Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

APPENDIX 2 41 1errors from rounding up at too early a stage appear in the final result. The techniqueemployed did not permit observations to be taken at the very early stages ofthe reaction; the time to was the time at which the dilatometer containing thereaction mixture was placed in the thermostat and was not the time at which thereactants were mixed together. Since the first value of a which was measured was0.7290, the fraction of the reactant which had disappeared prior to observationsbeing taken was 0.2710; this is rather greater than would be the case in most kineticstudies and, of course, is undesirable in that valuable information can sometimesbe obtained from a study of the initial period. However, the fact that only a portionof the reaction has been studied causes no difficulty since the arguments are basedon the comparison of the slopes of the least squares lines which are not constrainedto pass through the point {to, 0) (the value of f(cr,) is In 1, i.e. zero, forafirst orderreaction). Fig. 5 shows graphically the accuracy with which the data fit the equationlncr = 2-k(t-to)TABLE 4CONCENTRATION OF ISOPRENE AT A SERIES OF TIMES, AND COMPARISON OF OBSERVEDAND CALCULATED VALUES OF In a FOR RUN 1 OF THE SET DISCUSSED IN THE TEXTr-r, [Isoprene] a In a In QCEIC 6 In acslc 5min mole . litre-l These values were cal- These values were calculatedfrom least culated from leastsquares estimates of I squares estimates of 1and k, weighting each and k weighting eachpoint according to point equally, i.e.w, = a9w, = 12.253.506.257.759.5011.5013.0015.5018.0020.5022.0026.0028.003 1 S O34.0037.0040.0043.0046.0050.0055.0060.001.23201.16301.02700.97290.89730.82580.77430.68640.62530.56310.52790.44520.41 130.35060.31660.281 10.24810.21500.19080.16540.13470.10780.72900.68820.60770.57570.53090.48860.45820.40620.37000.33320.31240.26340.24340.20750.18730.16630.14680.12720.11290.09790.07970.0638-0.3161 -0.3218-0.3737 -0.3751-0.4981 -0.4922-0.5522 -0.5560-0.6331 -0.6305-0.7161 -0.7157-0.7805 -0.7796-0.9010 -0.8860-0.9943 -0.9925- 1 .@90 - 1.0990-1.1636 -1.1628-1.3340 -1.3332-1.4132 -1.4183-1.5728 -1.5674-1.6748 -1.6738-1.7938 -1.8016-1.9187 :i.9293-2.0618 -2.0571-2.1813 -2.1848-2.3241 -2.35S1-2.5294 -2.5680-2.7522 -2.78100.00570.0014-0.00590.0038-0.0026-0.0004-0.0009-0.0150-0.0018O.oo00-0.oob8--0.00080.0051-0.0054-0.00100.00780.01060.00470.00350.03 100.03860.0288-0.3293-0.3819-0.4976-0.5608-0.6344-0.7186-0.7818-0.8870-0.9922- 1.0974-1.1606- 1.3289- 1.4131-1.5604-1.6657-1.7919-1.9182-2.0445-2.1707-2.3391-2.5496-2.76000.01320.0082-0.00050.00860.001 30.00250.0013-0.0140-0.0021-0.0016-0.0030-0.0051-0.o001-0.0124-0.0091-0.0019-0.0005-0.0173-0.01060.01 500.02020.0078