Petroleum Chemistry Volume 49 Issue 5 2009 [Doi 10.1134_s0965544109050016] T. S. Pokidova; E. T....

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ISSN 0965-5441, Petroleum Chemistry, 2009, Vol. 49, No. 5, pp. 343353. Pleiades Publishing, Ltd., 2009.Original Russian Text T.S. Pokidova, E.T. Denisov, A.F. Shestakov, 2009, published in Neftekhimiya, 2009, Vol. 49, No. 5, pp. 363373.

High-temperature cracking of organic compoundsproceeds either in the chain mode involving free radi-cals or via a molecular mechanism, suggesting the deg-radation of one molecule into two or more molecules[1, 2]. The theoretical treatment of these two routes ofdegradation of different molecules needs a method forthe calculation of the activation energies and the rateconstants of such reactions. In our previous works, weanalyzed the degradation of alkyl and alkoxyl radicals

using the method of crossing parabolas (MCP) [3, 4].

This study is devoted to the treatment of experimen-tal data on the degradation kinetics of alkanol and alk-enol molecules in terms of the crossing parabolasapproach [5

8]. The parameters obtained to describethe activation energy of these reactions as a function oftheir enthalpy were used to calculate the activationenergies and the rate constants of a broader variety ofreactions of structurally different alcohols. Quantum-chemical calculations relevant to the computation ofthe activation energy and the transition state geometryfor the degradation of unsaturated alcohols occurringby two different routes via the six or four-memberedtransition state [9] were performed.

CALCULATION PROCEDURE

Method of Crossing Parabolas

The decomposition of the aforementioned alcoholsis characterized in terms of MCP by the followingparameters [6, 7]:

(1) Classical enthalpy

H

e

, which includes the dif-ference between zero-vibration energies of the reactingbonds:

H

e

=

H

+ 0.5

hN

A

(

i

f

), (1)

where h

andN

A

are Plancks constant and Avogadrosnumber, respectively, and

i

and

f

are the frequenciesof the stretching vibrations of the reacting bonds.

(2) Classical potential barrier of the reaction E

e

,

which includes the zero-vibration energy of the break-ing bond and the average kinetic energy of motion ofthe particle and is related to the experimentally deter-mined activation energy

by the simple equation:

E

e

=

+ 0.5

hN

A

i

0.5

RT

, (2)

whereR

is the gas constant and T

is the temperature in K.

(3) Parameter r

e

equal to the total elongation of thebreaking and forming bonds in the transition state.

(4) Parameter b

i

(2 is the force constant of the

breaking bond), parameter

b

f

2 is the force constant

of the forming bond and coefficient

= b

i

/

b

f

.

(5) Experimental activation energy

exp

, which wasdetermined according to the Arrhenius equation

exp

=RT

(

ln

nA

/

k

), (3)

where

is the preexponential factor, which is constantfor reactions of the same class; k

is the empirical reac-tion rate constant; and n

is the number of equireactivebonds.

The degradation of alcohols is a reaction with theconcerted breaking of some bonds and the formation of

bi2

bf2

Kinetic Parameters and Geometry of the Transition Statein the Unimolecular Degradation of Alcohols

T. S. Pokidova, E. T. Denisov, and A. F. Shestakov

Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia

e-mail: [email protected]

Received April 16, 2009

Abstract

Experimental data on the unimolecular degradation of structurally different alcohols, alkanols intowater and an olefin and alkenols into a carbonyl compound and an olefin, were analyzed in terms of the methodof crossing parabolas. The kinetic parameters characterizing such decomposition were calculated and factorsthat affect the activation energy of the reaction (the cycle strain energy, the steric factor, and the effect of

elec-trons neighboring the reaction center) were determined. The activation energies and the rate constants were cal-culated for 30 alcohol degradation reactions. The enthalpies, the activation energies, and the rate constants ofdegradation of unsaturated alcohols were compared for two different degradation routes yielding a carbonylcompound and an olefin or resulting in water and an olefin. Quantum-chemical calculations of the transitionstates for three model reactions were performed. The activation energies and the rate constants were obtainedfor the first time for 13 reverse reactions of the addition of carbonyl compounds to olefins.

