《物理化学实验》课程教学资源（书籍文献）Liquid-Phase Reaction Rate Constants，E. T. Deni soy（PDF电子书）

MONOMOLECULAR REACTIONS11Nitrogen pentoxide decomposes with the rupture of anN-o bond:O,N-O-NO2-NO,+ NO,Theend products of the decomposition are 02and N204.Decomposition in solution proceeds with the same rate con-stant as in the gas phase.Nitro compounds decompose in accordance with first-order kinetics.It has been postulated (but not strictlyproved) that the decomposition is limited by the rate of O-Nbond rupture in the case of nitrate esters and by the rateof C-N bond rupture in the case of nitro compounds (themechanism of nitro compound decomposition is discussed in[179]).55.Decomposition of IodobenzeneDichlorideIodobenzene dichloride decomposes with the formation ofC6HsI and one molecule of chlorine:it is used in thelabora-tory as a chlorinating agent. The reaction proceeds with achange in the valence state of the I atom.IftheCl2isnotabsorbed by the solvent or lost into the gas phase, an equi-librium is established:CeH,IC1,CHgI+C12'forwhichH=9.9kcal/moleand△S=20.4cal/degree[194].Polar ortho-substituents on the benzene ring accelerate thedecomposition reaction by approximately two orders of magni-tude,apparentlytaking a direct part in the formation of anactive complex.s6.CorrelationEquationsHammett Equation. In the decomposition of compoundshaving structures that include a substituted benzene ring,a linear relation is often observed between log k and theHammett function,: i.e.,log(k/ko)po.The Hammettfunction is g = log(K/K.) where K is the dissociation con-stant of benzoic acid with a substituent in the para ormeta position, in aqueous solution at 25, and K。 is thecorresponding value without substituentFor electropositive

MONOMOLECULAR REACTIONS Nitrogen pentoxide decomposes with the rupture of an N-O bond: 11 The end products of the decomposition are 02 and N204. Decomposition in solution proceeds with the same rate con￾stant as in the gas phase. Nitro compounds decompose in accordance with first￾order kinetics. It has been postulated (but not strictly proved) that the decomposition is limited by the rate of O-N bond rupture in the case of nitrate esters and by the rate of C-N bond rupture in the case of nitro compounds (the mechanism of nitro compound decomposition is discussed in [179]). §5. Dec 0 m p 0 sit ion 0 flo d 0 ben zen e Dichloride Iodobenzene dichloride decomposes with the formation of C6HSI and one molecule of chlorine; it is used in the labora￾tory as a chlorinating agent. The reaction proceeds with a change in the valence state of the I atom. If the C12 is not absorbed by the solvent or lost into the gas phase, an equi￾librium is established: for which ~H = 9.9 kcal/mole and ~s = 20.4 cal/degree [194]. Polar ortho-substituents on the benzene ring accelerate the decomposition reaction by approximately two orders of magni￾tude, apparently taking a direct part in the formation of an active complex. §6. Cor r e 1 a t ion E qua t ion s Hammett Equation. In the decomposition of compounds having structures that include a substituted benzene ring, a linear relation is often observed between log k and the Hammett function, cr ; i.e., log(k/ko) = po. The Hammett function is 0 = 10g(K/Ko) where K is the dissociation con￾stant of benzoic acid with a substituent in the para or meta position, in aqueous solution at 250 , and Ko is the corresponding value without substituent. For electropositive

12CHAPTERIsubstituents such as CHa or CHgo, < O; and for electro-negative substituents such as Ci, NO2, or cN, > o.In thecase of decomposition of substituted benzoyl peroxides andsubstituted peroxides of the general formula xCgH4cooococH3,the coefficient p is negative (see Table 22); i.e., electro-positive substituents accelerate the peroxide decomposition.For decomposition of peroxides XCgH4CH2Coooc(CH3)3,a linear(Table 22).Thecorrelation exists between log k and g+functionot_ 1og(k/k.)Q。where k is the rate constant for solvolysis of XCgHyc(CH3)2Clin 90% acetone at 25°, k。 is the solvolysis constant forCgHgC(CH3)2C1,and1og(k/k。)P。0-00for substituents in the meta position.In this case also,pis negative. However, the correlation between k and isnot always observed.In the decomposition of N-nitroso-acylarylamines,the decomposition rate constant is indepen-dent of the substituent x (independent of ).Compensation Effect. For a group of monotypical reac-tions,an increase in the preexponential factor is observedas the activation energy increases:AlogA-a.AE orAHtβASt.At the isokinetic temperature β = 1/4.575α, the rate constantsof all reactions of a given series are identical. Since therelation between log A and E is approximately linear, then atthe isokinetic temperature the differences among the rateconstants of the series are minimal.The linear relation between log A and E is followedrather well for the decomposition of diacyl peroxides, di-alkyl peroxides, dinitriles of azo acids, etc.(see Table 23).However, in certain cases, for example, in the decompositionof polyphenylethanes, this relation is not followed; logA 16 for a change in E from 30 to 50 kcal/mole.Apparentlythe linear relation between Ast and Ht is fulfilled only fora variation ofHtwithin a certain interval, and at veryhigh or low values ofAHt this relation is not valid

