the handbook of food engineering practice crc press chapter 10 ...

A = -d[A]
dt = k [A] m (9)
r B = d[B]
dt = k' [B] m' (10)
The quality factors [A] and [B] are usually quantifiable chemical, physical, microbiological
or sensory parameters characteristic of the particular food system. Both k and k' are the
apparent reaction rate constants and m and m' the reaction orders. It should be again
stressed that equations (9) and (10) do not represent true reaction mechanisms and m and
m' are not necessarily true reaction orders with respect to the species A and B but rather
apparent or pseudo orders. The apparent reaction orders and constants are determined by
fitting the change with time of the experimentally measured values of [A] or [B] to
equations (9) or (10). The techniques used for the solution can be generally classified into
two categories: a) Differential Methods and b) Integral Methods (Hills and Grieger-Block,
1980).
In experimental kinetic studies, it is impossible to measure the reaction rate
itself. Instead, the concentration of A or B is measured (directly or indirectly) as a function
of time. If these concentrations are plotted against time and smooth curves are fitted either
graphically or using a statistical fitting method (e.g., polynomial regression) the reaction
rates may be obtained by graphical or numerical differentiation of the curves. By taking
the logarithm of both sides of equation (9) and (10), the following linear expressions are
obtained:
log r A = log k + m log [A] (11)
log r B = log k' + m' log [B] (12)
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