Energy & Fuels 1987, 1, 17-23
17
Master Equations for Calculating Heterolysis Energies in Solution Edward M. Arnett,* B. Chawla,? K. Amarnath, and L. G. Whitesell, Jr. Department of Chemistry, Duke University, Durham, North Carolina 27706 Received September 11, 1986. Revised Manuscript Received October 5, 1986
A simple “master equation” for predicting the heterolysis energies of bonds to give resonancestabilized ions is tested by reaction of six carbocations with 21 carbanions and four phenoxide anions. The original equation3bis enormously improved in precision and generality by replacing pKR+values as the measure of cation stability. If calculated A delocalization energies are used, data for 33 reactions are correlated by eq 5 with r = 0.9948 (instead of r = 0.8812) so that the standard deviation of m h e t is f 0.702 kcal/mol. With AHhe,for 9-(methoxycarbony1)fluorenide anion as the model anion, 66 values are correlated with r = 0.9960, proving the self-consistency of our data as well as the soundness of this approach. Equations such as (5) should provide a simple means for estimating quantitative heterolysis energies in solution for thousands of bonds that give resonance-stabilized ions as products.
Introduction The overwhelming majority of the bonds that constitute the skeletal frameworks of organic molecules, both large and small, are those between carbon, oxygen, and nitrogen. Large molecules and polymers are built-up by the successive formation of these bonds. Correspondingly, depolymerization processes or the cracking of large molecules must take place through their rupture by one means or another. The principal mechanisms for bond formation involve free radicals, carbocations, or carbanions as reactive intermediates although other pathways, e.g. electrocyclic reactions, are also possible. Correspondingly, these intermediates must be produced in most bond-breaking reactions. Thermodynamics of formation for various molecules and for the strengths of their component bonds have played a crucial role in the fossil fuel industry especially in those areas associated with petroleum processing. Although some comparable data are available for homolysis of compounds produced by coal processing, few if any data are available for estimating the energy required to break the important bonds that make up the frameworks of coal macromolecules. A reasonable approach toward estimating the homolytic bond energies for cleavage into free radical fragments is provided by the method of additive group contributions developed principally by Benson and co-workers.’ However, to our knowledge, there is nothing equivalent at this time for predicting the heats of heterolysis of the corresponding bonds through cleavage into carbocations and carbanions. A few data have been developed for such processes in the gas phase for small fragments,2but these are particularly unsuitable for transfer to condensed phases because of the enormous solvation energies of ions, a problem which is much smaller when dealing with free radicals. Over the past 5 years we have developed methods based on our previous experience with reaction calorimetry, for measuring the energies of formation of carbon-carbon bonds through the direct reaction of carbocations with carbanions in appropriate solvents. Heats of coordination determined in this way are convertible into heats of heterolysis simply by changing the sign. Present address: Kentucky Center for Energy Research Laboratory, Lexington, KY 40512-3015.
0887-0624/87/2501-0017$01.50/0
In several recent article^,^ we have presented our results for the relationships between heats of coordination-heterolysis for the reaction of resonance-stabilized carbocations and carbanions and the corresponding free energy terms and rates. Not surprisingly, good extrathermodynamic relationships were found between these various properties. Furthermore, there were surprisingly good correlations between the heats of reaction for carbocations with carbanions and the corresponding properties for reaction of the same carbanions with protons donors, a much more familiar Bronsted acid-base property. These observations led3b to the perfectly reasonable possibility that there might be a formal relationship be-
tween the stabilities of the carbocations and carbanions and their heats of reaction, or conversely, their heats of heterolysis (AHhet). Equation 1, our first attempt at producing a ”master equation” that would relate these three properties through the pKR+of the carbocation and the pKa of the carbanion, predicted the heats of heterolysis for 21 compounds covering a range of 40 kcal/mol with a correlation of coefficient of 0.998 from a linear fit and an average difference of 0.79 kcal/mol between the calculated and experimental values. The present report describes experiments of the ensuing period, which extend this treatment to 84 compounds of much wider structural variation than those in the original report. Not only do the results provide for the first time heats of heterolysis for a variety of types of bonds in solution but also they yield a remarkably simple means for predicting them from data that are extensively tabulated in the literature.
Experimental Section Materials. Fluorene (Aldrich) was purified by recrystallization from hexane (mp 116-118 “C). Substituted fluorenes were prepared and purified according to procedures reported in the lit(1) Benson, S.W. Thermochemical Kinetics; 2nd ed.; Wiley: New York, 1976. (2) Bartmess, J. E.;McIver, R. T., Jr. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 2, Chapter 1. (3) (a) Arnett, E. M.; Molter, K. E. Phys. Chem. 1986, 90,383. (b) Arnett, E.M.; Chawla, B.; Molter, K.; Amamath, K.; Healy, M. J. Am. Chem. SOC.1985, 107, 5288. (c) Arnett, E.M.; Molter, K. E. Acc. Chem. Res. 1985, 18, 339.
