Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

APPENDIX 2 417(d) CALcuLAnON OF FTABLE 7 (continued)636.6 x -3.743 x 104= 170.1The critical value of F,, (ix. F associated with 2 degrees of freedom in numerator and 99 degreesof freedom in denominator) is 3.09 (5 %) or 4.82 (1 %); these are the values which would beexceeded in 5 % or 1 % of cases if the group of rate coefficients were homogeneous. ClearlyF-1, >> FCrltlCaI and so the replicate experiments constituting the group are significantly differentfrom one another.to estimate s(E) from the residuals rather than from the equation sometimes used,uiz.1S2(Q = 1)=y i=,,1c c-o=l 151 S2(k,')In our case, this would give a totally misleading impression of the precision of thederived mean value of the rate coefficient (the actual value for s(Q calculated inthis way would be 0.006 x sec-'). It should be noted that we have used theresiduals (k,l-ko) as the basis of our calculation; it is quite permissible to usethe residuals calculated from the set mean rather than the group means-thisprocedure gives a slightly lower estimate for s(E) in our case but the general conclusionregarding our final value of li is not affected.The analysis of the data of the three replicate experiments shown in Table 7shows that significant differences exist between the rate coefficients. It is notdifficult to deduce the cause. Every value of k is the product of two factors: (a) therate coefficient k,, and (b) the active centre concentration [AC]. It is very likelythat the concentration of active centres is not exactly the same for each experimentof the groupt (and presumably the same comment applies to the whole set);within any one run, however, the value of [AC] remains constant giving a welldefinedstraight line of In a against ?- ?,. Consequently, the values of the variousrate coefficients are distributed about their mean to a greater extent than the scatterof the points about the corresponding straight lines would suggest.7 The presence in the reaction vessel of proton donating impurities such as water which destroythe lithiated polyisoprenes is a possible source of the irreproducibilities observed; small irreproducibleamounts of these impurities could give rise to a small variation in the active centreconcentration from run to run.