Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

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TABLE 1-- d [A1dtIntegrated form of rote equationk 1 -a = k[A],-l(t-t0) (34)1 kk[A]+[B] c=O - -1 = - [AIo+r(t-to)U* 2k[Al[Blc> 0 In {s]c 01 a+ kc
362 TREATMENT OF EXPERIMENTAL DATAIn principle, the procedure for the calculation of the rate coefficient is simple.For each run, the values of a and t are substituted in that integrated form of eqn.(1 1) which corresponds to the orders a and b suggested by the preliminary examinationof the data. Knowing the values of I, r, c, [A], and to, a series of values of kcan then be calculated which, provided that they show no systematic increaseor decrease with decreasing a, can be averaged to give a mean value. Alternatively,the appropriate function of a shown in Table 1 can be plotted against t and,provided that the experimental points show no systematic deviation from a straightline, an average value of k can be obtained from the gradient. If the values of kobtained in either of these ways do not vary from run to run, then not only do weobtain a reliable value for the rate coefficient but also we confirm the orders a andb deduced from the preliminary examination of the data. On the other hand, if asystematic drift of the calculated rate coefficient is observed within any one particularrun or from run to run, it can be concluded that either the incorrect integratedform of eqn. (1 1) has been chosen or that one of the more complicated rateexpressions such as eqns. (2), (3) or (4) is required; which of these two interpretationsis correct can be decided by attempting to fit the data to one of the otherintegrated forms of eqn. (1 1). If one cannot be found which gives a constant valuefor the rate coefficient, then another type of rate expression must be investigated.Within this general scheme, there are several different methods of performing thecalculation of the rate coefficient. As we shall show, each method weights theexperimental determinations rather differently and so each method yields a differentresult for the average value of the rate coefficient. The question as to which ofthese methods yields the best value of the rate coefficient will be deferred until themethods themselves are discussed. In the first place, we shall confine our attentionto the treatment of the data from a single run. In other words, we shall considerfirst the possible methods of calculating a value for the rate coefficient given oneset of values of t and a, uiz. (to, ao), (tl, al), (t2, a2), . . . (ti, aj), .. . (t", LX,,).Note that the first pair of values has been written (to, a,) instead of (to, 1) topreserve consistency in the symbolism.(a) Treatment of the data from a single runMethod I . Calculation of the rate coefficient from pairs of values of a and t.(i) Pairing each value oft and a with the initial values to and a,Each of the integrated forms of the rate equation may be writtenwheref(a,)-f(a) = k'(t-20) . (56)k' = mk
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COMPREHENSIVE CHEMICAL KINETICS
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P.O.ELSEVIER PUBLISHING COMPANY335
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Contributors to Volume 1L. BATTDepa
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XCONTENTS4.3 Gas chromatography ...
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XI1CONTENTS4.6 Magnetic measurement
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4 EXPERIMENTAL METHODS FOR SLOW REA
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8EXPERIMENTAL METHODS FOR SLOW REAC
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Reaction Furnace CircuitI10 EXPERIM
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12 EXPERIMENTAL METHODS FOR SLOW RE
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22 EXPERIMENTAL METHOD§ FOR SLOW R
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~~ ~36 EXPERIMENTAL METHODS FOR SLO
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100 EXPERIMENTAL METHODS FOR SLOW R
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Chapter 2Experimental Methods for t
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114 EXPERIMENTAL METHODS FOR FAST R
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;,124 EXPERIMENTAL METHODS FOR FAST
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178 REFERENCES46 M. EIGEN AND L. DE
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Chapter 3Experimental Methods for t
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182 EXPERIMENTAL METHODS FOR HETERO
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~~~ ._190 EXPERIMENTAL METHODS FOR
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192 EXPERIMENT A L MET H 0 D S F 0
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194 EXPERIMENT A L MET H o D s F o
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206 EXPERXMENTAL METHODS FOR HETERO
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222 EXPERIMENT A L METHODS F 0 R HE
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230 EXPERIMENT A L METHOD s FOR HET
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236 EXPERIMENT A L METHOD s FOR HE
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242 EXPERIMENT A L ME TH 0 D S FOR
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248 EXPERIMENT A L METHOD s F o R H
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254 EXPERIMENTAL MET HODS FOR HETER
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258 EXPERIMENT A L METHODS F 0 R HE
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266 EXPERIMENT A L MET H o D s F o
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270 EXPERIMENTAL MET HODS FOR HE TE
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274 EXPERIMENT A L METHOD s FOR HE
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280 DETECTION AND ESTIMATION OF INT
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Page 325 and 326: 310 DETECTION AND ESTIMATION OF INT
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41 2 TREATMENT OF EXPERIMENTAL DATA
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~~414 TREATMENT OF EXPERIMENTAL DAT
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41 8 TREATMENT OF EXPERIMENTAL DATA
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420 TREATMENT OF EXPERIMENTAL DATAA
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IndexAabsorption cross section, che
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424 INDEXbenzyl chloride, matrix ph
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426 INDEXchlorine (contdj—, react
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428 INDEXdeuterium oxide, addition
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430 INDEXentropy change, in radical
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432 INDEXfrequency of oscillation,
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434 INDEXhydrogen atoms (contdj—,
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436 INDEXisotopes (contd.J—, use
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438 INDEXmethyl radicals, chain ter
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440 INDEXoctadiene, ESR determinati
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442 INDEXphotoelectric measurement,
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444 INDEXrad, definition of, 66radi
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446 INDEXSchmidt number, and mass t
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448 INDEXTtailing reducer, in gas c
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450 INDEXviscosity, and diffusion c
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Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

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