0 1987 American Chemical Society
18 Energy & Fuels, Vol. 1, No. 1, 1987
erat~re.~-'' (p-Methoxypheny1)malononitrilewas synthesized by K. Molter following a published procedure.12 The remaining anion precursors were commercially available (Aldrich Chemical and Trans World Chemicals) and purified by standard proced u r e ~ .The ~ ~purity of these materials was confirmed by melting point, 'H NMR, and HPLC. Sulfolane (Phillips Petroleum Co.) was stirred with NaOH pellets overnight at 100-150 OC while argon was bubbled through the solvent. The sulfolane was decanted from the NaOH and stirred overnight with CaHz under an argon atmosphere at a temperature high enough to keep the Sulfolane from solidifying. The dry solvent was then vacuum distilled (bp = 110-111 OC (1 Torr)). Upon solidifying, the pure dry Sulfolane (mp = 28.5 "C)14 formed a colorless, transparent glass, which was protected from contact with air. 3-Methylaulfolane(Parrish Chemical Co.) was stirred ovemight at room temperature with CaHzunder an argon atmosphere and then vacuum distilled (bp = 101-102 OC (1torr)). The purified solvent was transferred to an argon-filled drybox where the melted Sulfolane and 3-methylsulfolane were mixed to form a 5%/95% 3-methylsulfolane/Sulfolane solvent mixture. This mixture was stirred over CaH2 for 1 day, filtered, and degassed by the freeze-thaw method. A water content of less than 60 ppm was considered acceptable. An oil dispersion of potassium hydride was washed thoroughly with dry pentane under an argon atmosphere to remove the mineral 0i1.l~ The resulting hydride powder was dried under vacuum and then transferred to an argon-filled drybox. Triphenylcarbinol (Aldrich),triphenylcyclopropene (Alpha), 9-phenyl-9-xanthenol (Fluka) and xanthene (Aldrich) were converted to their corresponding tetrafluoroborate salts by using the procedures described by Dauben et al.lS These carbocations were washed with anhydrous ethyl ether and dry ice-cold chloroform under an argon atmosphere. Commercially available tropylium tetrafluoroborate(Aldrich)was recrystalked from a CH3CN/Eh0 mixture. Trimethylcyclopropenylium tetrafluoroborate was prepared by K. Molter following the procedure of Closs et al." All the carbocations were dried under vacuum and transferred to an argon-filled drybox. Generation of Fluorenyl Anions. The anion precursor (0.04-0.06 g) was dissolved in 40 mL of degassed 5%/95% 3methylsulfolane/Sulfolane,and then an excess amount (0.02-0.04 g) of KH was added to it. All of the operations for preparing the anion solutionswere done in an argon-fied oxygen-free Vacuum Atmospheres drybox. The mixture was stirred for about 30-60 min at room temperature. After a high enough anion concentration was obtained (visualizedby the anion color),the solution mixture was filtered directly into the reaction vessel. Calorimetry. Heats of reaction (AHm) of the carbocations with the various anions in the Sulfolane mixture were measured by using a Tronac 450 titration calorimeter at 25 "C. The operation of the calorimeter was checked periodically by measuring the heat of protonation of an aqueous solution of THAM [tris(hydroxymethy1)aminomethanel or NaOH with a standard aqueous HC1 solution. (4) Anet, F. A.; Bavin, P. M. G. Can. J. Chem. 1966, 34, 991. (5) Ullman, F.;Wursternberger, R.Ber. Dtsch. Chem. Ges. 1904,37, 73. (6) Bavin, P.M.G . Can. J. Chem. 1960,38,917. (7) Matthews, W. S.;Bares, J. E.; Bartmess, J. E.; Bordwell, F. G.; Cornforth, F. J.; Drucker, G. E.; Margolin, Z.; McCallum, R. J.; McCollum, G. J.; Vanier, N. R. J. Am. Chem. SOC.1976,97, 7006. (8) Wislicenus, W.; Rues, K. Ber. Dtsch. Chem. Ges. 1910, 43, 2719. (9)Von Holbro; Tagmann, E. Helu. Chim. Acta. 1960, 2181. (IO)Murphy, W. S.; Hauser, C. R. J. Org. Chem. 1966,31, 85. (11) Bordwell, F. G.; Clemens, A. H. J. Org. Chem. 1982, 47, 2510. (12) Troughton, E.B.; Molter, K. E.; Amett, E. M. J.Am. Chem. SOC. 1984,106, 6726. (13) Perrin, D. D.; Armarego, W. L. F.; Perrin, D. R. Purification of Laboratory Chemicals, 2nd ed.; Pergamon: 1980. (14) Martinmaa, J. In The Chemistry of Nonaqueous Solvents; Lagowski, J. J., Ed.; Academic: New York, 1976. (15) Schilling, S. L. Ph.D. Thesis, Duke University 1984. (16) Dauben, H. J., Jr.; Honnen, L. R.; Harmon, K. M. J. Org. Chem. 1960,25, 1442. (17) Closs, G . L.; Bell, W. A.; Heyn, H.; Dev, V. J. Am. Chem. SOC. 1968, 90,173.