DOI: 10.1134/S0965544109050016


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other bonds. For such reactions, the preexponential fac-tor

in the Arrhenius expression of the reaction rateconstant depends on the activation energy of degrada-tionE

and the number of simultaneously broken bonds(

m

). According to the oscillation model of concerteddegradation, this dependence is described by the for-mula [10]:

A

=A

0

(

m

/2

(

m

1)

)(

mRT

/

E

)

(

m

1)/2

. (4)

The reactions under consideration are an example of aconcerted two-center reaction in which two bondssimultaneously break. The equation for the degradationrate constant of an alcohol (concerted degradationinvolving two bonds, m

= 2) takes the following form:

k

=A

0

(2

RT

/

E

)

1/2

exp

(

E

/

RT

). (5)

Since the preexponential factor in this equation is tem-perature-dependent as well, the activation energy ofdegradationE

is related to the experimental activationenergy

exp

=RT

2

d

ln

k

/

dT

by the following expression:

E

=

exp

0.5

RT

(6)

(ln

k

= const + 1/2 ln

T

E

/

RT

and

exp

=RT

2

d

ln

k/dT=RT2(0.5/T+E/RT2) = 0.5RT+ E, wherefrom Eq. (6) isobtained). The parameters specified above are related toone another by the equation [6]:

bre= (Ee He)1/2 (7)

The parameter bre, in turn, makes it possible to calcu-late the classical barrier for a thermoneutral reactionanalogous to the reaction in question with He = 0,bre= const, and = const.

Ee0= {b/(1 + )}2 (8)

If the parameters and breare known for the class of

reactions of interest and the condition Hemin< He 0, ranges within 46.654.9 kJ mol1) and has a high activation energy (rang-

R1 C C

R2

R4

R3

H OH

R1R2CHCR3R4OH R1R2C=CR3R4+ H2O.

Bond b1010, kJ1/2mol1/2m1 0.5hNA, kJmol1

37.43 17.4

H 48.68 22.5

Table 1. Kinetic (kexp,E, bre) and thermodynamic (T, H) parameters of the transition state for the degradation reactions ofalcohols (= 0.769, He= 5.1 kJ mol

1, Ee= 14.1 kJ mol1,Ad= 1.02 10

14s1)

ReactionH T kexp(800 K) Eexp E A0 Refer-

encekJ mol1 K s1 kJ mol1 s1

Me2CHOH MeCH=CH2+ H2O 50.7 721801 1.47 103 262.6 259.3 28.14 1.63 1014 [13]

Me3COH Me2C=CH2+ H2O 54.0 10501300 3.58 104 282.0 278.7 29.12 5.1 1014 [14]

Me3COH Me2C=CH2+ H2O 54.0 9351400 6.77 104 277.7 274.4 28.89 5.0 1014 [15]

Me3COH Me2C=CH2+ H2O 54.0 9201180 3.26 104 282.6 279.3 29.15 5.1 1014 [16]

Me3COH Me2C=CH2+ H2O 54.0 10201200 3.76 104 281.6 278.3 29.09 5.0 1014 [17]

Me2CHCMe2OHMe2CHCMe=CH2+ H2O

52.9 10801160 4.03 104 278.5 275.2 29.14 5.0 1014 [18]

Me2CHCMe2OHMe2C=CMe2+ H2O

46.6 10801160 7.93 105 277.4 274.1 29.05 5.0 1014 [18]

= 29.04 0.11

a(kJ mol1)1/2.

brea

brea

28.14=

brea


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POKIDOVA et al.

ing from 259.3 to 279.3 kJ mol1), a fact that can be dueto the formation of a strained four-membered transitionstate (see above). From the data in Table 1, it is seen thatthe degradation reactions of secondary and tertiaryalcohols have different values of bre(28.14 and 29.04 0.11 kJ1/2 mol1/2, respectively) and, correspondingly,have the classical barrier to the thermoneutral reactionof 0 = 253.0 kJ mol

1 for secondary and 0 =269.6 kJ mol1 for tertiary alcohols.

The increase in the classical thermoneutral-reactionbarrier by 16.5 kJ mol1in the case of the degradationof the tertiary alcohol can be associated with theincrease in the strain of the four-membered transitionstate due to substutuents (steric factor (s) [7]).

