Chain Initiation of Neopentane Pyrolysis and a SuggestedReconciliation of the Thermochemically Calculated andMeasured Rate Constants for the Recombinationof t-Butyl RadicalsBY ROGER M. MARSHALL,* HOWARD PURNELL AND PETER D. STOREYDepartment of Chemistry, University College of Swansea, Singleton Park,Swansea SA2 8PPReceived 15th April, 1975The rates of initiation of neopentane pyrolysis over the temperature range 756-845 K have beenmeasured at reactant pressures in the range 100-200 Torr, by processing of data relating to the forma-tion of the termination product, ethane, using an exact algebraic procedure. Thus, the data are freeof the ambiguities introduced by the empirical extrapolation procedures used in previous directdeterminations of the initial rates and the derived Arrhenius parameters ofneo-CSH12 -+ CH3 + t-C4H,. (1)The result obtained islog (k,/s-l) = 16.1 k 1.0-(3302 15 kJ mol-')/2.303RT.Values of kl are in agreement with previously measured values but the Arrhenius parameters areinconsistent with the presently accepted thermochemistry of reaction (1).A modified thermochemistryfor the t-butyl radical is proposed leaving the heat capacity unchanged but using the new values for298 K,AHfjkJ mol-I = 39, S(l mol c ~ - ~ ) / J mol-I K-I = 210.8.These, and the presently derived k , values allow the calculation for 800 K oflog (k-,/cm3 mol-I s-l) = 12.9with essentially zero activation energy and hence, via the geometric mean rule, lead tolog (k9/cm3 mol-l s-l) = 11.9for the mutual recombination reaction,2t-C4H, --f 2,2,3,3-tetramethylbutane.(9)The new thermochemistry suggested for t-butyl reconciles most thermochemically calculated valuesof k9 with directly measured values over a wide temperature range. However, further experimentaland theoretical justification is necessary before the new thermochemistry can be unequivocally accepted.log (k3k6/ks/cm3 mol-' s-l) = 13.2+ 1.5-(1275 12 kJ mol-')/2.303RTConcurrently evaluated with kl is the resultCH3 + neo-C5H1, + CH4 + C5H1CH3 + i-C4Hs --f CH4 + C4H7(3)(6)2CH3 -+ CZH6 (5)which is shown to be in excellent agreement with that calculated from the independent results ofother workers.886 NEOPENTANE PYROLYSISThere appears to be no dispute that the mechanism of the initial stages of neo-pentane pyrolysis isC5H12 + t-C,H,+CH, (1)t-C,H, + i-C4H8 + H ( 2 4H+CSHIZ + Hz+CSH11 (2b)(3)C5H1 + i-C4H8 + CH3 (4)2CH3 + C2H6 (5)(6)(7)(8)CH3 + C5H12 + CH4 + CsH11CH, + i-C4H8 + CH4 + C4H7CH3+C4H7 + CsHlo or CH4+C4H62C4H7 -+ C8H14 Or C ~ H G 4- C4H8.Two detailed analytical studies * established the general, mechanistic featuresof the reaction and differed in interpretation only on points of detail.Both groupsof workers attempted to evaluate the Arrhenius parameters, Al and El, of reaction (1)by measurement of the trivial yields of hydrogen. The raw data were in close accordbut differences in interpretation, although minor, led to somewhat different Arrheniusparameters. Our previous study also included measurement of ethane yields whichcould also be employed to estimate A l and El with results which were compatiblewith those based on the hydrogen yield data.However, in both studies, the earlyonset and substantial magnitude of self-inhibition introduced uncertainty since curve-fitting procedures designed to give initial reaction rates were necessitated, the basesof which were purely empirical.The results obtained for the approximate temperature range, 713-823 K, werelog(A,/s-') = 18.05, E,/W mol-' = 359 ;andlog(A,/s-l) = 16.8, E,/kJmol-' = 343.*However a shock tube study in the range, 1070-1240 K, had yielded significantlydifferent values, the recently slightly revised figures beinglog(A,/s-l) = 16.2, E,/kJmol-l = 326.Subsequently, Pacey has carried out a study in the intermediate temperature range,793-953 K, and obtained the resultslog(A,/s-') = 17.7, E,/kJmol-l = 356.We have restudied the reaction using a more sensitive analytical system and adopt-ing a more acceptable method of data-processing which does not involve any graphicalcurve-fitting procedures. In essence, we have treated the above mechanism in itsentirety and derived the explicit equation for