12 CHAPTER I substituents such as CH3 or CH30, 0 < 0; and for electro￾negative substituents such as Cl, N02, or CN, 0 > 0. In the case of decomposition of substituted benzoyl peroxides and substituted peroxides of the general formula XC6H4COOOCOCH3, the coefficient p is negative (see Table 22); i.e., electro￾positive substituents accelerate the peroxide decomposition. For decomposition of peroxides XC6H4CH2COOOC(CH3)3' a linear correlation exists between log k and 0+ (Table 22). The function + a . log( k/kol Po where k is the rate constant for solvolysis of XC6H4C(CH3)2Cl in 90% acetone at 2So , ko is the solvolysis con.stant for C6HSC(CH3)2Cl, and 0-00 for substituents in the meta position. In this case also, p is negative. However, the correlation between k and 0 is not always observed. In the decomposition of N-nitrosa￾acylarylamines, the decomposition rate constant is indepen￾dent of the substituent X (independent of 0 ). Compensation Effect. For a group of monotypical reac￾tions, an increase in the preexponential factor is observed as the activation energy increases: tJ. log A" o· AE or AH~" ~AS". At the isokinetic temperature S = 1/4.S7S a, the rate constants of all reactions of a given series are identical. Since the relation between log A and E is approximately linear, then at the isokinetic temperature the differences among the rate constants of the series are minimal. The linear relation between log A and E is followed rather well for the decomposition of diacyl peroxides, di￾alkyl peroxides, dinitriles of azo acids, etc. (see Table 23). However, in certain cases, for example, in the decomposition of polyphenylethanes, this relation is not followed; log A ~ 16 for a change in E from 30 to SO kcal/mole. Apparently the linear relation between ~S~ and ~H~ is fulfilled only for a variation of ~~ withi~ a certain interval, and at very high or low values of ~H this relation is not valid

MONOMOLECULARREACTIONSof57EffectPressureSolyentandonMonomolecular ReactionsEffect of Pressure. The theory of absolute reaction rategives the following relation between the pressure P and thechange in molar voiume vt in the formation of an activatedcomplex:4V+alogkRTaPITFor a monomolecular reaction,in which one bond is broken, thevolume of the activated complex must be greater than that ofthe original molecule, and k must decrease with increasingpressure. This is indeed observed in the majority of cases(see Table 24). From the magnitude of v+one can calcu-late approximatelythe lengthening of the broken bond in theactivated complex.Forexample,inthedecomposition ofbenzoyl peroxide, V+ = 1o cm3/mole,which corresponds to anextension of the O-0 bond in the activated complex by .4 A[2oo].In the decomposition of the peroxide of isobutyricacid,v+ has a negative value, i.e.,the decomposition isaccompanied by a compression of the molecule.This is ex-plained by the rupture of several bonds and by the followingstructure ofthe activated complex:OO.OR-OCRO-CRR.0-aIt is possible that the activated complex in the decomposi-tion ofO=-0-0-C(CHg'3CeH,CH,C(see Table 24) has a similar structure.Three factors affect the decomposi-Effect of Solvent.tion of a molecule in solution:the internal pressure of thesolvent, the cage effect, and the polarity of the solvent.The internal pressure in,organic solvents can vary over therange 1-7-103 atm.If Av+-10 cm3/mole and P changes by5.103 atm, then at 4000KAPAV?alogk-or1ogk=-0.66,RT

