Solvation Enthalpies of Free Radicals: O-O Bond Strength in Di-tert-butylperoxide

Transcription

1 12670 J. Am. Chem. Soc. 2001, 123, Solvtion Enthlpies of Free Rdicls: O-O Bond Strength in Di-tert-butylperoxide Rui M. Borges dos Sntos,*, Vâni S. F. Murlh, Ctrin F. Correi, nd José A. Mrtinho Simões*, Contribution from the Deprtmento de Químic e Bioquímic, Fculdde de Ciêncis, UniVersidde de Lisbo, Lisbo, Portugl, nd Fculdde de Engenhri de Recursos Nturis, UniVersidde do AlgrVe, Cmpus de Gmbels, Fro, Portugl ReceiVed Mrch 16, 2001 Abstrct: The photolysis rection of di-tert-butylperoxide ws studied in vrious solvents by photocoustic clorimetry (PAC). This technique llows the determintion of the enthlpy of this homolysis rection, which by definition corresponds to the O-O bond dissocition enthlpy of the peroxide in solution, DH o sln (O-O). The derived vlue from these experiments in benzene, ( 9.9 kj mol -1, is very similr to widely ccepted vlue for the gs-phse bond dissocition enthlpy, DH o (O-O) ) ( 2.1 kj mol -1. However, when the PAC-bsed vlue is used together with uxiliry experimentl dt nd Drgo s ECW model to estimte the required solvtion terms, it leds to ( 10.2 kj mol -1 for the gs-phse bond dissocition enthlpy. This result, significntly higher thn the erly literture vlue, is however in excellent greement with recent gs-phse determintion of ( 6.6 kj mol -1. The procedure to derive the gs-phse DH o - (O-O) ws tested by repeting the PAC experiments in crbon tetrchloride nd cetonitrile. The verge of the vlues thus obtined ws DH o (O-O) ) ( 4.5 kj mol -1, confirming tht the erly gs-phse result is lower limit. More importntly, the present study questions the usul ssumption tht the solvtion terms of homolysis rections producing free rdicls in solution should cncel, nd suggests methodology to estimte solvtion enthlpies of free rdicls. Introduction The stndrd solvtion enthlpy of substnce AB, sln H o - (AB,g), is defined s the stndrd enthlpy ssocited with the dissolution of gseous AB in given solvent, usully t K. AB(g) f AB(sln) (1) Solvtion enthlpies re commonly determined s the difference between two quntities, obtined from seprte experiments nd different techniques. The first of those quntities, sln H o (AB,cr/l), is the stndrd solution enthlpy of crystlline or liquid AB in the solvent (see eq 2); the second quntity, sub/vp H o (AB,cr/l), is the stndrd sublimtion or vporiztion enthlpy of AB. sln H o (AB,g) ) sln H o (AB,cr/l) - sub/vp H o (AB,cr/l) (2) Stndrd clorimetric techniques cn be used to mesure both terms in eq 2. 1 Alterntively, sub/vp H o (AB,cr/l) cn be obtined by vpor pressure vs temperture plot. 1 In either cse, the finl vlue of sln H o (AB,g) cn be known with n error smller thn c. 1 kj mol -1. While the ppliction of eq 2 is strightforwrd for mny long-lived species, it hs never been used to evlute solvtion enthlpies of free rdicls, simply becuse the vilble * To whom correspondence should be ddressed. Phone: Fx: E-mil: jms@fc.ul.pt. Universidde de Lisbo. Universidde do Algrve. (1) Cox, J. D.; Pilcher, G. Thermochemistry of Orgnic nd Orgnometllic Compounds; Acdemic Press: London, experimentl techniques re not suited to del with trnsient species. This ccounts for the scrcity of solvtion energetics dt for free rdicls, despite their importnce. The strtegy to obtin the solvtion enthlpy of free rdicl must therefore rely on different pproch. Usully, this strtegy consists simply in compring the enthlpy of rection where the rdicl is rectnt or product with the enthlpy of the sme rection in solution. This involves, of course, the use of severl gsphse nd solution experimentl techniques. There re some exmples where this pproch could be followed. For instnce, in molecule AH, the mesurement of the oxidtion potentil of A - coupled with the pk of AH nd uxiliry dt yields the A-H bond dissocition enthlpy in solution, DH o sln - (A-H). 