Physical Chemistry of Foods

first is due to changes in solvation; its quantity is rarely of the order of
magnitude of a covalent bond energy. The second is the mixing entropy,
which changes for many reactions, e.g., when AþB?AB; it is quite
generally given by

Smix¼nR

X

i

lnxi ð 4 : 7 Þ

wherenis the total number of moles in the mixture andxstands for mole
fraction. Sample calculations show that the change in mixing entropy per
mole of reactant in a dilute system is mostly smaller than 10R, i.e.,jTDSmixj
would be< 10 RT. All this means that for formation of a covalent bond,
jDGjoften is not greatly different fromU. Taking the latter at 100RT(see
Table 3.1) and assumingDGto be no less than 90RT, Eq. (4.6) yields an
equilibrium ratioaA=aB&e
^90 & 10
^39. This truly means that the reaction
would be completed: there is nothing of component A left, taking into
account that Avogadro’s number is ‘‘only’’ 6? 1023.
In several other cases, significant quantities of both molecules A and B
occur at equilibrium, because the net change in free energy is far smaller.
Often, besides formation of a covalent bond, another one has to be broken,
and the two terms (having different signs) may almost cancel. This is
presumably the case in the mutarotation reactions mentioned, where the
equilibrium constant generally is of the order of unity. Another case is a
small bond energy, for instance due to van der Waals attraction. In these
situations, entropy changes may play a considerable part, and a mixture of
components may have a particular composition because it is in equilibrium;
the composition then isthermodynamically controlled. Good examples also
are the salt association equilibria described in Section 2.3; here the Coulomb
energy for bond formation in water is of the order of a few timesRT.In
other situations, a mixture may have a certain composition that is far
removed from equilibrium, but it nearly remains so because the reactions
leading to equilibrium are very slow; the composition then is said to be
kinetically controlled.
Another situation may be that of asteady state. The observation that
the concentration of a reactant remains constant does not necessarily imply
that it is in equilibrium, nor that it does not react at all. Consider, for
example, a reaction scheme of the type A?B?C, with consecutive rate
constantsk 1 andk 2. If [A] is quite large andk 1 is not very small, molecules B
will soon be formed, at a ratek 1 ½AŠ, assuming the reaction to be first order.
B is in turn converted into C at a ratek 2 ½BŠ. Unlessk 24 k 1 , this will lead to
an increasing concentration of B untilk 2 ½BŠ¼k 1 ½AŠ, at which stage the
formation and disappearance of B occur at equal rates. Because [A] is very