CHAPTERI6and the kinetics of acceptor consumption are described bythe formula2eC。kt[InH]-[InH]-(1or[InH]。-[InH]-kt.[In-TInHFrom the straight-line slope on coordinates of[InH]。 [InH].1og [Ing[In]vs.tk is found; from the difference [InH]。-[InH]o, e isdetermined:([In。-[IH。a2℃。Rate of Chain Reaction in Presence of Initiator (RIcR)e.Substances that decompose into free radicals are oftenused as initiators of chain reactions.In theliquid phasein the absence of inhibitors, chains are broken as a resultof encounters between two free radicals, at a constant ratekt.Therefore, the concentration of free radicals is(Wi/2kt)i72and the rate of the chain reactionWy=k,(2kg)-1/2[RH]VWi, where k, is the rate constant for thechain propagation reaction, and [RH] is the concentration ofthe reacting substance.1i the ratio kp/(2kt)1/2 is knowm,then, having measured Wy, one can determine W, according totheformulaV2kW[RH]whence one finds ki -Wi/Co.The experiment is generallyconducted in such a manner that the inhibitor concentrationremains practically constant during the time of measurement.If the chains are not very long (v < 20), one should takeinto account that the experimentally measured chain reactionrate W - Wy + Wi, and Wy = W - Wi.The ratio of the con-stants kp/ V2kt can be determined if the reaction is con-ducted with an initiator for which ki is known
6 CHAPTER I and the kinetics of acceptor consumption are described by the formula [InH] - o 2eCo -kt [InH] . -r- (1 . e ) or [InH] - [InHJ oo m 9 ~~~- - kt. [InH] - [InH]oo From the straight-line slope on coordinates of [InH] . log 9 [In H] '" vs. t k is found; from the difference [InH]o - [InH]oo, e is determined: f e=- 2 C o ([ In H] - o [InH] ). 00 e. Rate of Chain Reaction in Presence of Initiator (RICR) Substances thaL decompose into free radicals are often used as initiators of chain reactions. In the liquid phase in the absence of inhibitors, chains &re broken as a result of encounters between two free radicals, at a constant rate k t • Therefore, the concentration of free radicals is (Wi/2kt)1/2, and the rate of the chain reaction Wv = k (2kt)-1/2[RHJVWi' where kp is the rate constant for the cgain propagation reaction, and [RH] is the concentration of the reacting substance. If the ratio kp /(2kt )1/2 is known, then, having measured Wv ' one can determine Wi according to the formula =(W" V2k;)2, k [RH] p whence one finds ki = Wi/Co. The experiment is generally conducted in such a manner that the inhibitor concentration remains practically constant during the time of measurement. If the chains are not very long (v < 20), one should take into account that the experimentally measured chain reaction rate W = Wv + Wi' and Wv = W - Wi. The ratio of the constants kp / V2kt can be determined if the reaction is conducted with an initiator for which k i is known
MONOMOLECULARREACTIONS7f.Kinetics of Chain Reaction in Presence of(KICR)InitiatorIf the initiator is the sole source of radical formationin the system, and if the ratio k,/ /2kt does not changeduring the course of the experiment, then the chain reac-tion kinetics can be used to determine k and e for the ini-tiator,carrying the experiment upto complete consumptionof initiator [3]. The rate of the chain reaction, measuredas the rate of accumulation of product P,isP= kg(2 k, )-1/2 [RH] (kac)]1/2,dtPand C - Coe-kt. Consumption of the starting material issubject to the kinetic lawx(1 -。-0.5kt)[P]" [P] ,or[P]2k.[RH]Ikt[P]Inle[P]可2Vk,k11AXFromthe slope of the straight line on coordinates oflog [1/(1 - x)] vs. t, where x =[P]/[P]max,we find k;from [P]max we find e.Another method for determining k is to measure the rateof the chain reaction as it changes along thecourse of theexperiment (owing to initiator consumption):W~- k,(2 k,)-1/2 [RH) ( kec。)1/2。 - 0.5 kt,whenceInW,=InW-1/2kt.Chemiluminescence Method (CL)g.The oxidation of hydrocarbons is accompanied by a weakchemiluminescence generated by the reaction between twoperoxy radicals [4]. The intensity of chemiluminescenceI = 2nk,[RO;]2, where n is the quantum yield of light inthis reaction. If an initiator is added to the hydrocarbon,and if radicals are formed only from this initiator duringthe entire period of the experiment, then, by following the