MONOMOLECULAR REACTIONS 97. Effect of Pressure and Solvent on Monomolecular Reactions Effect of Pressure. The theory of absolute reaction rate gives the following relation between the pressure P and the change in molar volume f, vi: in the formation of an activated complex: ( Hog k ) AV'" -=-. ~p T RT For a monomolecular reaction, in which one bond is broken, the volume of the activated complex must be greater than that of the original molecule, and k must decrease with increasing pressure. This is indeed observed in the ~jority of cases (see Table 24). From the magnitude of f, V, one can ca 1cu￾late approximately the lengthening of the broken bond in the activated complex. For example, in the decomposition of benzoyl peroxide, f,V# = 10 cm3/mo1e, which corresponds to an extension of the 0-0 bond in the activated complex by 0.4 K [200]. In the decomposition of the peroxide of isobutyric acid, f,V# has a negative value, i.e., the decomposition is accompanied by a compression of the molecule. This is ex￾plained by the rupture of several bonds and by the following structure of the activated complex: ~ 0 0 Cjf R-~-O-O-~R - R . ~ . O~R. ~ It is possible that the activated complex in the decomposi￾tion of o C6H5CH2~-O-O-C(CH3)3 (see Table 24) has a similar structure. Effect of Solvent. Three factors affect the decomposi￾tion of a molecule in solution: the internal pressure of the solvent, the cage effect, and the polarity of the solvent. The internal pressure in organic solvents can vary over the range 1-7.103 atm. If f,V# = 10 cm3/mo1e and P changes by 5.103 atm, then at 400~ ~p flV'" fl10g k '=' - .;;;,-;;;.:.- or fl log k = -0.66, RT

CHAPTERI14i.e., k/k = 0.22. Thus, the internal pressure of the solventcan change k as much as twofold or fivefold.If only one bond is broken in the decomposition of acompound, and if the radicals that are formed do not undergoinstantaneous rearrangement or decomposition, then the radi-cals may recombine in the solvent cage, reverting back to theoriginal compound.In this case, one determines experimental-ly the apparent rate constant for consumption of the startingmaterial, k.app-k(1 e),wherek is the true constantaofdecompositior.For acetyl peroxide, the existence of such aform of recombination of acetyl radicals was demonstrated in[206] by means of the isotope o18 (for more detail on thecage effect, see Chapter III).Such a back-recombinationapparentlycan takeplacefor peroxides that decomposewiththe rupture of only one O-o bond, for polyphenylethanes, andforpolyphenylhydrazines.Apparently these two factors are the extent of the sol-vent effects on the decomposition of such compounds as hexa-phenylethane and a number of peroxides (see Table 25).Azocompounds R-N=N-R decompose simultaneously at two C-N bonds.Therefore, the cage effect should not affect k as measuredby the kinetics of starting-material consumption or nitrogenevolution.As is evident from Table 25, k for the decomposi-tion of the azobisisobutyronitrile or azoethylbenzene is verylittle changed from solvent to solvent.The decomposition of benzoyl peroxide or the peroxide ofisobutyric acidis strongly dependent on the solvent, which isexplained by the influence of solvent polarity.The benzoylperoxide molecule may be regarded as two mutually repellingdipoles, each of which is readily polarized by the surroundingmolecules (easy polarizability is caused by the -electrons ofthe benzene ring).This leads to a certain change in the bondenergy in the benzoyl peroxide molecule when the polarity ofthe medium is changed.The effect of solvent polarity on kfor decomposition of the peroxide of isobutyric acid is ex-plained by the polarity of a transitional complex having thestructure.Oc.8The formation of such a complex is facilitated in a polarsolvent, since the solvation energy of the transitional com-

14 CHAPTER I i.e., k/ko = 0.22. Thus, the internal pressure of the solvent can change k as much as twofold or fivefold. If only one bond is broken in the decomposition of a compound, and if the radicals that are formed do not undergo instantaneous rearrangement or decomposition, then the radi￾cals may recombine in the solvent cage, reverting back to the original compound. In this case, one determines experimental￾ly the apparent rate constant for consumption of the starting material, kapp = k(l - e), where k is the true constant of decomposition. For acetyl peroxide, the existence of such a form of recombination of acetyl radicals was demonstrated in [206] by means of the isotope 018 (for more detail on the cage effect, see Chapter III). Such a back-recombination apparently can take place for peroxides that decompose with the rupture of only one 0-0 bond, for polyphenylethanes, and for polyphenylhydrazines. Apparently these two factors are the extent of the sol￾vent effects on the decomposition of such compounds as nexa￾phenylethane and a number of peroxides (see Table 25). Azo compounds R-N=N-R decompose simultaneously at two C-N bonds. Therefore, the cage effect should not affect k as measured by the kinetics of starting-material consumption or nitrogen evolution. As is evident from Table 25, k for the decomposi￾tion of the azobisisobutyronitrile or azoethylbenzene is very little changed from solvent to solvent. The decomposition of benzoyl peroxide or the peroxide of isobutyric acid is strongly dependent on the solvent, which is explained by the influence of solvent polarity. The benzoyl peroxide molecule may be regarded as two mutually repelling dipoles, each of which is readily polarized by the surrounding molecules (easy polarizability is caused by the ~-electrons of the benzene ring). This leads to a certain change in the bond energy in the benzoyl peroxide molecule when the polarity of the medium is changed. The effect of solvent polarity on k for decomposition of the peroxide of isobutyric acid is ex￾plained by the polarity of a transitional complex having the structure o + II ~c . c . oc. 8 The formation of such a complex is facilitated in a polar solvent, since the solvation energy of the transitional com-