The values of brecalculated from the experimentaldata for the degradation of alcohols of two classes werefurther used for the calculation of the activation energy(Eq. (9)) and the rate constant kfor a number of indi-vidual reactions relevant to these classes, according toEq. (5) (0= 5.0 10

14 s1, the average from Table 1).

Along with the reactions described in the literature, thereactions that we simulated for the degradation of otheralcohols were calculated. The results of the calculationof and rate constants kare presented in Table 2. Thecondition Hemin


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KINETIC PARAMETERS AND GEOMETRY OF THE TRANSITION STATE 347

results of calculation of the MCP parameters (exp, ,H, bre, andA0) from experimental data are presented inTable 3. The following values of band 0.5hNAcalcu-lated from spectral data were used for this purpose:

The degradation of alkenols, like that of alkanols, isan endothermic process, > 0 ranges within30.362.1 kJ mol1. It is seen that the enthalpies of deg-radation of alkanols and alkenols are close to oneanother (see Tables 1 and 3). The exception is the aro-matic alcohol PhCH=CHCH2CH2OH, its enthalpy ofdegradation is = 102.2 kJ mol1. The activationenergy () of degradation of alkenols is high (rangingfrom 160.3 to 179.4 kJ mol1); however, its value is~100 kJ mol1 below that of alkanols (see Tables 1and 3). The classical potential barrier of the thermoneu-

tral reaction for the degradation of alkenols is likewiselower by ~100 kJ /mol (149.0 versus 253.0 kJ mol1).As has been already noted, the degradation of alcoholsthat contain the C=C bond to the OH group followsthe concerted mechanism through the six-memberedtransition state. It is obvious that the major contributionto the reduction in the activation energy is made by theformation of the stable, unstrained six-membered tran-sition state as compared to the four-membered state inthe case of the degradation of alkanols; the strain energy

Bond b1010, kJ1/2mol1/2m10.5hNA,kJ mol1

(in alcohol) 46.98 21.7

37.43 17.4

of the four-membered carbon cycle is 110.4 kJ mol1[22].Comparing the values of breand the value of the classi-cal potential barrier of the thermoneutral reaction 0for the degradation of alkenols, we can distinguishthree classes of reactions of structurally alike alcohols:

Substituents in the -position to the OH groupsincrease the classical potential barrier of the thermo-neutral reaction 0by 11.9 kJ mol

1(steric factor). Thepresence of the phenyl group at the carbon atoms of theC=C bond leads to a reduction in the classical potentialbarrier of the thermoneutral reaction 0by 11.7 kJ mol

1

(see above). It is obvious that the electrons of the phe-

nyl ring stabilize the transition state via the mesomericeffect and thereby reduce the energy of the potentialbarrier of the thermoneutral reaction.

The values of brecalculated from the experimentaldata for the degradation of alcohols of three classeswere further used for calculation of the activationenergy (Eq. (9)) and the rate constant kfor a varietyof individual reactions relevant to these classes, accord-ing to Eq. (5) (0= 2.8 10

12 s1, the average fromTable 3). Along with the reactions described in the lit-

bre 0 s

(kJ mol1)1/2 kJ mol1

CH2=CHCH2CH2OH 27.53 0.28 149.0 3.0

CH2=CHCH2CR2OH 28.60 0.24 160.9 2.7 11.9

PhCH=CHCH2CH2OH(CH2=CPhCH2CH2OH)

26.42 0.42 137.3 4.6

Table 3. Kinetic (kexp,E, bre) and thermodynamic (T, H) parameters of the transition state for the degradation reactions ofalcohols (= 1.255, He= 4.3 kJ mol

1, Ee= 19.0 kJ mol1,Ad= 6.61 10

11s1)

ReactionH T kexp(800 K) Eexp E A0 Refer-

encekJ mol1 K s1 kJ mol1 s1

CH2=CHCH2CH2OHMeCH=CH2+ CH2O

61.9 650 7.37 103 173.6 170.9 27.73 2.8 1012 [19]

CH2=CMeCH2CH2OHMe2C=CH2+ CH2O60.3 616676 1.89 10

2

168.5 165.8 27.33 2.8 1012

[20]