MONOMOLECULAR REACTIONS f. Kinetics of Chain Reaction in Presence of Initiator (KICR) 7 If the initiator is the sole source of radical formation in the system, and if the ratio kp/ ~2kt does not change during the course of the experiment, then the chain reaction kinetics can be used to determine k and e for the initiator, carrying the experiment up to complete consumption of initiator [3]. The rate of the chain reaction, measured as the rate of accumulation of product P, is dt and C = Coe-kt • Consumption of the starting material is subject to the kinetic law or In [p] max . J kt [p] lIIax - [p] 2 From the slope of the straight line on coordinates of log [1/(1 - x)] vs. t, where x = [p]/[p]max' we find k; from [Plrnax we find e. Another method for determining k is to measure the rate of the chain reaction as it changes along the course of the experiment (owing to initiator consumption): whence InW . = In W - 112 kt. o g. Chemiluminescence Method (CL) The oxidation of hydrocarbons is accompanied by a weak chemiluminescence generated by the reaction between two peroxy radicals [4]. The intensity of chemiluminescence I = 2 n k t [ROi] 2, where n is the quantum yie ld of Ugh t in this reaction. If an initiator is added to the hydrocarbon, and if radicals are formed only from this initiator during the entire period of the experiment, then, by following the
8CHAPTER1change in chemiluminescence intensity, one can measure therate constant for initiator decomposition k [4].In thestationary state-ktI-2nk, [RO,nw-2enkC-2enkc.Io-kt.-ktandI=Ior1og-5IIn the experiment, the light intensity i is recorded.From a plot of log(Io/I) vs. t, we find the decompositionrate constant k. This method can be used to determine k insubstances that are subject to oxidation accompanied bychemiluminescence.The conditions are selected so that theoxidation products(peroxides)give practically nochaininitiation in comparison with that of the added initiator.52.RateConstants for DecompositionofPeroxideCompoundsBenzoyl peroxide decomposes as a result of O-o bondrupture:CgH,co-0o-cocgHs-+2 CgH,coo.Alongwithmolecular decomposition,inductivedecompo-sition of peroxide under the action of free radicals is oftenobserved.Therefore, to measure k,either the peroxidede-composition is carried out in the presence of a free radicalacceptor, or the decomposition rate constant measured in theexperiment is extrapolated to zero concentration of peroxide(see sl).The introduction of substituents into the benzenering changes k: Electropositive substituents accelerate,and electronegative substituents retard the peroxide decom-position (see Table 3). This is explained on the basis thatthe two benzoyloxy groups in the peroxide molecule are twomutually repelling dipoles.Substituents affect the dipolemoment of each of the groups and consequently affect theperoxide decomposition.For aromatic solvents (benzene, styrene, alkylaromatichydrocarbons),the averaged rate constant for benzoyl per-oxide decomposition is1ogk=14.48-30.8/0
