Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]"[B]' 359[A],, . . . [A],, , but at the same value of [B], , the relative values being such thatin every case [B],/[A],, was always greater than vB/vA. If the fundamental kineticequation, eqn. (1 l), correctly describes the disappearance of the reactants, eachof the resulting curves of a against log,, (t-to) should superimpose on the samecurve of a against log,, 8 shown in Fig. 1 with a scale displacement ofOn the other hand, there is a good case for performing the series of experimentsat different values of [A], and [B], chosen such that the ratio, [B],,i/[A]o,i, isthe same throughout and considerably greater than vs/vA. Again each of the curvesof a against log,, (t-to) should superimpose onthe same curve of a againstlog,, 8of Fig. 1 if eqn. (11) applies, but now each is displaced bylog,, k[A]:T!-'I*Since both k and Z are constants and a is known from the superimposition, anestimate of b can be obtained from the slope of the linear plot of scale displacementagainst log,, [A],, i.The fractional life methods can also be used to determine a. As already indicated,the fractional life method of treating the data of a single experiment has fewadvantages over the superimposition method and consequently need not be consideredfurther. On the other hand, the measurement of a particular fractional lifeof the reactant A in a series of experiments in which its initial concentration isvaried provides a means by which a can be determined which sometimes offersexperimental advantages. The only point to remember is that throughout the seriesof experiments [B], must be kept constant at such a value that [B],/[A],,, >>v,/v,. From the condition thatO(a*) = constant, a* = constantand eqn. (30), we have the expressionk[A]::/[B)b,(t,(a*)- to) = constantwhich clearly enables a to be found. Note that if [B], were varied with [A], sothat Z remained constant, these, experiments would yield (a+b) not a. Suitablevalues of a* lie in the range 0.5 to 0.8. -Finally, it should be obvious that the method of tangents can be equally wellapplied to the determination of a utilizing eqn. (29) in precisely the same way aseqn. (15).References p. 407