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The conformational free energy difference for the trideuteromethyl substituent in cyclohexane
HAROLD BOOTH A N D JEREMY RAMSEY EVERETT~ Department of Chemistry. Uniuersity of Nottingham, Nottingham, England NG72RD
Received June 16, 1980 This paper is dedicated to Prof. Raymond U. Lemieux on the occasion of his 60th birthday
HAROLD BOOTH and JEREMY RAMSEY EVERETT. Can. J. Chem. 58,2714 (1980). Studies at 169 K to 194 K of the 13C nmr spectrum of ~is-l-ethyl-[4-Me-~H~]-4-methylcyclohexane show that the conformational
enthalpy difference -AHo(C2H3) is 1.82 + 0.07 kcal m ~ l - ~ and the conformational entropy difference ASo(C2H3) is -0.28 + 0.4 cal K-I mol-l, values which do not differ significantly from the values for CH,. However, analysis of the room temperature 13C nmr spectrum of a mixture of cis-1-ethyl-4-methylcyclohexane and cis-l-ethyl-[4-Me-2H3]-4-methylcyclohexane showed that -AG"(C2H3) at 298 K is 11.89 + 1.46 cal mol-I less than that for CH,, i.e. C2H3 has a slightly greater preference than CH3 for the axial orientation. The 13C nmr spectrumof a mixture of trans-1-ethyl-4-methylcyclohexaneand tran~-l-ethyI-[4-Me-~H~]4-methyl- cyclohexane indicates that deuterium-induced 13C nmr isotope shifts, all upfield, occur across 1 ,2 ,3 , and 5 bonds.
HAROLD BOOTH et JEREMY RAMSEY EVERETT. Can. J. Chem. 58, 2714 (1980). Une etude des spectres de rmn du 13C de I'ethyl-1 [Me-4-2H3]-methyl-4 cyclohexane cis, mesur6es entre 169 et 194 K, montrent
que la difference d'enthalpie conformationnelle - AW(C2H3) est de 1,82 + 0,07 kcal mol-I et la difference d'entropie conformation- nelle ASo(C2H3) est de -0,28 + 0,4 cal K-I mol-'. Ces valeurs ne different pas de f a ~ o n significative de celles de CH3. Cependant I'analyse du spectre de rmn du I3C 21 la temperature ambiante d'un melange d'ethyl-1 methyl-4 cyclohexane cis et d'kthyl-1 [Me-4-2H3] methyl-4 cyclohexane cis a montr6 que le AG"(C2H3) 21 298 K est de 11,89 + 1,46 cal mol-I plus faible que celle du CH3 i.e. la preference du C2H3 pour une orientation axiale est ICgkrement plus grande que celle du CH3. Le spectre rmn du "C d'un melange d'ethyl-1 methyl-4 cyclohexane trans et d'kthyl-1 [Me-4-2H3] methyl-4 cyclohexane trans indique que tous les dkplace- ments chimiques vers les champs forts du I3C induits par le deutirium se produisent a travers 1 ,2 ,3 et 5 liaisons.
[Traduit par le journal]
Introduction There is a growing interest in the effects of
isotopic replacement of nuclei on the position of conformational equilibria. As recently reported, we failed to detect, by nmr methods, a change in the conformational equilibrium in cis-1 ,4-dimethyl- cyclohexane after replacement of a methyl group by a 13C-methyl group (1). However, a change re- sulting from the replacement of CH, by C2H3 should be detected with greater ease. For example, using chemical shift measurements, Baldry and Robinson (2) succeeded in showing that the con- formational equilibrium in tr~ns-[l-Me-~H~I-l ,3- dimethylcyclohexane favours that conformation with CZH3 axial by about ll .0cal mol-I. More- over, circular dichroism studies have estab- lished that axial deuterium is preferred to axial hydrogen at the 3- and 4-positions of 2,2-dimethyl- cyclohexanone (3, 4); the shorter bond length of C-2H (as against C-'H), and the smaller vibra- tional amplitudes may well provide sufficient ex- planation.
