xxviABBREVIATIONSNMRNuclear magneticYaMRcresonanceNRNR[not identified]Pol.Pol.PolarographicmethodPOLPOL[not identified]PRIPPulse radiolysisPSDFPPPhotochemical space discontinuityRICRRate of initiated chain reactionSTsIRRRCPRProducts of radical recombinationin cageRUCRRate of unbranchedchainreactionSTsNRSUNRSUNR[not identified]TIMITMTritium isotope methodTJTSTemperaturejumpTsINR[not identified]TsINRNote:For a Iisting of abbreviations for names ofligandsin metal complexes, see Chapter X, p. 482
xxvi NMR NR Pol. POL PR PSD RICR RRC RUCR SUNR TIM TJ TsINR Nuclear magnetic resonance [not identified] Polarographic method [not identified] Pulse radio lysis Photochemical space discontinuity Rate of initiated chain reaction Products of radical recombination in cage Rate of unbranched chain reaction [not identified] Tritium isotope method Temperature jump [not identified] ABBREVIATIONS YaMR NR Pol. POL IP FPP STsIR PR STsNR SUNR ITM TS TsINR Note: For a listing of abbreviations for names of ligands in metal complexes, see Chapter X, p. 482
PARTONEOFREACTIOONSMOLECULES
PART ONE REA C T ION S OF MOLECULES
ICHAPTERMONOMOLECULARREACTIONSl. MethodsforMeasuringRateConstantsofMonomolecularReactionsKinetics of Consumption of Starting Material (csM)a.A simple and widely used method for measuring rate con-stants is the calculation of k from the kinetic curve ofstarting material consumption.Monomolecular,decompositionis described by an exponential law, C = Coe-kt or in(C/c)= kt.The constant is found from the slope of the straightline plotted on coordinates of log Co vs.t. It is evidentthat k should not depend on Co.Nevertheless,in some cases,along with the monomolecular decomposition, an induced de-composition occurs.For example, benzoyl peroxide in certainsolvents decomposes monomolecularly with a velocity kC,andunder the action of free radicals with a velocity k'c3/2 (k'is the effective rate constant ofthe induced decomposition).The constant found experimentally from the initial section ofthe kinetic curve is ke - k + k'ci/2.The rate constant formonomolecular decomposition, k, is found by extrapolation:k=lim ke as cg/2+0, whereke=k +k'cj/2.Kinetics of End Product Formation (KEPF)b.The kinetics of the consumption of starting material canbe followed from the formation of a stable product of theThe rate of end-product accumulation isconversion.C = k[A] = k(Co - c),dt3
CHAPTER I M 0 NOM 0 L E C U L A R REA C T ION S §l. Methods for Measuring Rate Constants of Monomolecular Reactions a. Kinetics of Consumption of Starting Material (CSM) A simple and widely used method for measuring rate constants is the calculation of k from the kinetic curve of starting material consumption. Monomolecular decomposition is described by an exponential law, C = Coe-kt or In(Co/C) = kt. The constant is found from the slope of the straight line plotted on coordinates of log Co vs. t. It is evident that k should not depend on Co. Nevertheless, in some cases, along with the monomolecular decomposition, an induced decomposition occurs. For example, benzoyl peroxide in certain solvents decomposes monomolecularly with a velocity kC, and under the action of free radicals with a velocity k'C372 (k' is the effective rate constant of the induced decomposition). The constant found experimentally from the initial section of the kinetic curve is ke = k + k'Cb/ 2 • The rate constant for monomolecular decomposition, k, is found by extrapolation: k = lim ke as cb/2 ~O, where ke = k + k'Cb /2 • b. Kinetics of End Product Formation (KEPF) The kinetics of the consumption of starting material can be followed from the formation of a stable product of the conversion. The rate of end-product accumulation is iQ. = k [A] dt 3 k (Coo - C)
CHAPTERI4where A is the starting material and C@ is the concentrationof the end product when t +oo.The kinetics of end-product accumulation are described bythe formulaCooInkt.Coo- CThe rate constant is found from the slope of the straightline on coordinates ofCoovs.t,1ogCo-CSuch a method is widely used,particularly in studyingazocompounds,which decompose with N, evolution.The reactionkinetics are followed by measuring the volume of evolved gasand the rate constant is found from the relationVookt.10gVo-Initial Rate of Consumption of Free Radical Acceptorc.(ICA)In the decomposition of a molecule, two free radicals areformed; and for a certain time (1o-io sec) they exist side byside, surrounded by molecules of solvent(cageeffect).Partof the free radicals will react with each other to form mo-lecular products, and the remainder (which we will designateas "e") escape into the bulk volume as a result of diffusion.If a free radical acceptor is present in the solution, therate of free radical formation can be measured by the rate ofacceptor consumptionMaterials used as acceptors includeiodine, which reacts rapidly with radicals having a free va-lence on a c atom; oxidation inhibitors such as phenols,naphthols, and aromatic amines, which react rapidly withradicals of the Ro' and ROz type [1], and stable free radicals.If the acceptor is itself a free radical, then it reacts withone radical; the rate of change of acceptor concentrationW -Wi, where Wi is the rate of radical formation.If the ac-ceptor is, for example, molecular iodine, the disappearance ofone molecule of acceptor is accompanied by the destruction oftwo free radicals:R'+I2RI+I;I+R'W-1/2Wi.-RI;
