net solvent–solute interaction, and q ¼12, the approximate value for
sucrose in water. It is seen that the correction is somewhat overestimated in
this case.
- Solvent–solute interaction. If there is net attraction or association
between solute molecules and water molecules (‘‘hydration’’),b>1. If the
association is strong, i.e., the solvent quality is very good, it isas ifsome
water molecules were removed. This then isas ifthe mole fraction of water
were decreased. The resulting decrease ofawis only appreciable ifxsis fairly
large. For instance, ifxs¼0.02, and thusaw(ideal)¼0.98, ‘‘removal’’ of
1 mol water per mol solute would yieldaw¼ð0.980.02Þ/ð0.02þ0.96Þ¼
0.9796, which is hardly different. On the other hand, ifxs¼0.3, andaw
(ideal)¼0.70, the same ‘‘removal’’ would result inaw¼0.4/0.7¼0.57,
which is a substantial decrease.
If the solvent quality is poor,b<1, and solute molecules tend to
associate with each other. This isas ifthere were fewer solute molecules,
hence a higherxw, hence a higheraw. The latter effect occurs in the sucrose
solution, partly compensating for the volume exclusion effect; the results
reasonably fit Eq. (8.4) withb¼0.64. This then implies that sucrose is
(slightly) hydrophobic.
Figure 8.1. also gives an approximate curve for solutions of caseinate,
i.e., aprotein. Here all nonidealities mentioned are involved. Casein has an
isoelectric pH of about 4.6 and at neutral pH it is thus negatively charged,
having about 14 net charges per molecule. This would mean that the
(univalent) counterions present increase the molar concentration by a factor
of 15. (Actually, most protein preparations contain more salt than strictly
needed for electroneutrality.) Casein has a large molar mass (about 23 kDa),
implying that the molar volume ratio solute/solventq&900. This implies a
large nonideality, as is the case for all polymers; see Section 6.4. Solvent–
solute interactions also play a part, but it is difficult to find out in what
manner, since for some groups on the protein (especially ionized groups)
water is a good solvent, whereas for hydrophobic groups solvent quality is
poor. It is known that the caseinate molecules tend to associate, forming
clusters of, say, 15 molecules at about 1%concentration. Presumably, the
overall solvent quality therefore is such as to (slightly) increaseaw.
Most foods show marked nonideality, and calculation ofawfrom the
composition is generally not feasible. For a mixed solution, calculation may
be done according to the so-called Ross equation,
aw¼aw; 16 aw; 26 aw; 36 ð 8 : 5 Þwhereaw,imeans the water activity as determined for soluteiat the same
molar ratio ofito water as in the mixture. Equation (8.5) can be derived