Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

364 TREATMENT OF EXPERIMENTAL DATAvalue of k. In fact, the mean value of k is determined essentially by the earlyconcentration observations and the heavily overweighted initial value if thismethod of averaging is employed. The main objection to the use of this methodarises from the fact that large errors in the values of r, - to are probable at the earlystages of the reaction owing to the experimental difficulty of determining the exactvalue of to. Consequently the weighting factors in the most important contributionsto k,, are subject to fairly considerable errors particularly if the early timeintervals are very small. This, in turn, leads to considerable uncertainties in key and,therefore, this method of treating the data cannot be recommended.(ii) Using successive pairs oft and aTo avoid undue emphasis on the initial values of t and a, an average value of kcan be calculated by taking the pairsWriting, as before, k, for the rate constant derived from the jth pair, we havewhere k; is now given byPerforming the summation, we findIt is clear that each value of f(a) is weighted by the factor2rj-t,-1-t,+1&,- 2,- lW,+ 1 -tJwith the exception of the fist and last values of the set, f(ao) and f(q). Apart fromthe two times to and t,, any particular time t, is not usually very different from the