Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

410 TREATMENT OF EXPERIMENTAL DATAsimplify considerably once all the n-butyl lithium had reacted. This was found tobe the case. The procedure adopted was as follows: n-butyl lithium was allowed toreact with isoprene, the initial concentrations and the temperature being chosenso that no n-butyl lithium remained when all the isoprene had disappeared; theresulting mixture consisted of active centresCH.3CHSb I IC4H, (CH2-CH= C-CH,}! CH,-CH=C-CH,-Li+in equilibrium with an associated complex, probably involving four such molecules,which is incapable of initiating the polymerization of isoprene. The importantfeature from our point of view is that the active centres were capable ofinitiating the polymerization of a further sample of isoprene. Following thisargument one stage further, it was obviously possible in principle to study the rateof disappearance of this second charge of isoprene at a constant active centreconcentration and so obtain particularly simple kinetic behaviour, thusd[isoprene]- = k,[AC][isoprene]dt= k[isoprene]where k, the first order rate coefficient, includes the bimolecular rate coefficient,k,, and the constant active centre concentration, [AC].To prove these assertions, the rate of disappearance of isoprene had to be shownto be first order with respect to isoprene at a given active centre concentration.For this purpose, the concentration of isoprene was measured dilatometrically ata series of times following its addition to a solution of active centres; a series ofsuch experiments were carried out, some to test the reproducibility of the data andsome at different initial concentrations of isoprene. These data were analysed onthe basis of eqn. (36), the rate coefficients being obtained from the particular formof the general rate expressionnamely,f(a) = Z-k’(t-to)ha = 1-k(t-to)It should be noted that t%e iate coefficient k and the slope of the straight line off(a) uersus t - to, k‘, are identical in this case.Table 4 gives the results of a typical run; the concentrations of isoprene aregiven to rather more figures than the basic experimental data warrant so that no