Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

370 TREATMENT OF EXPERIMENTAL DATAcare being taken to avoid including measurements of a obtained in the very earlystages of the reaction where the rate is not characterized by a single value of therate coefficient. It is not suggested that the time taken for temperature equilibrationis the sole factor introducing systematic errors in the reaction time; indeed, it issometimes possible to design the experimental procedure so that such errors arepractically eliminated. The point is that the calculated value of the rate coefficientis unaffected by systematic errors in the reaction time provided that the data arenot constrained to eqn. (56).For the ith run, therefore, we determine the parameters of the weighted leastsquares line through the points {(rij- tie), f(aij)}, viz. Zi and k; in the equationf(aij1 = k-k;(tij-tio) (57)where k’i = miki. WritingandYij = f(aij)xij = tij-t,,and assigning a weight wij to the jth point, these quantities are obtained from thefollowing equationsj=ni j=ni~~‘wijXij)~~wijuij)-( c wij)( c wiwhereIn addition, two other quantities should be calculated. These arewhere Jij, the deviation of the experimental value of f(aij) from the value calcufrom eqn. (57), is given by .