A time-lag method for second-order kinetics

2Kezdy,F.J.,Kaz,J., Bruylants, A.,Bu11. SOC. Chim. Belges 67,687. (1958). 3Swinbourne, E. S., J. Chem. Soe., 2371 (1960). 'Raseaveare, W. E., J. Arner...
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James H. Espenson Iowa State University Ames, IA 50011

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A Time Lag Method for Second-Order Kinetics

When reaction rates are studied by instrumental methods such as spectrophotometry, it often happens that the "end point" (or "infinity") reading may be unknown or uncertain. For first-order reactions the familiar Guggenheim' and K ~ z r l ~ - J w i n h ~ , ~mt.thcnda l r ~ , e ~ ~afford ' onr means of circumvrntlng the need l m a relial~lrend point. These are termed time I:IE mefhds. in that the kinetic data are divided into two groups, each member of which consists of a pair of values seoarated bv a constant time interval 7. A similar method does not appear to have been developed4 for reactions followina a rate law with a second-order dependence on the conceint;ation of a single component (eqn.~l): -d[A]ldt = k[AI2 (1) The purpose of this paper is to present such a method, which is applicable also for the mixed second-order rate equation, -d[A]ldt = h[A][B], hut only when the reactants and products are present a t equivalent concentrations. The integrated form of the rate law is [Alt = [ A ] d l l + h[A]otJ.This can be transformed into a relationship involving an experimentally measured property P to which each reactant and product contributes in direct proportion5 to i t s concentration; other c