the yield of ethane as a function of timeof reaction. The derivation is outlined below.A steady-state treatment of the mechanism consisting of reactions (1) to (8),making the usual assumption of long chains and also assuming that k? = 4ksk8,gives the resulR .M . MARSHALL, H . PURNELL A N D P . D. STOREYClearly, d[CH,],/dt = k,[CH,],[C,H,,J and, since [i-C4H8], = [CH,],,87This may be directly integrated since, at the low conversions used, [C5H12] is effectivelyconstant in any one experiment, hence,Also, from the steady state treatment,dCC2H6" = k,[CH,]: = kl[CSHI2]dtExpansion of the denominator and subsequent substitution of eqn (I) then givesHence.by integration,where a = (k3k6/k5).The principle of the data processing method is to find the value of a which makesa plot of [C,H,], against log,(l+a[C5Hl,]t) a straight line, common for all initialpressures of neopentane at a fixed temperature, passing through the origin. Theproduct of the slope of this line and a then gives a value of k l . In practice, measuredvalues of [C2H6]? as a function of t and of [C5H12], at a fixed temperature, wereprocessed by computer using a suitably chosen range of values of a.For each valueof a, a least squares line was calculated, and hence, the value of a providing zerointercept was eventually evaluated.[C,H61, = (Wa) lo,oe(l +aLHl2lt) (11)EXPERIMENTALPhillips research grade (99.99 %) neopentane, in which n-butane was the only impuritydetectable, was used. The neopentane was thoroughly outgassed at the temperature of anisopentane/liquid nitrogen mixture.The pyrolysis was studied in a clean quartz reaction vessel in a conventional static reactionsystem operated at temperatures within the range, 756-845 K. The details have beendescribed elsewhere.6 Initial reactant pressures ranged between 100 and 200 Torr.The analytical problem was not simple since ethane was present only in amounts in theorder of Torr and this, in presence of a two-thousand-fold excess of methane.Thus,because of overlap of these two peaks, a much better than usual resolution of these substanceswas demanded. This in turn reduced ethane peak heights and increased the need for highdetector sensitivity. An 80 x 0.45 cm stainless steel column containing 2 % (w/w) silicone oilon 100/120 mesh (A.S.T.M.) alumina provided the separation and a modern flame detectorthe sensitivity. The column was operated at 329 K at a nitrogen flow rate of 15.3 cm3 min-l.RESULTSDetailed measurements of ethane yields as a function of time were carried out ateach of eight temperatures at up to five initial pressures of neopentane.Fig. 1 showsa plot of the data, for reactions at 766 K and five initial pressures plotted accordingto eqn (11) with the value log(a/cm3 mol-l s-l) = 4.60, which leads to zero interceptof the least squares line which is shown. The results for all temperatures ar88 NEOPENTANE PYROLYSISsuminarised in table 1 where we list the corresponding values of a( = kdk3/kJ and thederived values of k l . The Arrhenius parameters calculated by least squares analysisof these data are :log(A,/s-l) = 16.1 & 1.0, EJkJ mol-1 = 330+ 15 ;log(A,/cm3 mol-1 s-l) = 13.2f 1.5, E,/kJ mol-1 = 127f 12where the error limits quoted are 95 % confidence limits.,+0UI I I I0 0 . 5 I .o I .5 2 .o 010g(l +a[C5H121t)FIG. 1.-Data for 766 K plotted according to eqn (11) with log (a/cm3 md-' s-') = 4.60.Initialpressures/Torr: 0,120; a, 145; 0,160; A, 180; 0,200.TABLE 1 .-EXPERIMENTAL VALUEStemperature/K 756 766 784 794 795 806 826 845log (Ws-l) -6.72 -6.41 -5.91 -5.72 -5.52 -5.27 -4.81 -4.32log(a/cm3 mo1-I s-') 4.42 4.60 4.70 4.95 4.79 4.82 5.22 5.34DISCUSSIONThe presently derived Arrhenius parameters for reaction (1) are in obvious dis-agreement with those of other workers determined in similar temperature ranges.Nevertheless, the actual values of k , measured in the present work are in excellentagreement with the actual measured values of other workers. It is only in theapportionment of the rate constant between A l and El in which the discrepanciesoccur. Since we feel that the data-processing techniques used in our present workare superior to those used in earlier work, we believe