2 On the other hnd, the mesurements of the cidity of AH nd the dibtic electron ffinity of A fford the gs-phse A-H bond dissocition enthlpy, DH o (A-H). 3 Unfortuntely, however, the solution methodology involves uxiliry dt nd ssumptions tht re controversil. Hence, the bsolute vlues of DH o sln (A-H) my be ffected by significnt errors. To void these errors, the electrochemicl method is usully clibrted by using gs-phse results. Photocoustic clorimetry (PAC) is probbly the most relible method for obtining solution-phse bond dissocition enthlpies. 4 Surprisingly, however, the results from this technique were seldom used to derive informtion on free rdicl solvtion energetics. Exceptions include n erly study by Knbus- (2) Bordwell, F. G.; Zhng, X.-M. Acc. Chem. Res. 1993, 26, 510. (3) Lis, S. G.; Brtmess, J. E.; Liebmn, J. F.; Holmes, J. L.; Levin, R. D.; Mllrd, W. G. Gs-Phse Ion nd Neutrl Thermochemistry. J. Phys. Chem. Ref. Dt 1988, 17, Suppl. 1. (4) Lrhoven, L. J. J.; Mulder, P.; Wyner, D. D. M. Acc. Chem. Res. 1999, 32, /j010703w CCC: $ Americn Chemicl Society Published on Web 11/27/2001

2 SolVtion Enthlpies of Free Rdicls J. Am. Chem. Soc., Vol. 123, No. 50, Scheme 1 These uxiliry dt re vilble from the literture, 8 nd some were subject to recent reevlution. 12,13 DH o sln (PhO-H) ) r H/2 + f H o (H,g) + o sln H(H,g) + f H o (t-buoobu-t,l)/2 - f H o (t-buoh,l) + sln H o (t-buoobu-t,l)/2 - sln H o (t-buoh,l) (6) Kminsk et l., 5 where the solvtion enthlpies of crboncentered rdicls were investigted, nd three more recent publictions where the solvtion of phenoxy rdicls is discussed. 6-8 In the present pper we wish to report our studies on the solvtion of tert-butoxyl rdicl, species tht is often used s rectnt in photocoustic clorimetric experiments. Results nd Discussion A widely ccepted vlue for the oxygen-oxygen gs-phse bond dissocition enthlpy in di-tert-butylperoxide, ( 2.1 kj mol -1, relies on the determintion of the ctivtion energy for the O-O bond homolysis of tht compound. 9 This result ws very recently corroborted by nother study using the sme method, yielding ( 2.1 kj mol -1, 10 but given the greement between the two vlues, we will refer only to the first one in the following discussion. 11 To compre gs-phse nd solution energetics of tht bond, we decided to use photocoustic clorimetry to determine the bond dissocition enthlpy of di-tert-butylperoxide in solution, DH o sln (O-O). This involves mesuring the enthlpy of rection 3 (Scheme 1) in the photocoustic clorimeter (see Experimentl Section), which cn be directly identified with DH o sln (O-O). The ppliction of the PAC technique to the generl problem of the determintion of bond dissocition enthlpies hs been described in detil 6,8 nd is beyond the scope of the present pper. However, brief description is useful to highlight the importnce of di-tert-butylperoxide in those studies. The pproch is illustrted in Scheme 1, using the O-H bond in phenol s n exmple, where the photochemiclly produced tert-butoxyl rdicl is employed to brek the bond of interest, yielding PhO. o The O-H bond dissocition enthlpy in phenol, DH sln (PhO-H), cn be derived from the enthlpy of the net rection 5 in Scheme 1, r H. The reltionship cn be estblished from thermodynmic cycle, yielding eq 6, which contins severl solution enthlpy terms ( sln H) nd enthlpies of formtion. (5) Knbus-Kminsk, J. M.; Gilbert, B. C.; Griller, D. J. Am. Chem. Soc. 1989, 111, (6) Wyner, D. D. M.; Lusztyk, E.; Pgé, D.; Ingold, K. U.; Mulder, P.; Lrhoven, L. J. J.; Aldrich, H. S. J. Am. Chem. Soc. 1995, 117, (7) de Heer, M. I.; Korth, H.