Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

404 TREATMENT OF EXPERIMENTAL DATA4.1 INFLUENCE OF TEMPERATURETheories of reaction rates suggest that the rate coefficient is related to absolutetemperature by the expressionk = A(T) exp (-E(T)/RT) (90)where E(T) is termed the activation energy and A(T) is the pre-exponential factor.In the majority of rate studies, the temperature variation of the activation energyand pre-exponential factor can be disregarded over the small temperature rangesnormally employed and so eqn. (90) may be writtenk = A exp (-E/RT) (91)Our object in this section is to indicate how the best values of A and E togetherwith their standard errors are obtained from the experimental data. We writeEInk = 1nA- -RTand fit a weighted least squares line through the points (l/T, In k) assuming thatthe temperatures are error-free; this assumption needs no defence for data obtainedin the usual way since accurate thermostatting presents few problems. The equationsare exactly similar to eqns. (58)-(64), namelyE-=RIn Awhere N is the number of different temperatures used in defining the line1xs = -T,and k, represents the (weighted) mean value of the rate coefficients determinedat the temperature T,. The value of the weight, w,, attached to each point is foundin the usual way, thus