^7 (pronounced mu
plimsoll) of the solute in this particular solvent (m^7 may also depend on
pressure). For an ideally dilute solution the chemical potential thus is given