40
--
:
30
-
20
-
10
Arnett et al.
D
m
..
-
TMCP 0
O. l o
Trnyl TPCP 9.PhXa Tqyiium
10
-1.178pKR+
20
30
XanViylium
Y
+ 1.176pKa
Figure 1. Correlation of measured heats of heterolysis for 72 C-C and C-0 bonds to give resonance-stabilized ions by the original "master equation" (eq 1) (r = 0.8812). The solutions of the carbocations (0.08-0.1M) were prepared inside the argon-filled drybox by using an analytical balance and volumetric flask. Before each calorimetric run, the calibrated motor-driven buret, filled with carbocation solution, and the reaction vessel, containing about 40 mL of carbanion solution, were connected to the calorimeter insert assembly. A dry argon atmosphere was maintained at the top of the reaction vessel to protect the carbanion solution/solvent from air. The operation of the Tronac 450 titration calorimeter has been described elsewhere.lB All AHm measurements were conducted in the isoperibolic mode at 25 "C. Each reported AHH,, is the average of at least four and usually six or more enthalpy measurements with the same stock solution of carbocations. Reproducibility of the AHm results was verified by using different samples of carbocations and several carbanion solutions prepared on different days over a period of several months. Product Analysis. The number of products formed by the reaction between the carbocations and anions was determined by HPLC analysis using an Alltech 4.6 mm X 25 cm C18 reverse phase column and THF/H20 (60/40) pumped at 0.9 mL/min. The UV detector was set at 254 nm. The samples of the reaction mixturea were either taken directly from the calorimeter's reaction vessel after completing the enthalpy measurements or the reaction was run on a small scale (-50 wmol) inside an argon-filled drybox. The reaction samples were protected from air, and the excess carbocation and anion were quenched with degassed water prior to injection of the sample into the HPLC. Products from anion/carbocation reactions in the Sulfolane mixture were isolated from reactions run in the drybox. The anions were prepared as described earlier except on a larger scale (0.2 g), and a slight excess of a carbocation, dissolved in the Sulfolane solvent mixture, was added slowly. The reaction was stirred for 1 h at room temperature, and the reaction mixture was removed from the drybox and poured into NaC1-saturated water (100 mL). The water layer was extracted with EhO (2 X 50 mL). The ether layer was washed exhaustively with deionized HzO (5 X 100 mL) and allowed to evaporate slowly. During evaporation crystals formed. The solid was isolated, recrystallized, and characterizedby melting point, 'H NMR, and elemental analysis.
Results The success of a broad-scale study of carbocation-carbanion reactions requires a solvent that is stable t o these types of reactive intermediates and t o the acids and bases (18) (a) Amett, E. M.; Chawla, B.; Bell, L.; Taagepera, M.; Hehre, W.
J.; Taft, R. W. J. Am. Chem. SOC.1977, 99, 5729. (b) Arnett, E. M.; Chawla, B. J. Am. Chem. SOC.1978, 100,217. (c) Arnett, E.M.; Petro, C. J. Am. Chem. SOC.1976,98, 1468.