MONOMOLECULARREACTIONS15plex is greater than that of the original peroxide A linearrelation is observed between log k and (e - 1)/(2e + 1) [29],where e is the dielectric constant of the medium.Comparison of Gas-and Liquid-Phase Decomposition.Inthe decomposition of a molecule in the gas phase,the freeradicals that are formed are immediately scattered.The de-composition of a molecule in a liquid requires an additionalexpenditure of energy in overcoming the internal pressure ofthe liquid in the formation of an activated complex.As anapproximation,the change in the decomposition rate constantdue to an increase in pressure will beAV*△PAinke-RTTherefore, one should expect a decrease in k when going froma gaseous medium to a nonpolar solvent. A second factor thatwiil decrease k in the liquid phase (as compared with the gasphase) is the cage effect, when a pair of radicals recombinesto form the original molecule. The cage effect does not playany role if the decomposition proceeds through the simulta-neous rupture of several bonds with the formation of three ormore particles, as evidently occurs in the decomposition ofazo compounds:R-N=NRR.+N,+R.Apparently these two factors explain why acetyl peroxide inthe gas phase decomposes more rapidly,than jn liquid:Inthe gas phase, at 85.20, k = 2.24.10-4and E =29.5seckcal/mole [23];in cc14.at 85.2°, k =1.17.10-4 sec-1, andE=33.4kca1/mole[27].The reverse picture is observed for tertiary butylperoxide:In benzene, cumene,or tri-n-butylamine solution,it decomposes somewhat more rapidly (1log k=15.63-37.2/9,with k - 1.5.10-5 at 1250) [43] than in the gas phase,,wherelogk-16.505-39.1/e,withk=1.0.10-5at 1250[50],or1ogk-15.845-38.0/e,withk=0.9.105at 1250[207],or1ogk=14.78-36.0/9,withk=1.0.10-5at1250[208].The more rapid decomposition of a polar molecule in solutionthan in thegasphase canbeexplained bystrong solvationof the activated complex (in comparison with the originalstate)by polar or readily polarized solvent molecules

MONOMOLECULAR REACTIONS 15 plex is greater than that of the original peroxide. A linear relation is observed between log k and (E - 1)/(2E + 1) [29], where E is the dielectric constant of the medium. Comparison of Gas- and Liquid-Phase Decomposition. In the decomposition of a molecule in the gas phase, the free radicals that are formed are immediately scattered. The de￾composition of a molecule in a liquid requires an additional expenditure of energy in overcoming the internal pressure of the liquid in the formation of an activated complex. As an approximation, the change in the decomposition rate constant due to an increase in pressure will be A.v+1l. p Il. In k ';J - RT Therefore, one should expect a decrease in k when going from a gaseous medium to a nonpolar solvent. A second factor that will decrease k in the liquid phase (as compared with the gas phase) is the cage effect, when a pair of radicals recombines to form the original molecule. The cage effect does not play any role if the decomposition proceeds through the simulta￾neous rupture of several bonds with the formation of three or more particles, as evidently occurs in the decomposition of azo compounds: R- N= N= R - R' + N 2 + R· Apparently these two factors explain why acetyl peroxide in the gas phase decomposes more rapidlY4than in liquid: In the gas phase, at 85.20 , k = 2.24·10- sec-l , and E = 29.5 kcal/mole [23]; in CC14 at 85.20 , k = 1.17.10.4 sec-l , and E = 33.4 kcal/mole [27]. The reverse picture is observed for tertiary butyl peroxide: In benzene, cumene, or tri-n-butylamine solution, it decomposes somewhat more rapidly (log k = 15.63 - 37.2/9, with k = 1.5.10-5 at 1250 ) [43] than in the gas phase, where log k 16.505 - 39.1/9, with k - 1.0.10-5 at 1250 [50], or log k = 15.845 - 38.0/9, with k = 0.9.105 at 1250 [207], or log k = 14.78 - 36.0/9, with k = 1.0.10-5 at 1250 [208]. The more rapid decomposition of a polar molecule in solution than in the gas phase can be explained by strong s0lvation of the activated complex (in comparison with the original state) by polar or readily polarized solvent molecules