8 CHAPTER I change in chemiluminescence rate constant for initiator stationary state intensity, one can measure the decomposition k [4]. In the 1 . 2 'Ikt [R02 ·] 2 ~ 'I wi and I . -kt e or o 10 10g_ . h. 1 In the experiment, the light intensity i is recorded. From a plot of 10g(Io/I) vs. t, we find the decomposition rate constant k. This method can be used to determine k in substances that are subject to oxidation accompanied by chemiluminescence. The conditions are selected so that the oxidation products (peroxides) give practically no chain initiation in comparison with that of the added initiator. §2. Rat e Con s tan t s for Dec 0 m p 0 sit ion of Peroxide Compounds Benzoyl peroxide decomposes as a result of 0-0 bond rupture: Along with molecular decomposition, inductive decomposition of peroxide under the action of free radicals is often observed. Therefore, to measure k, either the peroxide decomposition is carried out in the presence of a free radical acceptor, or the decomposition rate constant measured in the experiment is extrapolated to zero concentration of peroxide (see §1). The introduction of substituents into the benzene ring changes k: Electropositive substituents accelerate, and electronegative substituents retard the peroxide decomposition (see Table 3). This is explained on the basis that the two benzoyloxy groups in the peroxide molecule are two mutually repelling dipoles. Substituents affect the dipole moment of each of the groups and consequently affect the peroxide decomposition. For aromatic solvents (benzene, styrene, a1kylaromatic hydrocarbons), the averaged rate constant for benzoyl peroxide decomposition is log k . 14.48 - 30.8/(1
9MONOMOLECULARREACTIONSThe averaged value of the initiation rate constant fortertiary butyi peroxide in aromatic solvents (benzene,toluene,styrene, cumene) is1ogk-14.86-35.0/e.The averaged value of k for cumyl peroxide in aromaticand paraffinic hydrocarbons is1ogk=14.60-34.4/0.The rate constants and activation energies for decompo-sition of RooR peroxides (where R is ethyl, propyl, orprimary, secondary, or tertiary butyl)are very similar.Peroxides of the type0o-IC.H,CoOC(CHg'sandO-RSC.HAo1OOC(CHg'so-CR,"CC.H,COOOC(CH's"as is evident from Table 9, decompose with rate constantsthat are several orders of magnitude larger than k for thedecomposition of analogous peroxides that do not have anysubstituents in the ortho position or have only alkyl sub-stituents in the ortho position.This is explained on the basis that the I and S atomsand the double bond do participate in the act of decomposi-tion, formingabond withoxygen:..OC(CHg'sproducts.An analogous picture is observed in the decomposition ofsubstituted benzoyl peroxides (see Table 3).Hydroperoxides react actively with solvents having weakC-Hbonds,double bonds,or alcohol,or carboxyl groups.Evidently it is only in inert solvents such as benzene, ccl4,or fluorocarbons that one may observetrue monomoleculardecomposition of hydroperoxides at the O-o bond
MONOMOLECULAR REACTIONS The averaged value of the initiation rate constant for tertiary butyl peroxide in aromatic solvents (benzene, toluene, styrene, cumene) is log k a 14.86 - 35.0/8. The averaged value of k for cumyl peroxide in aromatic and paraffinic hydrocarbons is log k a 14.60 - 34.4/9. The rate constants and activation energies for decomposition of ROOR peroxides (where R is ethyl, propyl, or primary, secondary, or tertiary butyl) are very similar. Peroxides of the type o II 0- I C6H4COOC(CHS)S' /.,0 o-R S C6H4C", OOC(CHS )3 o-C R2 ~C6H 4COOOC (CH 3) 3' and as is evident from Table 9, decompose with rate constants that are several orders of magnitude larger than k for the decomposition of analogous peroxides that do not have any substituents in the ortho position or have only alkyl substituents in the ortho position. 9 This is explained on the basis that the I and S atoms and the double bond do participate in the act of decomposition, forming a bond with oxygen: An analogous picture is observed in the decomposition of substituted benzoyl peroxides (see Table 3). Hydroperoxides react actively with solvents having weak C-H bonds, double bonds, or alcohol, or carboxyl groups. Evidently it is only in inert solvents such as benzene, CC14, or fluorocarbons that one may observe true monomolecular decomposition of hydroperoxides at the 0-0 bond