-G.; Mulder, P. J. Org. Chem. 1999, 64, (8) Borges dos Sntos, R. M.; Lgo, A. L. C.; Mrtinho Simões, J. A. J. Chem. Thermodyn. 1999, 31, (9) () McMillen, D. F.; Golden, D. M. Annu. ReV. Phys. Chem. 1982, 33, 493. (b) Mllrd, W. G.; Westley, F.; Herron, J. T.; Hmpson, R. F. NIST Chemicl Kinetics Dtbse, version 6.0; NIST Stndrd Reference Dt, Ntionl Institute of Stndrds nd Technology: Githersburg, MD, (10) Reints, W.; Prtt, D. A.; Korth, H.-G.; Mulder, P. J. Phys. Chem. A 2000, 104, (11) The uthors in ref 10 clim tht the relibility of their vlue for DH o (O-O), nd thus for fh o (t-buo, g), is supported by the excellent greement between their result derived for DH o (t-buo-h) nd the one recommended in the literture (Stein, S. E.; Rukkers, J. M.; Brown, R. L. NIST Structures nd Properties Dtbse, version 2.0; NIST Stndrd Reference Dt; Ntionl Institute of Stndrds nd Technology: Githersburg, MD, 1994). However, the greement is not surprising since the literture vlue relies on the results reported in ref 9. This reference nd the work by Reints et l. report very similr DH o (O-O) vlues. The PAC technique llows the determintion of the net rection enthlpy, r H, through simple energy blnce. Prt of the energy of the bsorbed lser photons (e.g., E m ) kj mol -1 for nitrogen lser) is used to cleve the O-O bond in t-buoobu-t, thus inititing the rection. The remining lser energy, in this exmple incresed by the exothermicity of the fst hydrogen bstrction in rection 4, is deposited s het in solution nd produces shock wve. This het ( obs H), which cn be determined becuse it is proportionl to the wve mplitude, is then relted, by eq 7, to the enthlpy of the net rection 5 (Φ r is the quntum yield of rection 3). r H ) E m - obs H + r V Φ r χ The lst term in eq 7 represents correction due to the soclled nontherml expnsion. If rection is ccompnied by nonnegligible molr volume chnge ( r V), s in the cse of rection 5, frction of the observed wve mplitude will be due to tht physicl expnsion; i.e., the true vlue of the het deposition will be less thn the one observed. This, in turn, implies positive correction of r H. The prmeter χ is the dibtic expnsion coefficient of the solvent nd depends (eq 8) on its thermoelstic properties, nmely the isobric expnsion coefficient, R p, the het cpcity, C p, nd the density, F. In the present exmple, the volume chnge of the net rection 5 is ssumed to be equl to the volume chnge for the homolysis of the di-tert-butylperoxide lone, since the volume chnge for rection 4 should be negligible. The focus of the present pper is the homolysis of di-tertbutylperoxide lone. It is now cler tht this work is intimtely linked with the broder experimentl procedure illustrted bove. In both studies, eq 7 (with the sme uxiliry vlues Φ r nd r V) cn be used to determine the enthlpy of the overll rection in solution (3 nd 5, respectively). In the first cse, the rection enthlpy corresponds directly to the bond dissocition enthlpy of di-tert-butylperoxide in solution. We strted our work by studying rection 3 in benzene. Using the estimted vlue of r V) 13.4 ( 4mLmol -1, 6,14 r H ) DH o sln (O-O) ws clculted through eq 7. The results, displyed in Tble 1, re in very good greement with the vlues reclculted from nother PAC study in benzene. 