Physical Chemistry of Foods

slightest force is applied). In this case, the Arrhenius type relation

directly derives from the Maxwell–Boltzmann distribution. The

same holds true for diffusion.

4.3.3 Absolute Rate Theory

The Arrhenius theory cannot readily account for the mechanism in
monomolecular reactions, and the so called frequency factor is in fact not
more than a fitting factor. Moreover, it considers an activation energy only,
whereas there is sufficient reason to believe that there may be a positive or
negative activation entropy as well. One tries to overcome these deficiencies
in the theory of theactivated complex, also called absolute rate theory; it is
largely due to Eyring. Here it is assumed that the molecule or molecules to
react attain an activated or transition state of higher free energy (denoted by
superscript {). The activated state is induced by collision with other
molecules, be they reactants or solvent. An effective collision will not merely
enhance the kinetic energy of a molecule but will also cause distortion of
bonds, hence a local increase of bond energy. The activated complex formed
is very short-lived, and it is in equilibrium with the reactants. Hence we can
apply Eq. (4.6) with B being the activated complex. The latter spontaneously
decomposes into the reaction products, at a rate derived from the theory of
statistical mechanics. The result, for a first-order reaction, is

k¼

kBT

hp

exp



DG{

RT



¼

kBT

hp

exp



DH{

RT



exp



DS{

R



ð 4 : 11 Þ

wherehpis Planck’s constantð 6 : 626? 10
^34 J?sÞandDG{is the standard
molar activation free energy, etc. The frequency factorkBT=hp& 6? 1012 s
^1
at room temperature.
The Eyring theory is generally considered to be fairly rigid and it has
been shown to be in good agreement with results for several reactions.
Nevertheless, in many cases, especially when we are interested in the
temperature dependence, the Arrhenius theory may suffice. For reactions in
solution, theactivation enthalpyDH{¼Ea
RT.IfEa is not very small,
RT 5 Ea and the temperature dependence is virtually the same in both
equations. The relative change inTin the frequency factorðkBT=hpÞthen is
small compared to that in the factor expð
Ea=RTÞ, and the difference
betweenEaandDH{is also small.
At this stage it may be good to emphasize that a reaction rate constant
isnotdetermined by the difference in standard free energy between the
reactants and the products to be formed, but by the standardactivation free