Nonisothermal kinetics — comparison of two methods of data treatment

Abstract

A kinetic study of the acid-catalyzed hydrolysis of p-nitrophenyl acetate was carried out by subjecting the reaction mixture to a linear increase in temperature. Two commonly used methods of data treatment were compared to determine the precision and limitations of each. In the first method, the concentration data were transformed by a function dependent on reaction order. The resulting function was fitted to a power series with time. The derivative of this equation provided a rate constant at each temperature. A subsequent Arrhenius plot gave an estimation of the pseudo first-order rate constant at 25°C. After a correction was made for the rate of uncatalyzed hydrolysis, the second-order rate constant for acid-catalyzed reaction was determined. The values of E (activation energy) and Z (pre-exponential factor) determined by this method were dependent on the number of terms used in the polynomial fit (see Table 1). In a second data treatment, the temperature values were fitted to a polynomial with respect to time. Using initial estimates of E and Z, predicted concentrations were evaluated by numerical integration of the rate expression. A sequential simplex algorithm (Deming and Parker, 1978) located values for E and Z that satisfied the least-squares criterion. The integration method generated approximations of E, Z, and the second-order rate constant, k H, which to 3 significant figures did not vary with the number of polynomial terms. The latter method did, however, require an extensive amount of computer time, depending on the initial estimates used in the algorithm. Both techniques yielded similar rate parameter estimates which agreed favorably with literature values (Tucker and Owen, 1982; Eriksen and Stelmach, 1965; Connors, 1963; Bruice and Schmir, 1957).