Physical Chemistry of Foods

Question

In a study on heat inactivation of a peroxidase enzyme (EC 1.11.1.7), it was found
that 5 min heating at 72 8 C left 55%, and 5 s at 80 8 C left 2.7%, of the enzyme activity.
Calculate the molar activation enthalpy and entropy of the reaction.

Answer

To do the calculation, we have to make some assumptions: (a) The heat inactivation
is controlled by the heat denaturation. (b) The latter is a first-order reaction; this
should, of course, be checked by determining residual activities for various heating
times. (c) The reaction rate can be derived from absolute rate theory.
We then have from Eq. (4.2b) that at 72C (i.e., 345 K)
lnð½AŠ=½AŠ 0 Þ¼ln 0: 55 ¼
300 ?k; hencek¼ 0 :0020 s
^1 ; similarly at 80 8 C (353 K)
k¼ 0 :72 s
^1. We can now write (4.11) in logarithmic form as

lnk¼lnð 8 : 7? 1012 Þþ

DS{

R




DH{

RT

and filling in the values for k and T we obtain two equations with
two unknowns. The result isDH{¼745 kJ?mol
^1 andDS{¼1860 J?mol
^1 ?K
^1.

4.3.4 Diffusion-Controlled Reactions

Equation (4.11) applies to a first-order reaction. For asecond-order reaction
it becomes

kE; 2 ¼

kBT

hP

?

RT

p

?exp



DG{

RT



ð 4 : 12 Þ

Now the rate constant is in m^3 ?mol
^1 ?s
^1 , and to obtain it in
L?mol
^1 ?s
^1 , it has to be multiplied by 10^3. At ambient temperature, the
factorRT/pthen is about 25 liters per mole¼ 0 :025 m^3 ?mol
^1 .phas to be
taken as the standard pressure, i.e., 10^5 Pa, at which the standard molar
energies are given.
There is, however, a problem for a second-order reaction: it is
implicitly understood that the rate at which the molecules—say, A and B—
encounter each other is not limiting the reaction rate. In other words, the
system is considered to be ideally mixed (i.e., as if it were stirred at an
infinite rate). This is not always reasonable, and we need to consider the