Physical Chemistry of Foods

as well, thereby traveling over some distance (Brownian motion); in

vapor (or air) the molecules travel over far larger distances in the

same time. See further Section 5.2.

4.3.2 Activation Energy

The first useful theory of reaction rates was due toArrhenius, and it is easiest
to envisage for a bimolecular reaction. It is assumed that the molecules have
to overcome an energy barrier before they can react. This is depicted in
Figure 4.4. The energy barrier per mole is called theactivation energy,
symbolEa. As mentioned, the average translational kinetic energy of a
molecule isð 3 = 2 ÞkBT, and the average kinetic energy involved in a collision
of two molecules is given by 2 times 1/3 of that value, i.e.kBT; the factor 1/3
arises because the molecules move in 3 dimensions and when they collide
this happens in one dimension. The collision may now provide the
activation energy needed for the molecules to react. From Eq. (4.9), the
proportion of collisions of which the energy is higher than a given valueU
can be derived to equal expð
U=kBTÞ. By changing from molecules to
moles and by puttingU*NAV¼Ea, it follows that the rate constant would
be

k¼Aexp

Ea

RT



ð 4 : 10 Þ*

where A often is called the frequency factor. It is also called the

FIGURE4.4 Arrhenius theory. Illustration of the energy state of the reactants, the
reactants in the activated state, and the reaction product(s).Ea represents the
activation energy.