Physical Chemistry of Foods

of 10^3 Pa?s is not exceptional in a low-moisture food, Eq. (4.16) would yield
7? 103 , and then the reaction may still be diffusion controlled.

4.3.5 The Bodenstein Approximation

We may conclude that in most aqueous solutions, simple bimolecular
reactions will proceed according to Eq. (4.12). For bimolecular reactions in
a system containing very little solvent, however, the reaction rate will be
mostly diffusion controlled, implying that the rate is inversely proportional
to the viscosity. In low-moisture foods, the situation may often be
intermediate. It appears logical to combine Equations (4.12) and (4.16).
Since we must essentially add the times needed for encountering and for the
reaction itself, the resultant rate constant would then follow from

1

k

&

1

kS

þ

1

kE; 2

ð 4 : 17 Þ

which is a form of the so-calledBodenstein approximation. It is called an
approximation because a simple addition of the reciprocal rates is
mathematically not quite correct. The equation clearly shows, however,
that if eitherkSorkE; 2 is much smaller than the other, the other is the
effective rate constant.
Thetemperature dependenceofkaccording to Eq. (4.17) needs some
consideration. According to the Eyring equation, it is largely determined by
the factor expð
DH{=RTÞ, as discussed. Equation (4.16) shows thatkSis
proportional toT=Z, whereZis, for instance, inversely proportional toT.
This then would lead tokSbeing about proportional toT^2. However, Eq.
(4.15), on which this relation is based, is by no means valid for systems that
are not homogeneous solutions. One has to use the effective diffusion
coefficientðDÞdirectly, as is discussed in Section 5.3.2. For low-moisture
systems,Dmay strongly depend on temperature, the more so for larger
molecules; see also Figure 8.9. Altogether, in most situations where Eq.
(4.17) would be more or less applicable, there is no simple expression for
dk=dT. This implies that the temperature dependence of a reaction in such
systems must be experimentally determined over the full temperature range
of interest. Another consequence is that an analysis in whichDH{andDS{
are derived for inactivation of an enzyme, as given in Section 4.3.3, would be
questionable for low-moisture foods.

Some Complications. Apart from Eq. (4.17) being approximate,
it is only valid if Eqs. (4.12) and (4.16) are correct. Several objections can be
made and we will just mention the main ones.