Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

360 TREATMENT OF EXPERIMENTAL DATA(c) Estimation of the order, bThe simplest procedure is to deduce the value of b from the values of (a+b)and a determined in the manner previously described.AlternativeIy, it may be obtained independently by essentially the same procedureas outlined for the determination of a. It is clear that we can write for everyequation in a an exactly analogous equation in fi where fi represents the dimension-less ratio [B]/[B], and so all previous arguments concerning a are applicablewith minor modifications to fi. Thus the order with respect to B can be determinedby following the disappearance of B in the presence of a large excess of A usingsimilar arguments to those previously described.2.1.2 Calculation of the rate coescientAlthough the rate coefficient can be obtained as a by-product of the methodsdescribed for the estimation of the orders a and by it is best obtained from theintegrated form of the general rate equation--= d[A1dtk[AJ”[BIbIn terms of the parameters a, I, r and t, we may writebtda = k[A];+b-’1 a”(I-r+ra)b-Iwhich becomeswhereIc=- -1(33)rTable 1 lists the forms of the integrated expressions for common values of aand b; in certain cases, the integral differs according to whether c is positive ornegative and therefore both forms have been given in the table; in other cases,the general expression becomm indeterminate when c equals zero and a specialform of the integral must be used-where appropriate these special cases are alsoshown in the table. It should be appreciated that when c is less than zero, that is,when A is in excess of By the reaction stops when the value of a reaches -c; at thispoint, the concentration of reactant B is zero.