that the presently derived valuesof A l and El are the most reliable in the temperature range around 800 K.The currently accepted thermochemistry for reaction (1) which is based on directmeasurements for the alkane involved ' and on a combination of experimental resultsand group additivity principles * for the free radicals, yields the results for 800 KAUl/kJ mol-l = 321 and AS1/J mol-' K-l = 89.R.M . MARSHALL, H . PURNELL AND P . D. STOREY 89where AUl is the internal energy change and ASl the entropy change for a standardstate 1 mol ~ r n - ~ . Thus, using the equationsEl -El = AUl and log(A,/A-,) = (AS1 -R)/(2.303 R)we calculate from our Arrhenius parameters for reaction (1)E-JkJ mol-1 = 9 and log(A-,/cm3 mol-l s-l) = 11.9.It is almost universally believed that radical recombination reactions proceed withzero activation energy and therefore the origin in our calculation of a small activationenergy merits close attention. There are two obvious sources.First it could be dueto experimental error in our measured values of kl and indeed the 95 % confidencelimits on our value of El( k 15 kJ mol-l) do provide an adequate explanation for thenon-zero value of E- l . However, for reasons which are more fully explained below,we reject this, albeit perfectly acceptable, explanation in favour of the second alterna-tive, namely an error in the thermochemistry used. Since it is almost inconceivablethat there could be an error in the thermochemistry of neopentane, we must lookclosely at the thermochemistry of methyl and of t-butyl. The values for methyl seemto be very well founded and no serious discrepancy exists between the thermo-dynamically calculated value of the equilibrium constant forand the kinetically determined one based on the measured values of the forwardand reverse rate constants.Thus, if thermochemical error exists it is most probablethat it is in the values for t-butyl. There are three factors to consider here, namelythe heat capacity as a function of temperature, the heat of formation at 298 K andthe entropy at 298 K. It seems impossible that the heat capacity could be so muchin error as to account for the discrepancy and so we reject this and concentrate onthe values at 298 K of the heat of formation and of the entropy.The value of AHf used up to this point is the group additivity value, 28 kJ mol-l.Published values based on iodination studies are,l0 32k5 and 34-F 5 kJ mol-l, i.e.somewhat higher.Thus, if we were to use the value 37 kJ rnol-l, we would still beconsistent with these measured values and, moreover, we would have eliminated theapparent activation energy far reaction ( - 1). We propose however, for reasonswhich will become apparent below, to proceed using the value 39 kJ mob1 which isstill in reasonable agreement with the measured values and also permits the calculationof essentially zero activation energy for reaction (- 1).It has been suggested by Choo, Beadle, Piszkiewicz and Golden l2 that the entropyat 298 K of t-butyl has been overestimated by an amount R log,8 due to an incorrectassignment of the symmetry number.If this view is correct, then an unfortunateerror has been made not only by the compilers of the group additivity tables 13 butalso by ourselves,' since an error of this magnitude has very profound effects. Weproceed on the assumption that R log,8( = 17.3 J mol-1 IS-l) is to be subtracted fromthe presently accepted value of the entropy of t-butyl at all temperatures.Making the appropriate adjustments due to the above suggested changes in theheat of formation and entropy of t-butyl leads to the revised thermochemical valuesshown in table 2. Then, using these results we calculate, from our data, for therecombination of methyl with t-butyl the rate constant log(k- Jcm3 mol-1 s-l) = 12.9with effectively zero activation energy.The results for k , of all other groups of workers infer, using the data of table 2,a finite activation energy for reaction ( - 1) in the range 5 to 26 kJ mol-' .We suggestthat these values are artefacts arising from wrong apportionments of the measuredrate constants, kl, between A, and El and that the best estimate of k- from