Physical Chemistry of Foods

preexponential factor and denoted ask?ork 0 , i.e., the value thatkwould
attain at infinite temperature or zero activation energy, respectively.

Temperature Dependence. Eq. (4.10) predicts that log k is
proportional to 1/T, and this is indeed very often observed, especially for
reactions of small molecules, involving breaking and formation of covalent
bonds. The Arrhenius theory can thus be said to be very successful, and as a
semiempirical relation Eq. (4.10) is indeed useful in many cases.
Chemists generally express the temperature dependence of a reaction
inQ 10 , i.e., the factor by which a reaction is faster if one increases the
temperature by 10K. Bacteriologists use theZvalue, i.e., the temperature
increase (in K) needed to increase the reaction rate by a factor of 10. These
parameters naturally depend on temperature, even if the activation energy is
constant. We have

Q 10 ¼exp

10 Ea

RT^2



and

Z¼ 2 : 3

RT^2

Ea

This implies that errors are made by assuming these parameters to be
constant. It is fairly common to plot the log of the timet’ needed to obtain a
certain effect (e.g., 90%inactivation of an enzyme, or the emergence of a
given quantity of a compound), not against 1/Tbut againstT, and within a
small temperature range an almost straight line is obtained. Extrapolation
of such plots beyond the temperature range studied may cause considerable
error, especially for largeEa, since it assumes in fact thatEa=T^2 is constant,
which is very unlikely.

Note The success of the Arrhenius theory has often induced

workers to apply it to other phenomena. Several physical properties

of a system tend to depend on temperature like an Arrhenius

relation, but this does not necessarily mean that we can assign an

activation energy to the phenomenon. A case in point is the fluidity,

i.e., the reciprocal of the viscosity, since there is no such thing as an

activation energy for fluid motion (a true fluid moves if only the