= 27.53 0.28 (kJ mol1)1/2

CH2=CHCH2CHMeOHMeCH=CH2+ MeCHO

42.7 650 1.51 102 169.7 167.0 28.43 2.8 1012 [19]

CH2=CHCH2CMe2OHMeCH=CH2+ Me2CO

30.3 650 2.85 102 166.3 163.6 28.78 2.8 1012 [19]

= 28.60 0.24 (kJ mol1)1/2

CH2=CPhCH2CH2OHMeCPh=CH2+ CH2O

62.1 650 5.21 102 163.0 160.3 26.73 2.7 1012 [19]

PhCH=CHCH2CH2OHPhCH2CH=CH2+ CH2O

102.2 650 1.54 103 182.1 179.4 26.11 2.9 1012 [19]

= 26.42 0.44 (kJ mol1)1/2

a (kJ mol1)1/2.

brea

br ea

br ea

br ea


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POKIDOVA et al.

erature, the reactions that we simulated for the degrada-tion of other alcohols were calculated. The results ofthe calculation of and rate constants kare presentedin Table 4 (the condition Hemin


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KINETIC PARAMETERS AND GEOMETRY OF THE TRANSITION STATE 349

~100 kJ mol1above that for the degradation of thesealcohols via the six-membered transition state (seeTables 4 and 5). The rate constant of degradationthrough the four-membered transition state, as we see,is four orders of magnitude below that in the case of thesix-membered state (e.g., 2.76 106 s1versus 1.12 102s1for CH2CHCH2CH2OH) (see Tables 4 and 5).Hence, it follows that the only route of degradation of

alkenols having the structure specified above is thedecomposition that passes through the six-memberedtransition state and yields an alkene and a carbonylcompound.

Results of Quantum-Chemical Calculation

The results of the MCP analysis of the degradationreaction of alkenols agree well with the data of quan-tum-chemical calculations on the degradation of alco-hols. The results of the calculation of the geometry oftransition states are presented in the figure, and theenergy parameters of the reactions are given in Table 6.

As is seen from the data in Table 6, the energy pro-files based on the aforementioned structures optimizedby the CCD and B3LYP quantum-chemical methodsalmost coincide if the coupled-cluster methodCCSD(T)/6-311++G** is used for the calculation ofthe energy of the system. This is an indication of theminimal differences between the CCD and B3LYPmethods in the geometry optimization results, althoughthese methods noticeably differ from one another inrequired machine time. However, the alternative calcu-lation by the density functional theory at the B3LYP/6-311++G**//B3LYP/6-31G* level gives somewhat dif-ferent results and, as a rule, underestimated activationenergies. The theoretical enthalpies of the reactions

insignificantly differ from their experimental values,and the theoretical activation energies slightly differfrom the values obtained by the MCP (see Tables 2 and6 and figure). The only noticeable difference is that theMCP gives a more clearly defined reduction in the acti-vation barrier upon the elimination of water in the pres-ence of double bonds in the reaction products. Thequantum-chemical approaches show that the energy

barrier to the degradation through the six-memberedtransition state into a carbonyl compound and an alkeneis considerably lower, approximately by 100 kJ mol1,than the energy barrier of the decomposition throughthe four-membered transition state into water anddiene. The activation energies of degradation ofalkanols through the four-membered transition state arequite close to one another and follow this rule: thelower the enthalpy of the reaction, the lower the activa-tion energy. On passing to the six-membered transitionstate for the degradation of ethanol by virtue of theinvolvement of another water molecule, the activationenergy is substantially reduced (by ~60 kJ mol1). Thiscircumstance definitely allows us to discriminate both

mechanisms on the basis of the experimental activationenergy. The consistence of its value with the theoreticaldata leads to the conclusion that the conditions for theautocatalysis by degradation products (water) are notcreated under the experimental conditions.

Addition of Carbonyl Compounds to Alkenes

Reverse to the decomposition of unsaturated alco-hols (b) are the reactions of the addition of carbonylcompounds to alkenes (d), with a six-membered transi-tion state similar to that in the degradation reactions:

(d)

Published data on the kinetic parameters of thesereactions are lacking. We used the kinetic parameters,obtained in this work for the degradation reactions ofalcohols (b), to calculate the parameters of some reac-

tions of the formation of alcohols via the addition of acarbonyl compound to an alkene (d). The degradationreactions of unsaturated alcohols are endothermic (seeabove); consequently, their formation reactions will beexothermic; thus, Hd= Hb, andEd=EbHb.

