Physical Chemistry of Foods

equilibrium situation. To be sure, the relaxation time has physical significance
only for a first-order reaction, and many changes do not follow such a
relation, for instance because more than one relaxation mechanism acts.
For asecond-orderreaction of the type AþB?AB we have

d½AŠ

dt

¼

d½BŠ

dt

¼

d½ABŠ

dt

¼k?½AŠ?½BŠð 4 :3bÞ

wherekis in L?mol
^1 ?s
^1. For the case that½AŠ¼½BŠ, a special case of
which is a dimerization reaction (i.e., A¼B), integration yields

1

½AŠ

1

½AŠ 0

¼kt ð 4 :3aÞ

which implies that a plot of 1/[A] versus time yields a straight line. Notice
that also the relative rate depends on concentration. A measure for the
(inverse of the) rate is the half timet 0 : 5 ¼ 1 =k½AŠ 0 , i.e., the time needed for
half of the reaction to become complete. Many reactions in foods
approximately follow second-order kinetics. Further information is given
in Table 4.1, also for the more complicated case of AþB?AB.
The reaction order is an empirical concept. Its value has to be
determined, since it cannot readily be derived from the stoichiometry, often

FIGURE4.1 First-order reaction of the type A!B. (a) Concentration relative to
the original one as a function of timeðtÞover relaxation timeðtÞ. (b) Example of log
concentration versus time; tana¼kloge¼ 0 : 434 k.Dis the decimal reduction time.