theseC2Hs +2CH90 NEOPENTANE PYROLYSISresults is obtained by calculating kl for the mean temperature of each group ofworkers and calculating k- from it using appropriate values interpolated from table 2.Values of log(k,,/cm3 mol-1 s-l) calculated in this way for the various groups ofworkers are : Halstead et aL,l 12.9 at 768 K ; Baronnet et aZ.,2 12.7 at 763 K ; P a ~ e y , ~12.9 at 873 K ; and T~ang,~* 13.2 at 1 I55 K.Clearly, except for the results calculatedfrom the data of Tsang and of Baronnet et al. there is very satisfactory agreementwith the value derived from our present results. Since the two discrepant resultsdiffer from the others only by a factor of two, it is with some confidence that we cannow propose that the best present estimate is10g(k-~/cm~ mol-' s-l) = 12.9.The geometric mean rule, k i ~ = 4kAAkBB, relating the rate constants of recombina-tion of radicals A with B, A with A and B with B is of proved validity for manypairs of radicals, including methyl and t-butyl, over wide temperature ranges.3-1Thus, using the long accepted value, log(k,/cm3 mol-'s-l) = 13.3 for the rate ofrecombination of two methyl radicals we may calculate the rate constant for therecombination of two t-butyl radicalsto be given by log(k9/cm3 mol-' s-') = 11.9.2t-C4H, -+ 2,2,3,3-tetramethylbutane (9)TABLE 2.-REVISED THERMOCHEMICAL VALUEStemperature/K 700 800 900 1000 1100 1200AUl/kJ mot1 335 332 329 326 323 320AS, /J mol-l K-' 76.5 72.4 68.8 65.7 62.8 60.1log(A1IA-d 3.6 3.3 3.2 3 .O 2.8 2.7This rate constant has been measured directly by several workers, the most recent(logarithmic) values being 11.7 by Choo et a l l 2 at 650 K, 12.1 by Parkes and Quinn l6at 298 K, -12 by Batt,,' - 11.5 by Golden et aZ.18 at -620 K and - 12 by Grillerand Ingold l9 in solution at 298 K.Clearly, there is very satisfactory agreementamong these and with the above calculation. Values have also been obtained withthe use of the currently accepted thermochemistry of t-butyl by three groups ofworkers. We now recalculate these using the modified thermochemistry proposedhere for t-butyl. In this way the (logarithmic) values obtained are 12.0 at 373 Kfrom Hiatt and Benson,20 11.9 at 462 K from McMillen, Golden and Benson 21(incidentally, in these two papers Benson et al. use the value 33 kJ mol-1 for theheat of formation of t-butyl at 298 K) and 13.7 at 500 K from our previous work.22We regard this last result as very unreliable since it is the end result of long extra-polations of two independent measurements and thus we will reject it in any furtherdiscussion.Clearly, the suggested modifications to the thermochemistry of t-butyl provideessentially total reconciliation between the directly measured and thermochemicallycalculated values of k9 as well as reconciling the majority of data for k- ,.Never-theless, before the new thermochemistry can be unequivocally accepted, new experi-mental determinations of the heat of formation of t-butyl must be shown to be inagreement with the present postulation and furthermore the theoretical and practicalimplications of the proposed entropy of t-butyl will have to be considered.One further value of the rate constant, k9, may be calculated using the modifiedthermochemistry proposed earlier for t-butyl.on theshock-tube pyrolysis of 2,2,3,3-tetramethylbutane the (logarithmic) value obtained isFrom the results of TsanR . M . MARSHALL, H. PURNELL A N D P . D . STOREY 9113.0 at 1063 K, a high value in line with the correspondingly high value obtainedfor k,l from the results of Tsang already dealt with. Furthermore, the value E9/kJ mol-1 = 25 is obtained. This result for k9 is irreconcilable with the other valuesquoted without resorting to drastic changes in our view of the thermochemistry oft-butyl ; basically we would have to leave the presently suggested thermochemistryup to -900 K unchanged, to preserve the reconciliation already achieved, and topropose sudden substantial change in the heat capacity in the range 900-1200 K toreduce the apparent value of k9.Since the change in heat capacity required is atleast 50 %, such a procedure is wholly unacceptable. These results of Tsang dotherefore