15 (12) Diogo, H. P.; Mins d Piedde, M. E.; Mrtinho Simões, J. A.; Ngno, Y. J. Chem. Thermodyn. 1995, 27, 597. (13) Wyner et l. 6 estblished n lterntive method to the one bsed on the direct thermodynmic cycle illustrted by eq 6. Using n uxiliry rection, those uthors voided the need for thermochemicl dt on ditert-butylperoxide nd tert-butyl lcohol, including its solution enthlpies, in eq 6. Their method relies, however, on the C-H bond dissocition enthlpy in 1,4-dicyclohexdiene. Both methods give equivlent results. 8 It should lso be stressed tht both eq 6 nd the lterntive method do not require the vlue of the O-O bond dissocition enthlpy in di-tertbutylperoxide (see, however, note 14). (7) χ ) R p FC p (8)

3 12672 J. Am. Chem. Soc., Vol. 123, No. 50, 2001 Borges dos Sntos et l. Tble 1. PAC Determintion of Solution Bond Enthlpies, o (O-O), for Di-tert-butylperoxide in Vrious Solvents DH sln solvent obsh (kj mol -1 ) Φ r χ b (ml kj -1 ) DH o sln (O-O) (kj mol -1 ) C 6H ( 7.1 c ( ( 7.5 d ( 10.3 CCl ( 4.0 c ( ( 8.4 e ( ( 8.4 f ( 11.9 CH 3CN ( 3.3 c ( 6.3 From ref 6. b Dt used to clculte χ from Riddick, J. A.; Bunger, W. B.; Skno, T. K. Orgnic SolVents. Physicl Properties nd Methods of Purifiction; Wiley: New York, c This work. Averge of t lest five independent determintions. The experimentl uncertinties re twice the stndrd devition of the men in ech cse. d Reference 15. e Burkey, T. J.; Mjewsky, M.; Griller, D. J. Am. Chem. Soc. 1986, 108, f Clculted from dt in ref 6. Scheme 2 The vlue obtined for DH o sln (O-O) in benzene, ( 9.9 kj mol -1, is very similr to the gs-phse result presented bove, ( 2.1 kj mol -1, suggesting tht the solvtion effects involved in rection 3 should cncel. However, to further investigte this mtter, we need to consider the solvtion terms tht relte DH o sln (O-O) to DH o (O-O). These terms re shown in Scheme 2. In the cse of the peroxide, sln H o (t-buoobu-t,g) could be esily obtined (see eq 2) s ( 1.0 kj mol -1 through experimentl determintions of its vporiztion enthlpy, vp H o - (t-buoobuo-t) ) 39.3 ( 1.0 kj mol -1, 12 nd its solution enthlpy in benzene, sln H o (t-buoobu-t,l)) 1.21 ( 0.22 kj mol To estimte sln H o (t-buo,g), we hve used the electrosttic-covlent model, lso known s the ECW model, developed by Drgo nd co-workers, which permits clcultion of the difference between the solvtion enthlpies of tert-butyl lcohol nd tert-butoxyl rdicl in benzene. 16 This procedure is similr to the one used to estimte the sme difference for phenol nd phenoxyl rdicl, illustrted in the recent literture. 8,17 For instnce, solvents such s crbon tetrchloride, wek Lewis bse, will hve negligible interctions both with t-buoh nd t-buo, so tht sln H o (t-buoh,g) - sln H o (t- BuO,g) 0. On the other hnd, strong Lewis bse solvent like cetonitrile, which is lso hydrogen bond cceptor, is ble to form one hydrogen bond with t-buoh. The sme conclusion (14) An importnt feture of the indirect method of Wyner et l. 6 is tht it lso voids the need to correct for the rection volume chnge. Yet, for the PAC study of the simpler rection ddressed here, this estimtive is unvoidble. Those uthors lso mde criticl ssessment of rv, recommending the vlue used in the present pper. Interestingly, this vlue ws bsed on the ssumption tht the old DH o (O-O) for di-tertbutylperoxide is identicl in solution. Although this is not true, s demonstrted by our results, it ws fortunte choice becuse