from the Gibbs–Duhem relation [e.g., Eq. (2.13)], assuming interactions
(i.e., net attraction or repulsion) between different solute molecules to be
negligible. It gives fairly good results forawdown to about 0.8, the relative
error in ð 1 awÞgenerally being < 10 %. At lower water activity, the
situation becomes very complicated. To mention just one point, the
dissociation of ionogenic groups is suppressed, the more so at a loweraw,
thereby altering (decreasing) hydration of these groups.
Determination of water activitythus is generally needed. This can be
done by bringing the food in equilibrium with the air above it. At
equilibrium, theawvalues in the aqueous phases of the food and in air are
equal. Since moist air shows virtually ideal behavior at room temperature
and pressure, we simply have
aw;f¼aw;v¼
pv
pv;satð 8 : 6 Þ*where subscript f stands for food and v for vapor;pv, satis the vapor pressure
of pure water at the temperature of measurement. The water activity of the
food thus equals the relative humidity (expressed as a fraction) of the air
above it, provided that equilibrium has been reached.
Examples of the water activity of several foods, in relation to water
content, are shown in Figure 8.2. For some foods a range is given, in other
cases just one example. It is seen that most points fall within a band having a
width corresponding to a variation inð 1 awÞby a factor of about three.
Two kinds of exceptions are observed. The one is exemplified by the point
labeled ‘‘brine.’’ This represents a type of seasoning that is almost saturated
with NaCl. Because of the small molar mass of the molecules and ions
dissolved, the effectivexwis relatively small. Foods of a high fat content
form the other exception. Skim milk and cream have exactly the same
aqueous phase, and thereby the sameaw, despite the large differences in
water content. Margarine has an even lower content of aqueous phase, and
an extreme is cooking oil, which may have a water content of about 0.15%at
room temperature, but virtually no substances that can dissolve in water;
hence,awwill approach unity.