The rate constants k(650 K) for the formation reac-tions of alcohols were calculated by Eq. (5), as in thecase of their degradation, and the preexponential factor0d= 2.0 10

6l mol1s1was calculated from the equi-librium constant Kof the reaction

CH3CH2=CH2+ CH2O CH2=CHCH2CH2OH.

On one hand, K = exp(S/R)exp(H/RT); on theother hand, K= kd/kb= (Ad/Ab)exp[(Ed Eb)/RT] andAd= Abexp(S/R) = exp (S/R). At 650 K,S0(CH3CH2=CH2) = 334.6 J mol1 K1, S0(CH2O) =251.2 J mol1 K1, and S0(CH2=CHCH2CH2OH) =461.6 J mol1K1[26]. The entropy change in this addi-tion reaction is S0 = 461.6334.64251.2 =124.2 J mol1 K1; hence, it follows that Ad/Ab =exp(S/R) = 3.3 107 l mol1 and that Ad =Abexp (S/R) = 6.6 10

113.3 107= 2.2 105l mol1.Since the addition reaction is a two-center reaction,then Ad= A0d(2RT/E)

1/20.5= 2.0 106 l mol1s1 inaccordance with published data [10] and Eqs. (4) and

C

O

HCR1

R2

R3R4

R1R2CHCH=CH2+ R3R4CO R1R2C=CHCH2CR

3R4OH.


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POKIDOVA et al.

Table 5. Calculated kinetic (

E

, k

) and thermodynamic (

H

) parameters of the four-membered transition state for the degra-dation reactions of alkenols (

= 0.769,

H

e

= 5.1 kJ mol

1

,

E

e

= 14.7 kJ mol

1

,A

0

= 5.0

10

14

s

1

)

Reaction

H E k

(650 K)

kJ mol

1

s

1

br

e

= 28.14(kJ mol

1

)

1/2

CH

2

=CHCH

2

CH

2

OH CH

2

=CHCH=CH2 + H2O 18.8 244.3 2.8 106

CH2=CMeCH2CH2OH CH2=CMeCH=CH2+ H2O 18.9 244.4 2.7 106

CH2=CHCH2CHMeOH CH2=CHCH=CHMe + H2O 22.7 246.1 2.0 106

CH2=CHCH2CHMeOH CH2=CHCH2CH=CH2+ H2O 52.4 259.2 2.6 107

CH2=CPhCH2CH2OH CH2=CPhCH=CH2+ H2O 21.1 245.4 2.3 106

PhCH=CHCH2CH2OH PhCH=CHCH=CH2+ H2O 18.5 244.2 2.8 106

bre= 29.04(kJ mol1)1/2

CH2=CHCH2CMe2OH CH2=CHCH=CMe2+ H2O 27.3 264.5 6.3 108

CH2=CHCH2CMe2OH CH2=CHCH2CMe=CH2+ H2O 56.6 277.8 7.9 109

(6). The results of calculation of the enthalpies (H),the activation energies (E), and the reaction rate con-stant for the formation of alcohols (k, 650K) are pre-sented in Table 7.

As is seen from the data in Table 7, the addition ofcarbonyl compounds to alkenes has a high activationenergy ( = 99.5132.3 kJ mol1), with the rate con-stants varying from 3.8 103 to 2.3 105l mol1s1,respectively. Substituents in the alkene and the carbo-nyl compound affect the activation energy in differentmanners. With the same carbonyl compound (e.g.,formaldehyde), the introduction of a substituent intothe alkene decreases the activation energy of the addi-tion reaction (106.7 versus 99.5 kJ mol1, see Table 7).

As the structure of the carbonyl compound becomesmore complex, the activation energy of the addition topropylene increases in the order formaldehyde(106.7 kJ mol1) < acetaldehyde (126.2 kJ mol1)

Petroleum Chemistry Volume 49 Issue 5 2009 [Doi 10.1134_s0965544109050016] T. S. Pokidova; E. T....

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