ABSTRACT
The integral in eq. 6.13 is evaluated numerically by the trapezoidal rule in the computer program (see section 6.1.5). As a check, the numerical integration of the peak represented by equation 6.13 was unity (within single-precision roundoff error), which is as expected when integrating a unitless fraction. The choice of Tr does not effect the location or shape of the peak, with exception if Tr is chosen too high (such that the function to be integrated in eq. 6.13 deviates appreciably from zero), then the assumption in eq. 6.10 that X= 1 when t = 0 is not valid, hence eq. 6.13 would not be valid. This equation adopts an asymmetrical shape as shown (after multiplying by A1 or A2 ) by either one of the dotted lines in Figure 6.3. By inserting eq. 6.13 into eq. 6.6, and by designating coefficient values A1 = -1 W·min (-60 J), ko 1 = 9 x 107 min-1, Ea1 = 105000 Jfmol, A2 = -.7 W·min (-42 J), ko2 = 1 x 108 min-1, and Ea 2 = 120000 Jfmol (<P = 10 °C/min assigned), the plot shown by the thick-lined trace in Figure 6.3 was obtained.
