Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

352 TREATMENT OF EXPERIMENTAL DATAWe shall call the dimensionless quantity 8 the reduced time. It is related to actualtime through the equationwhere I, stands for the time at which the reaction commenced. Integration ofeqn. (la), thusgivesor1{ 1 - -@+b)}=8 a+b#1l-(a+ b)-1na = 8 a+b = 1 (19)It is perhaps worth mentioning that eqn. (19) is only a special case of eqn. (18)so that it is not necessary to separate the general discussion of reactions with anyvalue of the total order from those with a total order of unity; in future, therefore,we shall use the general form (18).(i) Determination of order from the plots of a against log,, 8From any of the above equations, we see'that a is a unique function of 8 for agiven value of a+b. Fig. 1 shows the characteristic curves of a against loglo 8for (a+b) values: 0,0.5, 1.0, 1.5,2.0; the numerical data for these curves are givenin Appendix 1.From these curves, the total order of any reaction following the rate expression(11) can be found. First, we make the initial concentration ratio identical with theratio of the corresponding stoichiometric coefficients. Second, we convert theobserved values of the concentrations of A to the dimensionless quantity a bysimply dividing by [A],. Third, we plot a against log,, (t-to) on transparentgraph paper. Finally we superimpose this graph on one of the curves of a againstlog,, 8 (clearly the same scale intervals must be used for both graphs); the curveof a against log, , 8 which best fits the experimental data gives the value of (a+ b).