Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

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3CHEMICAL RELAXATION METHODS129._ 6B+0U C8c y - . . . . .ITime -Fig. 5. Chemical relaxation in terms of the step-function model.reaction state in which there is no net rate of transformation, such as that foundat a fixed distance from the mixer in a flow-mix experiment, it is convenient to makethe derivation of relaxation times as general as possible.The full line in Fig. 5 represents the concentration of species i at times before andafter the application of the step-function (dashed line). cp is a time-independentreference concentration, while Ci is the corresponding (final) equilibrium value whichmight be time-dependent. Thenxi = ci-coand Xi = Zi-ci0and the rate can be written asi.e.,- d(Xi -xi) = (l/T)(Xi-xi)dtprovided that (Zi- xi)
130 EXPERIMENTAL METHODS FOR FAST REACTIONSand for small differences (Xi - xi)-when squared terms in xi and Xi can be neglectedNow, k,,CBZC = klzZA is the condition for equilibrium, hencewhich is the general equation (2) with (l/z) = [klz+kz1(CB+EC)].This illustrates an unusual feature about relaxation times: their expressions alwayscontain the sum of a contribution from the forward and the backward reaction.This has the convenient result that z is independent of the sign of the perturbation,i.e., it is immaterial for a determination of T whether the disturbance causesthe equilibrium to move to the left or to the right.TABLE 1RELAXATION TIMES IN TERMS OF EQUILIBRIUM CONCENTRATIONSAND RATE COEFFICIENTS FOR SINGLE-STEP REACTIONS (cf. Ref. 33)The expressions for T for a few single-step reactions are shown in Table 1. It isinteresting that in the case of a catalyzed reaction (5) (where the catalyst concentrationappears on both sides of the equilibrium) or a buffered system (6)(where theconcentration of the buffered species appears on one side of the equilibrium only)the only concentration term to appear in the relevant part of the expression for t-lis that of the catalyst (G) or the buffered reactant (EB). This is because the changesin concentration of these species (xc, and xB, respectively) are effectively zero,hence the terms in the relaxation expression which contain xc and xB must also bezero. The only terms which do not contain xc and xB are those in Cc and CB, respectively+.So far, only reactions which involve a single step have been considered. The na-t An important proviso for this is that the buffer equilibrium is established rapidly comparedwith the equilibrium under consideration.
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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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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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344 TREATMENT OF EXPERIMENTAL DATAf
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346 TREATMENT OF EXPERIMENTAL DATAp
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348 TREATMENT OF EXPERIMENTAL DATAg
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350 TREATMENT OF EXPERIMENTAL DATAT
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352 TREATMENT OF EXPERIMENTAL DATAW
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354 TREATMENT OF EXPERIMENTAL DATA[
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358 TREATMENT OF EXPERIMENTAL DATA(
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364 TREATMENT OF EXPERIMENTAL DATAv
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366 TREATMENT OF EXPERIMENTAL DATAW
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370 TREATMENT OF EXPERIMENTAL DATAc
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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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