We derived a general expression for the time and temperature dependenc
e of both the hardening and the softening rates of vegetables during c
ooking on the basis of rate laws. The vegetables studied were such roo
t vegetables as Japanese radish, carrot, burdock and potato. Our kinet
ic model was based on the following two assumptions: (1) Pectin is tra
nsformed into three forms, i.e., the unchanged pectin, the hardening p
ectin and the softening pectin. (2) Each pectin contributes additively
to the hardness of the vegetables. Considering the causes of the hard
ening and the softening as enzymatic deesterification and beta-elimina
tion, respectively, first-order rate laws were applied to the formatio
n of each pectin and to the inactivation of the enzyme. Rate constants
for relevant processes were determined at different temperatures by f
itting integrated rate equations to the cooking data by the least-squa
res method. The hardness calculated from the derived expression was in
good agreement with the experimental values for all samples. Using th
e kinetic parameters determined here, we could reproduce not only the
simultaneous occurrence of the hardening and softening processes but a
lso the desired cooking time for optimum hardness. The hardening rate
constant showed Arrhenius behavior between 54 and 63 degrees C, but a
non-Arrhenius one at higher temperatures. It was suggested that the ha
rdening process was complex in the high temperature region of 70-99.5
degrees C.