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

∂ ln K eq
∂ (1/T) = - ∆Eo
R (18)
The Arrhenius relation, developed theoretically for reversible molecular
chemical reactions, has been experimentally shown to hold empirically for a number of
more complex chemical and physical phenomena (e.g., viscosity, diffusion, sorption).
Food quality loss reactions described by the aforementioned kinetic models have also been
shown to follow an Arrhenius behavior with temperature. For m th order systems shown in
Table 1 the reaction rate constant is a function of temperature (with the rest of E j factors
assumed constant) given by the following equation, directly obtainable from equation (18)
with k in place of K eq :
k = k A exp (- E A
RT ) (19)
with k A the Arrhenius equation constant and E A the excess energy barrier that factor A
needs to overcome to proceed to degradation products (or B to form), generally referred to
as activation energy . In practical terms it means that if values of k are available at different
temperatures and ln k is plotted against the reciprocal absolute temperature, 1/T, a straight
line is obtained with a slope of -E A /R.
ln k = ln k A - E A ⎛1⎞
R ⎝ T ⎠ (20)
If the rate constants k 2 , k 1 at two temperatures, T 2 and T 1 are known the Arrhenius
parameters can be calculated by the equations
⎛k 2⎞ R T 1 T 2
E A = ln ⎝ k 1 ⎠ T 2 - T 1 (21)
⎛ T 1
and k A = k
⎝ ⎠ ⎞
T 1 - T 2
1 k
⎝ ⎛ T 2
⎠ ⎞
T 1 - T 2
2 (22)
19