Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]”[BIb 355a1 =fa0a2 =fa,aj = faj-lwhere f is a constant less than 1 and a. has been written in place of the initialvalue of a of unity to preserve a consistent symbolism. Note that we use the runningsubscript j to specify the general value of a or t in aparticular experiment; we shallreserve the subscript i to distinguish one experiment from another. From thegraph of ct against time, we read the corresponding times to, tl , t2, . . . tj . . . Itfollows from eqns. (17) and (18) thatIf we write ti for thejth time interval tj-tj- in which ci decreases by a factor fof its value at the beginning of the interval, eqn. (23) can be recast in the formlogl,zj = constant+{I-(a+b))logl, aj-, (24)Note that the first interval z, is the time taken for a to drop from a. to al, that isfrom 1 to$ The procedure to estimate (a+b) is thus:plot the experimental values of ci against (t- to) and draw a smoothed curvethrough the points;select a value off equal to 0.8 or thereabouts and read off from the abovecurve the times at which a,reaches the value f (i.e. al), f (i.e. a2), f (i.e. a3)etc.;hence calculate the time intervals for a to change from a, (i.e. 1) to cil, a,to a2, a2 to a3 etc., and plot the logarithms of these time intervals against thelogarithms of the values of a at the start of these intervals;measure the slope of the resulting straight line and hence, as shown in eqn.(24), calculate the value of @+b).Instead of utilizing the parameters +aj, the actual concentrations of the reactant A,[AIj, can be used; since [AIj = cij[Alb, eqn. (24) becomeslog,, zj = constant+(I-(a+b)} log,, [Alj-,References p. 407