Physical Chemistry of Foods

4.1 REACTION ORDER

Before coming to factors determining reaction rates, it is useful to review the
manner in which concentrations depend on time.
Thereaction rateis usually given as the change in concentrationc, i.e.,
as eitherþor
dc/dt. According to the units ofc, it may be expressed in
mol?L
^1 ?s
^1 (the most common way), mol?kg
^1 ?s
^1 , number?m
^3 ?s
^1 ,
etc.
For azero-orderreaction, the rate remains constant: see Table 4.1.
Approximately zero-order reactions occur, for instance, if small quantities
of a substance, say one causing an off-flavor, are slowly formed from a very
large reservoir of a parent component.
For afirst-orderreaction of the type A?BorA?BþC, we have

d½AŠ

dt

¼k½AŠð 4 :2aÞ

where [A] stands for the molar concentration of A andkis therate constant,
which in this case is in s
^1 .kvaries with temperature and pressure, but it is
generally assumed to be constant otherwise, i.e., independent of concentra-
tion; this is often (nearly) true, but not always. Integrating the equation, and
introducing the initial concentration of A, we obtain

ln

½AŠ

½AŠ 0



¼
kt ð 4 :2bÞ

or

½AŠ¼½AŠ 0 expð
ktÞ¼½AŠ 0 exp

t

t



ð 4 :2cÞ*

wheretis therelaxation time. If we plot the log of the concentration versus
time, we thus obtain a straight line. The relations are illustrated in Figure
4.1. If, for example, 10%of A is left afterDs, this means that 1%is left after
2 Ds, 0.1%after 3Ds, and so on;D, which equals 2.3/k, is called the decimal
reduction time and is mostly used by microbiologists. The killing of
microorganisms and the inactivation of enzymes at high temperature often
follow first-order kinetics, at least approximately. Also bacterial growth in
the so-called exponential phase follows first order kinetics, but now the sign
in Eq. (4.2a) is positive.
Therelaxation timeis mostly used by physical chemists and is the time
needed for a certain change to occur overð 1
1 =eÞ& 0 :63 of its maximum
value, after a specified change in conditions has been applied, say a change in
temperature or in pH. It is said then that the system relaxes toward a new