4 CHAPTER I where A is the starting material and Coo is the concentration of the end product when t + 00. The kinetics of end-product accumulation are described by the formula Coo In -::-::- =< kt. Coo - C The rate constant is found from the slope of the straight line on coordinates of Coo logc oo _ C vs. t. Such a method is widely used, particularly in studying azo compounds, which decompose with N2 evolution. The reaction kinetics are followed by measuring the volume of evolved gas and the rate constant is found from the relation v 0<) log = kt. Yoo - Y c. Initial Rate of Consumption of Free Radical Acceptor (ICA) In the decomposition of a molecule, two free radicals are formed; and for a certain time (10-10 sec) they exist side by side, surrounded by molecules of solvent (cage effect). Part of the free radicals will react with each other to form molecular products, and the remainder (which we will designate as "e") escape into the bulk volume as a result of diffusion. If a free radical acceptor is present in the solution, the rate of free radical formation can be measured by the rate of acceptor consumption. Materials used as acceptors include iodine, which reacts rapidly with radicals having a free valence on a C atom; oxidation inhibitors such as phenols, naphthols, and aromatic amines, which react rapidly with radicals of the RO· and ROZ type [1], and stable free radicals. If the acceptor is itself a free radical, then it reacts with one radical; the rate of change of acceptor concentration W = Wi, where Wi is the rate of radical formation. If the acceptor is, for example, molecular iodine, the disappearance of one molecule of acceptor is accompanied by the destruction of two free radicals: R' + 12 - RI + r; r+R'-RI; W:01l2W j
5MONOMOLECULARREACTIONSIn the general case,Wi-fw.Radical acceptors react only with those radicals thathave escaped into the bulk volume.Since the decompositionof a molecule with the rupture of one bond will form tworadicals, then, when the cage effect is taken into account,the rate constant for the formation of radicals by initiatordecomposition ki = 2ek.Since Wi =kiCo and Wi-fw, thenki - fw/Co, where W is the rate of consumption of the freeradical acceptor. The experiment is designed so that theinitiator concentration remains practically constant duringthe course of the experiment.Having measured W and knowingf and Co, one can find k. The radical acceptor is introducedin a concentration such that practically ali the radicalswill react with the acceptor and not with each other. Theacceptor and the products of its conversion must not reactwiththe initiator.Sometimes it is not the radical acceptor consumptionthat is measured, but rather the induction period of a chainreaction (e.g., oxidation or polymerization) when known con-centrations of initiator and inhibitor (free radical accep-tor) are introduced into the system.If, during the induc-tion period, the initiator remains the sole source of freeradicals, if the inhibitor is consumed only in reaction withfree radicals, and if all chains are broken in reactions ofradicals with inhibitor, then Wi= f[InHlo/t, where t is theinduction period and [InHlois the initial inhibitor concen-tration; aiso, ki = f [InH]。/Cot, The constants ki and kare little different, since in the majority of cases e - O.4to 0.8, and ki is .8 to 1.6 times k.The difference inactivation energies Ei - E = Ee, about 2 to 4 kcal/mole.Kinetics of Radical Acceptor Consumption (KRAc)d.When the initial rate acceptor consumption is measured,only ki can be determined.If the experiment is conductedin such a manner that all of the initiator has decomposedduring this time, then the kinetic curve for consumption ofthefree radical acceptor can be used to determineboth kand e [2].Here the acceptor is added in large excess, sothat the radicals formed from the initiator will react withthe acceptor.The rate of acceptor consumption isd[InH.2ek-ktdt
MONOMOLECULAR REACTIONS 5 In the general case, Wi - fW. Radical acceptors react only with those radicals that have escaped into the bulk volume. Since the decomposition of a molecule with the rupture of one bond will form two radicals, then, when the cage effect is taken into account, the rate constant for the formation of radicals by initiator decomposition ki = 2ek. Since Wi = kiCo and Wi = fW, then ki - fW/Co ' where W is the rate of consumption of the free radical acceptor. The experiment is designed so that the initiator concentration remains practically constant during the course of the experiment. Having measured Wand knowing f and Co, one can find k. The radical acceptor is introduced in a concentration such that practically all the radicals will react with the acceptor and not with each other. The acceptor and the products of its conversion must not react with the initiator. Sometimes it is not the radical acceptor consumption that is measured, but rather the induction period of a chain reaction (e.g., oxidation or polymerization) when known concentrations of initiator and inhibitor (free radical acceptor) are introduced into the system. If, during the induction period, the initiator remains the sole source of free radicals, if the inhibitor is consumed only in reaction with free radicals, and if all chains are broken in reactions of radicals with inhibitor, then Wi = f[InH]o/T, where T is the induction period and [InH]ois the initial inhibitor concentration; also, k i = f [InH]o/CoT, The constants k i and k are little different, since in the majority of cases e = 0.4 to 0.8, and ki is 0.8 to 1.6 times k. The difference in activation energies Ei - E ~ Ee , about 2 to 4 kcal/mole. d. Kinetics of Radical Acceptor Consumption (KRAC) When the initial rate acceptor consumption is measured, only ki can be determined. If the experiment is conducted in such a manner that all of the initiator has decomposed during this time, then the kinetic curve for consumption of the free radical acceptor can be used to determine both k and e [2]. Here the acceptor is added in large excess, so that the radicals formed from the initiator will react with the acceptor. The rate of acceptor consumption is d [InH] 2 ek - dt = -,-