Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]"BIb 357difficult and, therefore, the points on the graphs corresponding to either eqns.(26) or (27) are likely to show considerable scatter about a straight line. Thisscatter arising from incorrect construction of the tangents is liable to introduceconsiderable uncertainty into the estimated value of (u+b). For this reason, theapplication of this method to the problem of estimating the total reaction orderin the case of a comparatively simple reaction with constant, known stoichiometry(the case under discussion) has no advantages over either the superimposition orfractional life methods. With complicated reactions, however, the constructionof tangents is sometimes the only way of obtaining essential clues as to the type ofkinetic expression required and, therefore, this procedure is not without its merits.Before dismissing the tangent method, we should mention a slight variant whichbecomes possible when small concentrations of product are experimentally detectable(as, for example, in a reaction yielding a coloured product with a very highextinction coefficient). In these circumstances, the appearance of the product canbe followed under conditions where the concentrations of the reactants remaineffectively constant at their initial values and so we can writeinitialThis equation defines the initial rate of formation of product for a reactionproceeding at constant volume in which the initial concentration ratio I is identicatwith the stoichiometric ratio r. It follows from eqn. (15) by writing a = 1 andda = [A]; d[A], or more directly from eqn. (11) and the definition of r. Clearlythe product concentration-time curve is almost linear in the very early stagesof the reaction (say from a = 1.0 to 0.95) and, therefore, provided it can be accuratelydefined by making a series of accurate determinations of [PI and i in thisregion, the measurement of initial rate presents no problem. A series of suchmeasurements at differing values of [A], (and [B], to keep I = r) enables thevalue of (a+b) to be found on the basis of the analogous equation to (27), uiz.This method is very useful in that the total order of the reaction can be estimatedwithout having to follow the rwtbn to large extents; it must be remembered,however, that it requires accurate measurements of small concentrations of productand a procedure for mixing the reactants in a much shorter time than that requiredfor 1 % of either to disappear-from this latter point of view, the method canonly be applied to fairly slow reactions.References p. 407