10CHAPTERI53.DecompositionofAzoCompoundsThedecompositionof anazo compound,R-N2-R,results inthe formation of one molecule of nitrogen and two R radicals.Azo compounds are widely used in the laboratory as initiatorsand photoinitiators of radical chain reactions.They are alsoconvenient objects for studying the cage effect (see ChapterIII). Among the initiators of this class, the one that hasbeen studied in the most detail is azobisisobutyronitrile, thedecomposition rate constant of which changes very little fromsolvent to solvent (Table 12). The average value of decompo-sition rate constant for the azobisisobutyronitrile in aromat-ic solvents (according to the data of [108] is1ogk - 15.00 - 30.45e54.Decomposition at C-C,N-N,N-C,N-o,andC-Metal BondsThe C-C bond strength in paraffinic hydrocarbons is ap-proximately 80 kcal/mole, and these hydrocarbons do not decom-pose at C-c bonds at temperatures below 40oo. The introductionof phenyl groups into the hydrocarbon molecule weakens the C-cbond, owing to stabilization of the free radicals that areformed upon decomposition.For example, the strength of theC-c bond in butane,CH3CH2-CH2CH3,is Q=8o kcal/mole;in thehydrocarbon (CH3)2(CgH5)C-C(CgH5)(CH3)2,Q=50kcal/mole;inthe hydrocarbon (CH3)(CgHs)2C-c(CgHg)2(CH3), Q = 30 kcal/mole;and in hexaphenylethane, (cgH5)3C-c(CgHg)3, Q=19kcal/mole.In an analogous manner, the introduction of phenyl groupsinto compounds containing nitrogen will lead to a weakening ofN-N and N-c bonds (Tables 16 and 17).The decomposition ofdiazo compounds (Table 17) and triazene (Table 16) proceedswith the formation of a biradical and is facilitated to aconsiderable degree by the formation of the very stable nitro-gen molecule.The decomposition of N-nitrosoacylarylamines (Table 18)is apparently preceded by an intramolecular rearrangement withthe formation of an azo compound:C.HgN(N-O)COR- C.Hs-N=N-OCOR- CeHs* + N, + RCOO
10 CHAPTER I §3. Decomposition of Azo Compounds The decomposition of an azo compound, R-N2-R, results in the formation of one molecule of nitrogen and two R· radicals. Azo compounds are widely used in the laboratory as initiators and photoinitiators of radical chain reactions. They are also convenient objects for studying the cage effect (see Chapter III). Among the initiators of this class, the one that has been studied in the most detail is azobisisobutyronitrile, the decomposition rate constant of which changes very little from solvent to solvent (Table 12). The average value of decomposition rate constant for the azobisisobutyronitrile in aromatic solvents (according to the data of [108] is log k ~ 15.00 - ~ • 9 §4. Decomposition at C-C, N-N, N-C, N-O, and C-M eta 1 Bon d s The C-C bond strength in paraffinic hydrocarbons is approximately 80 kcal/mole, and these hydrocarbons do not decompose at C-C bonds at temperatures below 4000 • The introduction of phenyl groups into the hydrocarbon molecule weakens the C-C bond, owing to stabilization of the free radicals that are formed upon decomposition. For example, the strength of the C-C bond in butane, CH3CH2-CH2CH3, is Q = 80 kcal/mole; in the hydrocarbon (CH3)2(C6HS)C-C(C6HS) (CH3)2, Q = SO kcal/mole; in the hydrocarbon (CH3) (C6HS)2C-C(C6HS)2(CH3) , Q = 30 kcal/mole; and in hexaphenylethane, (C6HS)3C-C(C6HS)3' Q = 19 kcal/mole. In an analogous manner, the introduction of phenyl groups into compounds containing nitrogen will lead to a weakening of N-N and N-C bonds (Tables 16 and 17). The decomposition of diazo compounds (Table 17) and triazene (Table 16) proceeds with the formation of a biradical and is facilitated to a considerable degree by the formation of the very stable nitrogen molecule. The decomposition of N-nitrosoacylarylamines (Table 18) is apparently preceded by an intramolecular rearrangement with the formation of an azo compound: