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

In Fig. 12a aspartame concentration (APM or A) is plotted vs. time at the 5
temperatures. The best linear fit of the form Q(A)=kt was achieved for Q(A)=ln(A/A o ),
i.e. first order kinetics (Fig.12b). All measurements were included in the statistical analysis
(no averaging of the 3 samples per time) to increase the degrees of freedom and include the
measurement spread in the model. Calculated rate constants and 95% C.I. are given in
Table 10.
Table 10. Aspartame degradation reaction rate constants with confidence intervals at 5
temperatures.
Rate constant 30 o C 20 o C 10 o C 4 o C 0 o C
-k (hr -1 ) 0.0125 0.00356 0.00138 0.00121 0.000790
± 95% C.I. ± 0.0013 ± 0.00046 ± 0.00010 ± 0.00009 ± 0.000062
Figure 12.
Aspartame degradation kinetics at five temperatures plot as
function of time and as semi-log plot
To determine the Arrhenius parameters, -k is plotted in a semilogarithmic scale
vs.the inverse of absolute temperature (or ln(-k) vs. 1/T). To increase the degrees of
freedom and get a narrower confidence interval for the calculated parameters, the 95% C.I.
for k are included (Fig. 13). The Arrhenius plot gives by linear regression the values of
k o =3.163 108 hr -1 and activation energy E A = 14560 cal/mol. The coefficient of
determination, R 2 , is 0.952 and the 95% confidence interval 1830 cal/mol.
61