Heterolysis Energies in Solution
Energy &Fuels, Vol. 1, No. 1, 1987 19
Table I. Heats of Heterolysis (kcal/mol) = -AHfor the Reaction of Carbocations with Carbanion at 25 "C in 5%/95% 3-Methylsulfolane/Sulfolane Dh
Ph
1 0 Ph/'\Ph
4.63
S-I-BUFIH. FIH, SBzFIH 2-BrFIH QPhFIH 9-PhSFth 2-Br-9-PhSFIH QPhS0,FIH BCOfieFlH 9-CNflH 2.7-Br2-9-COfieFlH
24.35 22.80 21.37 20.40 17.90 15.40 13.20 11.55 10.35 8.30 8.52
Ph
Ph
3.1
1.1
4.7
7.4
-0.84
____________ ._._________ '53.49fl.70 '45.90f0.89 '52.77f0.44 '84.58f0.87 .___________ ._._._______ 38.45i1.00 ._________.. _____.-----'41.23t0.57 '80.38f0.93 ________._-33.84f0.32 29.34f0.28 35.51f0.58 '90.29f1.48 '51.57f1.41 '45.80f0.98
33.61f0.34 29.41f0.52 28.35f0.59 25.81f0.42 24.62f0.62 19.78f0.85
27.49i0.18 25.4ofO .50 22.23t0.36 20.62f0.12 19.58f0.30 18.22i0.10
needed to generate them. In our initial studies, acetonitrile and bewmitrile were employed, with sodium hydride used as the base for generating carbanions. However, further experience suggested that potassium hydride would give cleaner, faster reactions, but this base attacked the two nitrile solvents and often gave insoluble products. Sulfolane looked promising, but its high freezing point presented problems, which were finally solved by mixing it with 5 vol % 3-methylsulfolane. This mixture with potassium hydride for generating both carbanions and phenolate anions as used throughout the studies reported here. The mixture is also an excellent medium for carbocations, although their salts are more readily accessible and for the most part did not require generation inside the drybox. Table I presents heats of heterolysis for bonds formed from the reaction of six carbocations covering the pKRt range from -6.63 to 7.4; with 21 carbanions, whose pKa values range from 5.67 to 24.35 and four phenoxides, the pK, values of whose parent phenols range from 4.59 to 19.05. Figure 1portrays a "Milky Way" of points for these reactions scattered around the linear correlation of the original master equation, which was based simply on a small but wide ranging number of coordination reactions that fitted the equation on the x axis of Figure 1. Figure 2 recognizes the large structural variation of the new systems included since our previous report, which was
29.21f0.42 23.84f0.49
30.52f0.45 28.5eiO. 12 27.17fO.54 24.8ei0.53 22.52fO.22 19.45f0.11
._________._ 22.35f0.86 20.51f0.28 17.Uf0.43
based on reactions of three tertiary cations: trityl, triphenylcyclopropenium, and trimethylcyclopropenium. The new secondary cations, tropylium and xanthylium, generate a second correlation line lying considerably above that of the first master equation, while 9-phenylxanthylium, a tertiary cation, falls on the correlation line with the original tertiary cations. Not surprisingly, reactions with phenoxide ions generated a third correlation line, which lay considerably below that for reactions of the carbanions. Figure 2 indicates the resolution of the various scattered points on Figure 1into three separate correlation lines whose equations are listed in the Discussion. All of these have coefficients of correlation greater than 0.990 and their slopes appear to be relatively insensitive to the pKa values of the anions although there is a wide range of them including fluorenes, malonitriles, acetonitriles, and phenoxide ions. Some of the more reactive cationlanion mixtures gave very large heats of coordination and are not included on Figure 1or 2 although they are listed in Table I (e.g., the reaction of trityl cation with 9-tert-butylfluorene). All of these reactions gave multiple products as shown by HPLC analysis and at the present time are considered to be the result of single-electron transfer followed by a free-radical chain reaction. A second source of multiple products, which we have not yet been able to test, would occur if the
Arnett et al.
20 Energy & Fuels, Vol. 1, No. 1, 1987
0 4 5
'
.
I 5
15
ApKr+
35
25
+
BpKa
Figure 2. Resolution of data on Figure 1 into correlations for tertiary carbocations-carbanions (eq 2, r = 0.9950), secondary cations-carbanions (eq 3, r = 0.9902), and carbocations-phenoxy anions (eq 4, r = 0.9934) in the master equation form.
delocalized cation and anion systems formed covalent bonds at a variety of sites around their peripheries. At the present time we have no means for discriminating between these possibilities; however, the great majority of reactions whose points are presented on Figure 1 and 2 gave only one product by HPLC. Since virtually all reactions give some type of measurable heat change, only those that are clean are of thermochemical significance. In order to give further credibility to our studies, two products have been isolated (see Experimental Section) and fully characterized as shown below. N-C
n=c,
I
I1
n
111
111: mp 149-150 "C; 'H NMR CDCl,, 80 MHz) 6 2.5 (m, 1 H), 5.2 (m, 2 H), 6.2 (m, 2 H), 6.6 (m, 2 H), 7.3-7.9 (m, 8 H). Anal. Calcd for C21H15NC, 89.65; H, 5.37; N, 4.98. Found: C, 89.95; H, 5.03; N, 4.99.
IV
I1
V
V mp 203-210 "C; lH NMR (CDCl,, 300 MHz) 6 7.10 (dd, 4 H), 7.35 (m, 11 H), 7.60 (m, 6 H), 7.80 (m, 2 H). Anal. Calcd for C35H23N:C, 91.87; H, 5.07; N, 3.06. Found: C, 92.15; H, 5.05; N, 3.12.