tht erly gs-phse vlue is very close to DH o sln (O-O). (15) Clrk, K. B.; Wyner, D. D. M.; Demirdji, S. H.; Koch, T. H. J. Am. Chem. Soc. 1993, 115, (16) () Drgo, R. S.; Ddmun, A. P.; Vogel, G. C. Inorg. Chem. 1993, 32, (b) Vogel, G. C.; Drgo, R. S. J. Chem. Educ. 1996, 73, (c) Drgo, R. S. Applictions of Electrosttic-CoVlent Models in Chemistry; Surfside: Ginesville, FL, (17) Bizrro, M. M.; Cost Cbrl, B. J.; Borges dos Sntos, R. M.; Mrtinho Simões, J. A. Pure Appl. Chem. 1999, 71, Tble 2. Determintion of Gs-Phse Bond Enthlpies, DH (O-O), for Di-tert-butylperoxide from Solution Dt (Vlues in kj mol -1 ) solvent slnh (t-buoobu0t,l) slnh (t-buoh,l) H (ECW) b DH (O-O) C 6H ( ( ( 10.2 CCl ( ( c ( 7.5 CH 3CN 5.5 ( ( ( 6.7 Obtined by rection-solution clorimetry. Averge of t lest five independent results. The uncertinties re twice the stndrd devition of the men in ech cse. b Enthlpy for hydrogen bond formtion between tert-butyl lcohol nd the solvent using the ECW model (see text). c By definition. cn be drwn for weker hydrogen bond cceptor like benzene. The enthlpy of this hydrogen bond will therefore be good pproximtion of the difference sln H o (t-buoh,g) - sln H o (t- BuO,g). By providing n estimtion for the enthlpy of this hydrogen bond, the ECW model is convenient procedure to derive tht difference. It relies on eq 9, which contins four prmeters tht reflect electrosttic (E A E B ) nd covlent (C A C B ) contributions to the enthlpies of donor-cceptor interctions. Donor (B) nd cceptor (A) prmeters, optimized by lrge dtbse of experimentlly determined enthlpies, re vilble for mny substnces H(ECW) ) E A E B + C A C B (9) The ECW model predicts tht the difference H(ECW) ) sln H o (t-buoh,g) - sln H o (t-buo,g) ) -4.4 kj mol -1 in benzene. This result, together with sln H o (t-buoh,l) ) ( 0.35 kj mol -1, 8 nd vp H o (t-buoh) ) 46.7 ( 0.1 kj mol -1, 18 leds to sln H o (t-buo,g) )-26.8 kj mol -1 in benzene, with n uncertinty estimted s c. 1 kj mol -1. The bove solvtion enthlpy dt nd the PAC vlue for DH o sln (O-O) in benzene llow the determintion of DH o (O- O) using eq 10 (or Scheme 2). This procedure leds to ( 10.2 kj mol -1 for the gs-phse O-O bond dissocition enthlpy in di-tert-butylperoxide (Tble 2), which is some 13 kj mol -1 higher thn the presently ccepted vlue. DH o (O-O) ) DH o sln (O-O) + sln H o (t-buoobu-t,g) - 2 sln H o (t-buo,g) (10) Recent energy-resolved threshold collision-induced (TCID) experiments, by DeTuri nd Ervin, 19 fforded the gs-phse cidities of severl lcohols, including tert-butyl lcohol. These results were coupled with very ccurte vlues for the dibtic electron ffinities of the lkoxyl rdicls, 20 yielding gs-phse O-H bond dissocition enthlpies t K. In the cse of t-buoh, DH o (O-H) ) 446 ( 3kJmol -1, together with the gs-phse stndrd enthlpies of formtion of the lcohol ( ( 0.8 kj mol -1 ) 18 nd the peroxide ( ( 2.2 kj mol -1 ), 12 implies f H o (t-buo,g) )-84.5 ( 3.1 kj mol -1 nd DH o (O-O) ) ( 6.6 kj mol -1. This vlue is in excellent greement with the PAC result nd the ECW model to estimte the solvtion enthlpy of tert-butoxyl rdicl. To further test the combined PAC-ECW method, we hve repeted the determintion of DH o (O-O) using crbon tetrchloride nd cetonitrile s solvents. The sme procedure (18) Pedley, J. B. Thermodynmic Dt nd Structures of Orgnic Compounds, Vol. 1; Thermodynmics Reserch Center: College Sttion, TX, (19) DeTuri, V. F.; Ervin, K. M. J. Phys. Chem. A 1999, 103, (20) Rmond, T. M.; Dvico, G. E.; Schwrtz, R. L.; Lineberger, W. C. J. Chem. Phys. 2000, 112, 1158.

4 SolVtion Enthlpies of Free Rdicls J. Am. Chem. Soc., Vol. 123, No. 50, outlined bove for benzene ws followed, nd the results re summrized in Tbles 1 nd 2. To discuss the finl results, it is importnt to consider the uncertinties involved. First, it should be noted tht the min contribution to the overll uncertinty in the present study comes from the PAC result ( obs H), which cn esily scend to c. 8 kj mol The cumultive error from the correction to the gs phse should be less thn 3 kj mol -1. It cn be rgued tht our result in benzene, ( 10.2 kj mol -1, is not significntly different from the erly gs-phse vlue of DH o (O-O) ) ( 2.1 kj mol -1. Indeed, the mgnitude of the error br in our result brings the two vlues very close together. However, the results obtined from the experiments in crbon tetrchloride nd cetonitrile, which, within their uncertinties, gree with the one obtined from the benzene experiments, clerly fvor the high vlue for the gs-phse O-O bond dissocition enthlpy in the peroxide: the verge of those three results is DH o (O-O) ) ( 4.5 kj mol -1. Although the DH o (O-O) vlue obtined from the study in crbon tetrchloride grees, within the error brs, with those derived from the experiments in the other solvents, significnt discrepncy is still pprent. This my be prtly cused by the correction H(ECW) ) sln H o (t-buoh,g) - sln H o (t-buo,g), which ws estimted to be zero. However, the resonble ssumption of smll interction through hydrogen bond formtion, e.g., -2kJmol -1, will decrese DH o (O-O) in Tble 2by4kJmol -1. The lowest of the three vlues, obtined from the studies in benzene, my lso be ffected by shortcomings in the H(ECW) correction. There is spectrl evidence tht the tert-butoxyl rdicl forms π-complexes with electron-rich romtic molecules. 22 This interction ws first suggested by observing tht the chrcteristic til-end bsorption in the ner UV of these rdicls is red-shifted in romtic solvents such s benzene, reltive to those in nonromtic solvents such s crbon tetrchloride nd cetonitrile. This ws then tested by spectroscopic serch of such complex. When the bove rdicls were generted in the presence of 1,3,5-trimethoxybenzene, chrge-trnsfer bsorption ws observed in the visible region (440 nm). This bnd confirmed the formtion of the π-complex between the rdicl nd the electron-rich romtic, which shifts the bsorption into the visible. The interction between the tert-butoxyl rdicl nd benzene must then be considered when evluting the mgnitude of sln H (t-buoh,g) - sln H o (t-buo,g) in tht solvent. This difference should correspond to the hydrogen bond formtion between tert-butyl lcohol nd benzene, estimted by the ECW model, minus the enthlpy of the interction between the rdicl nd the solvent (lso negtive), which is not contemplted in tht model. This leds to more positive vlue thn the one used, -4.4 kj mol -1, thus bringing the finl vlue of DH o (O-O) derived from the benzene studies closer to the other two. The enthlpy of hydrogen bonding between tert-butyl lcohol nd the solvent, identified with the difference sln H o (t-buoh,g) - sln H o (t-buo,g), which is centrl to our clcultion of gsphse vlues from solution studies, cn be obtined by procedure lterntive to the ECW model. A method developed by Abrhm et l., 23 bsed on reltive hydrogen bond cceptor (21) This is twice the stndrd devition ssocited with obsh. In mny literture studies this thermochemicl convention is not followed; i.e., the errors re reported s the stndrd devitions. (22) Avil, D. V.; Ingold, K. U.; Di Nrdo, A. A.; Zerbetto, F.; Zgiersky, M. Z.; Lusztyk, J. J. Am. Chem. Soc. 1995, 117, We thnk reviewer for pointing out these results to us. nd donor properties, ws recently extended by Snelgrove et l. 24 to llow quntittive description of the kinetic solvent effect on the rte of hydrogen tom bstrction by rdicls. This extension of Abrhm s method cn lso be used to derive the Gibbs energy for hydrogen bonding, thus providing n lterntive estimte for the bove difference, with n estimted error of (1 kjmol Using this procedure, s outlined in ref 24, one obtins -2.1, -0.76, nd -6.7 kj mol -1 for the Gibbs energy of hydrogen bond formtion between tert-butyl lcohol nd the solvents benzene, crbon tetrchloride, nd cetonitrile, respectively. The corresponding gs-phse DH o (O-O) vlues re ( 10.2, ( 7.5, nd ( 6.7 kj mol -1, respectively, with n verge of ( 4.5 kj mol -1. The min conclusion of the previous exercise is tht the two methods to estimte sln H o (t-buoh,g) - sln H o (t-buo,g) yield essentilly the sme results. However, it is noted tht the method proposed by Snelgrove et l. 24 leds to better overll greement between the finl gs-phse vlues obtined from the different solution studies, nd to n even higher vlue for the verge gs-phse O-O bond dissocition enthlpy. The improvement of the overll greement cn prtly be explined by noting tht the procedure proposed by Snelgrove et l. includes n interction between tert-butyl lcohol nd crbon tetrchloride, bsed on experimentl evidence tht this compound cts s n hydrogen bond cceptor reltive to lknes. 24 A fundmentl difference between Drgo s model nd the procedure proposed by Snelgrove et l. is tht the former is bsed on enthlpies of complextion, wheres the ltter is derived from equilibrium constnts of hydrogen bond cidity nd bsicity, hence providing estimtes of Gibbs energy chnges. Despite the somewht better greement obtined with the method proposed by Snelgrove et l., the ECW model my provide better estimtes, simply becuse it directly ffords the enthlpy of the hydrogen bond. Nevertheless, it is ressuring tht both methods fforded essentilly the sme results nd conclusions nd my be used in future studies to complement ech other. The erly gs-phse literture vlue DH o (O-O) ) ( 2.1 kj mol -1, which is bsed on ctivtion energy dt for the homolysis of di-tert-butylperoxide, is some 20 kj mol -1 lower thn the result found in our studies. Although those dt, s listed in the NIST Chemicl Kinetics Dtbse, 9b vry between 130 nd 163 kj mol -1, nd the corresponding A fctors vry by few orders of mgnitude, most results lie in nrrower rnge (E ) kj mol -1 nd A ) s -1 ), so tht the correct vlue for the ctivtion energy is likely to be close to 159 kj mol -1. The source of the discrepncy my therefore be relted to the method used to extrct the O-O bond dissocition enthlpy t 298 K from n ctivtion energy obtined from mesurements t higher tempertures (typiclly, K). This method relies on severl ssumptions, including the structure of the trnsition stte nd the ssumption tht the recombintion of the tert-butoxyl rdicls hs negligible ctivtion energy. 9 Hence, the disgreement between the low nd the high vlues for DH o (O-O) my be cused by lrgerthn-expected temperture correction to E (i.e., the ctivtion enthlpy t 298 K would be considerbly higher thn tht t K) nd/or by negtive ctivtion energy for the (23) () Abrhm, M. H.; Priscill, L. G.; Prior, D. V.; Duce, P. P.; Morris, J. J.; Tylor, P. J J. Chem. Soc., Perkin Trns , 699. (b) Abrhm, M. H.; Priscill, L. G.; Prior, D. V.; Morris, J. J.; Tylor, P. J J. Chem. Soc., Perkin Trns , 521. (24) Snelgrove, D. W.; Lusztyk, J.; Bnks, J. T.; Mulder, P. Ingold, K. U. J. Am. Chem. Soc. 2001, 123, 469. (25) We re indebted to reviewer for illustrting this lterntive method for us.