stand alone in disagreement with those of other workers.The other function evaluated concurrently with kl in this work is the ratioa( = k3k6/kS) and our results may be compared with values calculated from literaturedata. Pacey has determined directly the rate of constant ratio10g(k~k~/crn~*~ mol-* s-*) = 6.8 -(67 kJ m01-~/2.303 RT)albeit in a slightly higher, though overlapping, temperature range. Konar et aZ.22determined the ratioin the same temperature range by making reasonable assumptions about the rate ofinitiation of isobutane pyrolysis. Combining these two independent experimentaldata gives the resultlog(a/cm3 mol-I s-l) = 14.2 - (141 kJ mol-'/2.303 RT)which is in very good agreement with the value determined in the present work.Indeed, at 800 K, the values of a calculated from the two expressions differ by only20 % which is certainly within any reasonable estimation of the possible error ineither expression.One further consequence of the presently suggested heat of formation of t-butylis worthy of note.The accepted thermochemistry of alkyl radicals based on groupadditivity leads to the conclusion that the bond dissociation energies (kJ mol-I) ofprimary, secondary and tertiary carbon-hydrogen bonds are almost in arithmeticprogression, viz. D(H--ethyl) = 410, D(H-isopropyl) = 394, D(H-t-butyl) = 381.Clearly, the suggested new value for the heat of formation of t-butyl destroys thissequence since it yields D(H-t-butyl) = 392.However it causes a new sequence ofbond dissociation energies (kJ mol-') to arise, viz. D(H3C-ethyl) = 354, D(H3C-isopropyl) = 350, D(H,C-t-butyl) = 348. Since no set of heats of formation couldlead to regular sequences of both C-H and C-C bond dissociation energies, it ispurely a subjective matter as to which, if either, of these sequences one would presumeto be reasonable. The presently suggested thermochemistry is not, therefore, to berejected on such grounds.10g(k6/kj/CM1" mol-+ S-') = 7.4-(74 kJ mol-'/2.303 RT)Note added in proof. The foregoing establishes, in our view, a need to identify the origin of the17 J mol-'l K-' overestimate of the entropy of t-butyl since we see no justification for the symmetrynumber proposal, a view shared, we now understand, by Golden who favours an explanation basedon a barrier to methyl group rotation in t-butyl.The authors thank the Foxboro Co., Foxboro, Mass.for the award of a studentshipto P. D. S .M. P. Halstead, R. S. Konar, D. A. kathard, R. M. Marshall and J. H. Purnell, Proc. ROJ~.SOC. A, 1969,310,52592 NEOPENTANE PYROLYSISF. Baronnet, M. Dzierzynski, G. M. Come, R. Martin and M. Niclause, Int. J. Chem. Kinetics,1971,3,197. ’ W. Tsang, J. Chem. Phys., 1966,44,4283.* W. Tsang, h t . J. Chem. Kinetics, 1973, 5, 651.P. D. Pacey, Canad. J. Chem., 1973,51,2415.R. S . Konar, J. H. Purnell and C. P. Quinn, Trans. Faraday SOC., 1968,64, 1319.A.P.I. 44 Tables, Selected Values of Properties of Hydrocarbons and Related Compounds (Thermo-dynamics Research Centre, Texas A. & M. University, 1971).H. E. O’Neal and S. W. Benson, Int. J. Chem. Kinetics, 1969, 1, 221.M. C. Lin and M. H. Back, Canad. J. Chem., 1966,44, 2357.l o H. Teranishi and S. W. Benson, J. Amer. Chern. SUC., 1963,85,2887,J. H. Knox and R. G. Musgrave, Trans. Furuduy Soc., 1967, 63,2201,l 2 K. Y. Choo, P. C, Beadle, L. W. Piszkiewicz and D. M. Golden, Abstracts, 168th Amer. Chem.SOC. National Meeting, Atlantic City, N.J., 1974.l 3 J. 0. Terry and J. H. Futrell, Cunad J. Chem., 1967, 45, 2327.l4 P. Camilleri, R. M. Marshall and J. €3. Purnell, J.C.S. Faraday Z, 1975, 71, 1491.l6 D. A. Parkes and C. P. Quinn, Clzem. Phys. Letters, 1975, 33, 483.l7 L. Batt, persona1 communication.I * D. M. Golden, 2. B. Alfassi and P. C. Beadle, Int. J. Chem. Kinetics, 1974, 6, 359.l9 D. Griller and K. V. Ingold, Int. J. Chem. Kinetics, 1974, 6, 453.2o R. Hiatt and S. W. Benson, Int. J. Chem. Kinetics, 1973, 5, 385.2 1 D. F. McMillen, D. M. Golden and S. W. Benson, J. Amer. Chern. SOC., 1972,94,4403.2a R. S. Konar, R. M. Marshall and J. H. Purnell, Znt. J. Chem. Kinetics, 1973, 5, 1007.J. A. Kerr and A. F. Trotman-Dickenson, Progr. Reaction Kinetics, 1961, 1, 105.(PAPER 5/712