Chemical reaction rate expressions are usually given in terms of temperature dependent ѕ concentration independent reaction rate constant(s) and terms expressing the concentration dependence of the rate of reaction. An empirical observation is that the temperature dependence of reaction rate constants can be written in terms of:
the Arrhenius Equation, where k is the reaction rate constant; k0 the pre-exponential “frequency factor” (units similar to k); Ea the energy of activation (kJoule/mole; 50-250 kJoule/mole for most reactions); R, the gas constant, kJoule/(mol) (degree Kelvin); T, degree Kelvin (Atkins, 1986). Units of k are normally defined by the formulation of the reaction rate expression. Collision Theory and Transition State Theory require the frequency factor to contain a temperature dependent component (e.g., k0 = k0′Tm; 4 > m > 0). However, in experimental determinations of k, rapidly changing values of the exponential term tend to mask the temperature dependence of the frequency factor.
Experimental data on ln(k) vs. 1/T can usually be plotted as a straight line, k0 and E a are calculated from the intercept and the slope, respectively:
The constants can also be calculated from adjacent data points; where these calculations are performed using experimental data, however, this method would lead to severe inaccuracies unless some form of averaging or data smoothing is introduced, since the differentiation would tend to amplify the effects of experimental scatter.
Departures from linearity may be encountered (i) if the temperature dependence of k0 cannot be ignored, e.g., over large ranges of temperature, (ii) if the rate expression does not adequately represent the actual reaction scheme, e.g., the reaction scheme is more complex, or, (iii) if the reaction rate is not entirely kinetically controlled, e.g., mass transfer resistances should not have been ignored [Perry and Chilton (1984); Richardson and Peacock (1994)].
Atkin, P. W. (1986) Physical Chemistry, OUP, Oxford, UK.
Perry, R. H. and Chilton, C. H. (Eds.) (1984) Chemical Engineers’ Handbook, McGraw-Hill, New York, USA.
Richardson, J. F. and Peacock, D. G. (Eds.) (1994) Coulson and Richardson’s Chemical Engineering, Volume 3 (3rd edition), Pergamon, Oxford, UK.