Discussion Figures 1and 2 compare the applicability of the original master equation (eq 1)to a wide range of carbocations and resonance-delocalized anions. In Figure 1, the results for 66 carbocation-carbanion combinations to produce cova-
lent products are accomodated within a band covering 35 kcal/mol with an average width of 6.8 kcal/mol distributed around our original correlation line. Considering the simplicity of eq 1and the relative accessibility of the pKR+and pK, data needed to use it, we consider it to be a practical successful tool for predicting the relative stability to heterolysis of large complicated macromolecules such as would be found in coal fractions. Equation 1 and the simple thinking that lies behind it are certainly of qualitative value and for many purposes can give a crude estimate within 7 kcal/mol of relative bond strengths, which should be useful for predicting the relative vulnerability of different bonds to cleavage to resonance-delocalized ions. As we shall see below, it can be improved considerably. Correlation of.the data on Figure 1 can be refined if account is taken of the types of ions that were combined, which, therefore, heterolysis should produce. In Figure 2, one line represents reactions of tertiary cations, either triaryl or trisubstituted cyclopropenium ions in their reactions with resonance-delocalized carbanions. A second group is produced by the use of secondary carbocations such as xanthylium or tropylium and the third line represents reactions of both classes of cations with phenoxy anions to form carbon-oxygen bonds. If these three groups are treated separately, the quality of each separate correlation equation is improved dramatically to give an average standard deviation from each line of less than 2 kcal/mol. The three equations AHhet = 8.577 - 0.627(pKR+)+ 1.328(pKa) (7 AHhet AHh,,
+ 1.302(pKa) = 3.556 - 1.892(pKR+)+ 1.322(pKa)
= 13.484 - 0.434(pKR+)
1 ,'\
each represent a clearly defied and easily identified ml' of compounds. At this point, it is appropriate to raise L 3 questions: (1)What are the experimental limitations of the proposed master equation treatment? (2) Why does the original master equation (Equation 1)fail as a precise general treatment for C-C bond heterolysis? (3) Why does the master equation approach work as well as it does? (1) Experimental Limitations. It is important at the outset to understand that both the methodology and formalism behind eq 1 require that it be applied only to resonance-delocalized ions. In fact, this is not a serious practical limitation since it is only those carbocations and carbanions which enjoy this type of stabilization that have been available for extensive study in aqueous sulfuric acid (for pKR+) or in MezSO (for pK,). The highly unstable aliphatic and alicyclic carbocations can only be approached at low temperatures in superacid media or in the gas phase, and the corresponding carbanions can only be studied in the gas phase by present methods. Nonetheless, many of the most important cleavable bonds, by both heterolysis and homolysis, in fossile fuel macromolecules are derivable from resonance-stabilized species. Many of the same structures that would stabilize an unpaired electron through resonance may also stabilize a carbocationic or anionic fragment. Beyond the requirement of resonance-stabilization, our correlation lines are limited at both ends. The most exothermic coordination reactions between the least stable carbocations and carbanions lead to reactions that are much more exothermic than predicted by the "master equations", which we have found by HPLC (see Experimental Section) to be accompanied by the formation of a number of products rather than the usual single product obtained from the reactions that fit the correlation lines in Figures 1and 2. These observations are consistent with the hypothesis that the abnormally exothermic reactions
Heterolysis Energies in Solution
Energy &Fuels, Vol. 1, No. 1, 1987 21 50
40
30
20
m Trityl TPCP 9.PhXa TraMium m TMCP Xanthylium b
b
kltyl TPCP bopqlium
A e
10
0 .5
.I5
-10.23AMI
5
10
20
+ 1.!MpKa
Figure 3. Correlation of AHw by master eq 5 (r = 0.9948)where *-delocalization energy of three cations replaces pKR+.
occur by single electron transfer to give a cascade of free radical products. At the lower end of the lines in Figures 1 and 2 the reactions are limited by the lack of thermodynamic driving force. In our early ~ t u d i e swe , ~ demonstrated that if the stabilities of the carbocationic and carbanionic partners are sufficiently great, the stabilized ions can coexist indefinitely without reaction. Other less stable species in turn may maintain a dynamic equilibrium with partial formation of a covalent product in the presence of,cations and anions. Accordingly, a heat of coordination of at least 5 kcal/mol is required to insure complete reaction. Another limitation which must be born in mind, for which we currently have very little information, is that the cations and anions may react a t several reactive sites on their frameworks and so may form bonds a t a different position than might be expected. This caveat follows simply from the fact that both types of species have their charges and, therefore, their reactive centers delocalized over their frameworks and are clearly candidates for ambient reactivity. (2) Reasons for Failure of the Original, Simple Master Equation. On careful consideration it is surprising that the 70-odd heats of reaction between a wide variety of carbocations and carbanions plotted as Figure 1can be fit so well with only two lines on Figure 2. After all, both pKR+and pK, are free energy terms, and both are obtained in media different from that used for determination of A H h e t . Thus, the separate lines in Figure 2 may be due to entropy effects (differences between enthalpies and free energies), to solvent effects, or to both. Several lines of evidence given below imply clearly that the discrepancies lie chiefly in the use of pKR+ data as the measure of carbocation stabilities. Figure 3 uses 7r delocalization energies19for three of the cations-two tertiaries and one secondary-with the pK, values of the carbanions. All of the 32 points fall on the same line with a correlation coefficient of 0.9948. This is not only reassuring for our basic strategy; it also increases its value considerably since only a rather small number of pKR+values have been determined, whereas a-delocaliza(19) Streitwieser, A. Molecular Orbital Theory for Organic Chemists; Wiley: New York, 1961;p 365. AMi for the three cations used to plot Figure 3 are trityl = 1.800, tropylium = 2.000, and triphenylcyclopropenium = 2.309.
30
-3.WAHSCMF
50
40
+
60
1.318pKa
Figure 4. Correlation of AH& for 54 C-C bonds by using master eq 6 (r = 0.9960)where the heats of reaction of the six carbocations with 9-(carbomethoxy)fluorenide ion replaced pKR+.
tion energies can be calculated by well-established molecular orbital procedures for a wide range of resonance stabilized carbocations. Figure 3 implies, although the data are limited, that Equation 1 can be replaced by a new equation of greater precision and of much wider generality. Mhet
= 30.74
- 10.23(AMi) + 1.34(pKa)
(5)
Further evidence that the use of pKR+ limits the precision of our approach lies in Figure 4. Here we have used the heats of reaction of the six carbocations with one carbanion (9-(carbomethoxy)fluorenyl)as the measure of their stabilities to replace the use of pKR+ in the original master equation. When this is done, all of the & A & ,I. data for the carbocation-carbanion combinations are accommodated to one line with r = 0.9960. Figure 4 provides in addition strong testimony for the self-consistency of the many data in Table I. With the thermochemical data that we have accumulated, which can obviously be extended by the same technique, a third equation of high precision and predictive value can be used. Mhet
= -12.046 - 0.935(hH0,)
+ 1.318(pKa)
(6)
This is useful for testing the self-consistency of our results and predicting A H h e t for any of the 120 C-C bonds generated from the combinations in Table I. However, it does not have the wide generality implied by equations of the type of eq 5 , which use calculated delocalization energies for the carbocations and the large data base of pK, values in Me2DMS0. It is fortunate that the pK, values of the anions can be used. Over 1300 such data have been measured with high precision by Bordwell and his co-workers in dimethylsulfoxide a t 25 O c a 7 With these pK, values available and the cation stabilities calculable, the estimation of A H h e t is feasible for thousands of C-C bonds. Interesting insight into the reason for the failure of pKR+ is suggested by Figure 5, which provides a good correlation (r = 0.9934) of C-0 heterolysis energies from the reaction of phenoxy ions with carbocations by using the original form of the master equation. Now no separation into lines for secondary and tertiary cations is seen. An attractive explanation of this difference between the behavior of carbocations with oxyanions as compared to carbanions is suggested by the source of pKR+data. These are derived
Arnett et al.
22 Energy & Fuels, Vol. 1, No. 1, 1987
24
-
22
-
9.phenylramhenylim
2Q-
18
-
16
-
14
-
12
6
-1.892pKr+
+
2
A
0
pKR+
1.322pKa
Figure 5. Correlation ( r = 0.9934) of AHhetfor 13 C-0 bonds from reeaction of various phenoxide ions with five carbocations by master eq 4.
Figure 6. Correlation (r = 0.9999) of the heat of ionixation of trityl alcohol, xanthenol, and 9-phenylxanthenolin a 5%/95% trifluoromethanesulfonic acid/sulfolane mixture with the carbinol’s pKR+.
by the cleavage of the carbinol precursors of the carbocations in aqueous acid solution:
heats of ionization to form a wide variety of anions in MezSO and the pK, values of their corresponding precursors. More recent comparisons of heats of coordination of carbanions with those of carbocations show close correlation with the proton basicities of these carbanion^.^ Again, the correlations by Arnett and H ~ f e l i c hbetween ~~ heats of formation of carbocations in various acidic media and their pKR+values in sulfuric acid all show that the extrathermodynamic correlations between heats of formation of these types of ions and their free energies of formation are excellent. This means that the concurrent entropy terms are small, constant, or proportional to AGi or AHHi. This general explanation is completely supported by the arguments in the previous section growing from Figures 3-6. Figure 3 is based on quantum mechanical calculations for Ah&, which correspond to the ?r-delocalizationenergies of the carbocations in the gas phase. Clearly this gives a better and more general fit than Figures 1 or 2, which are based on the inexact model of C-0 heterolysis in aqueous sulfuric acid with C-C heterolysis in the mixed-sulfolane solvent. Finally, Figure 4 demonstrates the excellent consistency obtained when heats of heterolysis for C-C bonds are compared with each other in the same solvent. Conclusion. Equations 5 and 6 as shown by Figures 3 and 4 represent an enormous improvement over the original master equation (eq 1). This improvement is derived from the use of improved models for the stabilization energy of the carbocation. No improvement of the anion stabilization energy appears to be needed for these taken directly from Bordwell’s large data base for pK, values in Me2S0, a nonhydroxylic dipolar solvent similar to Sulfolane. The proposed strategy of predicting bond heterolysis energies in terms of the resonance stabilization energies of the resulting ions is supported by the 70-odd data correlated here and should be extensible by simple calculation to thousands of compounds.
I I
-C-OH
+
H30+
I + I
-C+
2H20
Here a carbon-oxygen bond is being made and broken as is the case with the phenoxide ion reaction. Thus, Figure 4 and 5 imply strongly that our original attempt to use free energies of heterolysis of carbon-oxygen bonds in aqueous acid as a model for heats of heterolysis of carbon-carbon bonds in sulfolane solutions is the cause of the failure of the original equation (eq 1). Final evidence that the problem does not lie in solvation factors from replacing aqueous sulfuric acid with Sulfolane nor from entropy factors due to the use of free energy terms instead of enthalpies is shown by Figure 6. Here heats of ionization of trityl alcohol (AHi = 13.25 kcal/mol), xanthenol (AHi = 21.74 kcal/mol), and 9-phenylxanthenol (AHi = 24.42 kcal/mol) have been measured by using 5% trifluoromethanesulfonic acid in Sulfolane. An excellent correlation with their pKR+ values is seen. Thus, when heats of heterolysis of C-0 bonds are used to model AHhet for C-C bonds, the equation fails in contrast to the results shown in Figure 4.
(3) Why Does the “Master Equation” Work So Well? It is worth next considering why the very simple treatment represented by eq 1-4 covers such a range of reactions. The overall reason for our success is a direct result of the charge delocalization of all the reacting ions, which not only reduces their demand for stabilization by solvation but also means that solvation does not involve site-specific interactions of the types that complicate the solvation of charge-localized ions. Fundamental evidence for this claim is the excellent correlations between heats and free energies of ionization for both types of resonance-stabilized ions in the gas phase and the corresponding ionization properties (pK, in MezSO and pKR+ in aqueous sulfuric acid) reported respectively by Taft and Bordwell.20i21 Beyond that, studies of Arnett and VenkatasubramanianP show good correlation between (20)Wolf, J. F.;Abboud, J. L. M.; Taft, R. W. J. Org. Chem. 1977,42, 3316. (21)Taft, R.W.; Bordwell, F. G., private communication.
Acknowledgment. This research was supported by the Gas Research Institute to which we are most grateful. (22)Arnett, E.M.;Venkatasubramaniam,K. G. J. Org. Chem. 1983, 48,1569. (23)Arnett, E.M.;Hofelich, T. C. J.Am. Chem. SOC.1983,105,2889.
Energy & Fuels 1987, 1 , 23-28 Registry No. I, 26811-28-9; 111,105281-51-4;IV, 14039-14-6; V, 105281-52-5;Ph3C+,13948-08-8; g-PhXa-, 20460-07-5;TMCP', 26827-04-3;g-t-BuFlH-, 73838-69-4; FlHT, 12257-35-1;g-BzFlH-, 53629-11-1; 2-BrFlH-, 85535-20-2; g-PhFlH-, 31468-22-1; 9PhSFlI-I-? 71805-72-6;2-Br-9-PhSFlH-,73838-76-3;9-PhS02F1H-, 71805-74-8; 9-CO2MeF1H-, 12565-94-5;g-CNFlH-, 12564-43-1; 2,7-Br2-9-C02MeF1H-,73838-70-7; m-CNPhMN, 99726-50-8;
23
m-CF3PhMN,99726-51-9; m-ClPhMN, 99726-52-0;p-ClPhMN, 91880-07-8; PhMN, 45884-26-2; p-MePhMN, 91880-08-9; pMeOPhMN, 85535-17-7;2-NaphthylAN, 19268-56-5; p-CF,PhAN, 100859-08-3;p-N02PhAN,48129-94-8;p-N02PhOH,14609-74-6; 3,5-ClzPhOH, 65800-69-3;4-t-BuPhOH, 28528-33-8;4,6-dinitroo-cresol,46325-40-0; xanthylium, 25187-66-0; xanthenol, 90-46-0; 9-phenylxanthenol, 596-38-3;trityl alcohol, 76-84-6.
