dependent food properties (such as its stability) than gravimetric water
content, in the first place because several constituents may be inert with
respect to water. This is easily understood when we realize that for an ideal
solution the water activity equals the mole fraction of water, i.e.,
awðidealÞ¼xw:
mw
mwþSms;ið 8 : 2 Þ*where mis molar concentration of water (subscript w) and of solutes
(subscript s). It is thus the number concentration of solute molecules that
counts. Very large molecules (say, of starch) have very little effect onxw
(which equals 1xw), and water-insoluble components (fats, substances in
solid particles) not at all.
Note Equation (8.2) often is called Raoult’s law. Strictly speaking,
however, Raoult’s law only applies to lowering of vapor pressure by
a solute. Cf. Eq. (8.6).
Figure 8.1 gives some examples of the water activity versus mole
fraction of water for some simple solutions. It is seen that Eq. (8.2) is poorly
obeyed, except for sucrose at very smallxs. Deviations from ideality are
discussed in Section 2.2.5. They can be expressed in a virial expansion, as
given in Eq. (2.18) for the osmotic pressureP. The relation between the two
properties is
lnaw¼PMw
RTrw& 1 : 8? 10 ^5
P
RT
ð 8 : 3 Þ(in SI units) whereMis molar mass (kDa) andrmass density. Foraw> 0 :9,
lnaw& 1 aw. The quantity P=RTrw equals the osmolality of the
solution (for an ideal solution the number of moles of molecules, ions, and
particles per kg of water). For a single solute, an approximate relation
follows from the Flory–Huggins theory (see Chapter 6), and the
combination of Eqs. (6.10) and (8.3), with some rearrangement, leads to
lnaw&xs 1 þ1
2
bqxsþ1
3
q^2 x^2 sþð 8 : 4 Þwherexsis the mole fraction of solute,qis the volume ratio of a solute
molecule over a water molecule, andbis the solute–solvent interaction
parameter defined in Section 6.4.1. The relation would hold if the volume
fraction of solute is not too high, say< 0 :3.
Importantcauses of nonidealityare