5 12674 J. Am. Chem. Soc., Vol. 123, No. 50, 2001 Borges dos Sntos et l. recombintion of tert-butoxyl rdicls. These questions deserve to be further investigted. Conclusion Photocoustic clorimetry studies combined with the ECW model led to ( 4.5 kj mol -1 for the gs-phse O-O bond dissocition enthlpy of di-tert-butylperoxide. This result is significntly higher thn the widely ccepted gs-phse literture vlue (159.0 ( 2.1 kj mol -1 ) but supports nother gs-phse vlue, derived from cidity nd electron ffinity dt (172.5 ( 6.6 kj mol -1 ). The procedure proposed in the present study llows estimting the solvtion of free rdicls energetics nd indictes tht the frequent ssumption of cnceling solvtion enthlpies must be used with cution. The procedure is bsed on simple thermodynmic cycles, involving quntities esily determined by well-estblished experimentl techniques, nd on the ECW model. Experimentl Section All solvents were of spectroscopic or HPLC grde nd used s received. Di-tert-butylperoxide (Aldrich) ws purified ccording to literture procedure. 12 o-hydroxybenzophenone (Aldrich) ws recristlized twice from n ethnol-wter mixture. The uxiliry solution enthlpies of tert-butyl lcohol nd di-tertbutylperoxide were determined t T ) K in rection-solution clorimeter described elsewhere. 26 Photocoustic Clorimetry. Both the photocoustic clorimeter setup nd the experimentl technique hve been described in detil. 8 Briefly, c. 0.4 M solution of rgon-purged di-tert-butylperoxide in the pproprite solvent ws flowed through stndrd qurtz flow cell (Hellm 174-QS), where it ws irrdited with pulses from nitrogen (26) () Diogo, H. P. Tese de Doutormento, Instituto Superior Técnico, Lisbo, Portugl, (b) Lel, J. P.; Pires de Mtos, A.; Mrtinho Simões, J. A. J. Orgnomet. Chem. 1991, 403, 1. lser (PTI PL 2300, nm, pulse width 800 ps, c µj/pulse t the cell, flux < 40Jm -2 ). Ech pulse produced photolysis of the peroxide, nd the resulting wve ws detected by piezoelectric trnsducer (Pnmetrics V101, 0.5 MHz) in contct with the bottom of the cell. The signls were mplified (Pnmetrics 5662) nd mesured by digitl oscilloscope (Tektronix 2430A). The pprtus ws clibrted by crrying out photocoustic run using n opticlly mtched (within 1-2% bsorbnce units t nm) solution of o-hydroxybenzophenone, which dissiptes ll of the bsorbed energy s het. 27 Acknowledgment. We thnk Dr. Mnuel Mins d Piedde, Dr. Hermínio Diogo (Instituto Superior Técnico, Lisbo, Portugl), nd Dr. João Pulo Lel (Instituto Tecnológico e Nucler, Scvém, Portugl) for ssistnce with the rectionsolution experiments. This work ws supported by the PRAXIS XXI Progrm (PRAXIS/2/2.1/QUI/51/94), Portugl. V.S.F.M. thnks Fundção pr Ciênci e Tecnologi, Portugl, for reserch grnt (SFRH/BD/2828/2000). JA010703W (27) An importnt requirement of the PAC technique is tht the thermoelstic properties of the solution used in the clibrtion nd those of the smple solution, nmely their dibtic expnsion coefficient χ (eq 8), should be identicl. Since the solutions used re normlly very diluted, it is generlly ssumed tht both will hve χ equl to tht of the pure solvent. There hs been ngging doubt s to whether this ssumption is vlid for the experiments bsed on the pproch illustrted in Scheme 1, due to the fct tht the smple solution contins c. 7% (v/v) of di-tert-butylperoxide, wheres the clibrtion contins none. The sme doubt pplies to the experiments reported in this pper. We re currently investigting this mtter by determining experimentl vlues of χ for the solutions involved. However, ll the vilble evidence seems to corroborte the ssumption: (1) the shpe nd time-of-flight of the photocoustic wveform re the sme for clibrtion nd experiment; (2) incresing the mount of peroxide in the smple solution does not noticebly ffect the time-of-flight of the photocoustic wveform; (3) plot of the photocoustic signl versus the mount of peroxide dded during the experiment remins liner even beyond 12% (v/v) of peroxide in solution (ref 8, see lso Clrk, K. B.; Griller, D. Orgnometllics 1991, 10, 746).