Morphology of Retorted Oil Shale Particles D. C. Adamst and 0. P. Mahajan* Corporate Research, Amoco Research Center, Naperville, Illinois 60566 Received September 4, 1986. Revised Manuscript Received October 9, 1986
The formation of two distinct coked particle morphotypes, namely exfoliated and peripheral, during oil shale retorting and their implications toward the coking mechanism are discussed. Rapid heating causes swelling, exfoliation, and formation of a matrix of veinlets and cracks; these changes lead to uniform coking within the particle body. In contrast, slow heating produces the peripheral morphotype with a low coke density at the center and a high coke density at the periphery. The difference in the coking morphology of the two particle types has been explained on the basis of kerogen pyrolysis kinetics. Of the two morphotypes, peripheral coke makes the particles stronger and more resistant to size attrition. I n addition to the formation of coke in the particle body of the two morphotypes, coke is also formed on the outer surface of both the particle types. It has been concluded that more coke is produced from the secondary decomposition reactions than directly from the kerogen itself.
1. Introduction Coke formation is recognized as a limiting factor that detracts from high oil yield during oil shale retorting. Approximately 20% of Green River oil shale organic matter is converted to coke during conventional retorting.I2 Various approaches have been used to reduce coke formation, such as retorting in the presence of hydrogen3g4 and steam"' and use of high sweepgas rates,'+ reduced pressure,9Jo and rapid heatup The objective of this study was to correlate the retorted oil shale residue characteristics with processing conditions and to determine the effect of particle morphology on particle strength. 2. Experimental Section 2.1 Samples. Two samples of Green River oil shale from the
Rio Blanco (Colorado) C-a tract were used in this study. They are designated as S1and S2 in the text. The two samples were of 41 and 15 gal/ton grade, respectively. Oil shale samples were mixed with dry ice and ground to the desired particle size. The ground samples were placed in a nitrogen-filled glovebox where they were riffle-divided and packaged and sealed in bottles under nitrogen; the inert atmosphere was used during grinding and riffling to minimize weathering of shale kerogen. We believe this is important because shale kerogen, like coal, undergoes weathering even under ambient conditions.12 2.2 Retorting. For particle morphology studies, oil shale particles were dropped into a preheated fluidized bed of &dumina particles in a quartz tube to pyrolyze them at a maximum heatup rate; the bed was fluidized with nitrogen gas and maintained at
* To whom correspondence should be addressed.
Present address: Energy Recovery Technology, Naperville, IL
60540.
0887-0624/87/2501-0023$01.50/0
540 "C. The particle heating rate was estimated to be -1000 "C/min. When oil shale particles were dropped into the fluidized bed, they agglomerated with the alumina particles. While it was possible to isolate retorted oil shale particles for coke morphology studies, the agglomeration of the coke particles with the alumina particles complicated the friability measurements on the spent shale particles. This problem was circumvented by retorting 15 g of oil shale particles in a N2flow (300 cm3/min) up to 540 "C in a custom-built thermogravimetric analyzer (TGA). The TGA runs were made at a heating rate of 200 "C/min (maximum rate possible in the TGA) and 1.5 "C/min. The sample prepared at 1.5 "C/min was also used for coke morphology studies. The TGA was also used for combustion of the spent oil shale samples. For the combustion studies, -5 g of sample was heated in flowing air (300 cm3/min) from ambient temperature to 500 "C at 10 "C/min; the soak time at 500 "C was 30 min. N
( 1 ) Baughman, G. Synthetic Fuels Data Handbook, 2nd ed.; Cameron Engineers: Denver, CO, 1978; p 46.
( 2 ) Singleton, M. Lawrence Liuermore Lab., [Rep.] UCRL 1982, UCRL-53273. ( 3 ) Feldkirchner,H. L. Synth. Fuels Oil Shale, Symp. Pap. 1979,1980, 489-524. ( 4 ) Greene, M. I.; Damukaitus, J. Energy Prog. 1985, 5 ( 3 ) , 143-146. (5) Campbell, J. H. Lawrence Liuermore Lab., [Rep] LTCID 1978, UCID-17770, ( 6 ) Allred, V. D. Oil Shale Symp. Proc. 1978, 12th, 241-251. ( 7 ) Wall, G. C. Oil Shale Symp. Proc. 1984,17th, 300-309. ( 8 ) Campbell, J. H. Lawrence Liuermore Lab., [Rep.] UCRL 1977, UCRL-79034. ( 9 ) Sohn, H. Y.; Yang, H. S. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 265-270. (10) Yang, H. S.; Sohn, H. Y. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 271-273. (11) Richardson, J. H. Lawrence Liuermore Lab., [Rep] UCID 1982, UCID-19548. (12) Adams, D. C., unpublished results.
0 1987 American Chemical Society