Results and Discussion
in cis- 1-ethyl-4- methylcyclohexane 1 = 2 caused by the replacement of CH, by C2H3. The 13C nmr chemical shifts for carbons in 1 and 2, and molecu- lar proportions, are already available from a previ- ous study in the temperature range 141 K to 177 K (5). As the difference between the chemical shifts of C-7" and C-7' is as much as 7ppm, the room- temperature averaged shift of C-7 should be par- ticularly sensitive to any change in the position of equilibrium, i.e. the averaged shift of C-7 in 3 = 4
We chose '0 study the effect On the eq'ilibri'm should differ significantly from that of C-7 in 1 2. 'Present address: Department of Chemistry, McGill Univer- Moreover, a direct or intrinsic isotope effect On the
sity, Montreal, P.Q. chemical shift of C-7 is unlikely to occur across the
0008-4042/80/232714-06$01.00/0 @I980 National Research Council of CanadaIConseil national de recherches du Canada
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BOOTH AND EVERETT. 11. 2715
intervening six bonds. Initially, however, we analyzed the equilibrium 3 $ 4 by the low- temperature area method, followed by a compari- son of the derived thermodynamic parameters A H 0 (C2H3) and A S 0 (C2H3) with those previously de- termined for C1H3 (5).
The syntheses of cis- and trans- l-ethyl-4- methylc yclohexane have already been reported (6). A second synthesis also proved satisfactory and as illustrated in Scheme 1 was readily adapted to the preparation of molecules specifically trideuterated at the 4-methyl positions. The complete separation of cis- and trans-isomers was carried out by pre- parative gas-liquid chromatography after the final stage. Examination of the cis- and trans-l-ethyl- [4-Me-2H3]-4-methylcyclohexane by 2H nmr spec- troscopy proved conclusively that no scrambling of the deuterium had occurred during the synthesis.
Reagents: (1 ) Hz, PtO2 (4) CH3.C6H4S02CI (2) MeOH, HzSO, ( 5 ) LiAID,, ether (3) LiAlD,, ether
The 13C nmr spectrum of cis-1-ethyl-[4-Me- 2H3]-4-methylcyclohexane 3 = 4 was recorded within the range 169 K to 194 K, where ring inver- sion is slow compared to differences in chemical shifts between structurally identical nuclei in the two conformations. The proportions of 3 and 4 were obtained from the relative areas of well sepa- rated signals due to C-l ' and C-l"; signals due to C-8' and C-8" were similarly employed and the two equilibrium constants were averaged. The results were analysed as reported earlier (5) for cis- 1-ethyl-4-methylcyclohexane and the thermo- dynamic parameters for C2H3 were 1.82 + 0.07 kcal mol-I for -AH" and -0.28 + 0.4 cal K-' mol-I for AS0. Since the comparable parameters for CH, are 1.75 + 0.04 for -AH0 and -0.03 + 0.2 for AS0, it is obvious that the low temperature area
method is insufficiently accurate to distinguish C2H3 from CH,.
The theoretical background to the room- temperature chemical shift method is given below.
Let the mole fractions of 1 and 3 be x and y respectively. Let 67(H) and 67(D) be the observed chemical shifts of C-7 in 1 * 2 and 3 G 4, respec- tively, at room temperature. Let 67" and 67j be the chemical shifts of C-7 in 1 and 2 respectively. In the absence of intrinsic isotope shifts, ?j7" and tj7, are also the chemical shifts of C-7 in 3 and 4 respec- tively. Then
67(H) = ~6~ + (1 - ~)67#
and
67(D) = ~670 + (1 - ~)670
These equations give rise to
Now the mole fraction x can be calculated for any temperature from the thermodynamic parameters previously determined (5) for Me and Et. The shifts 67n and 671 are known at eight temperatures between 160 and 194 K, and extrapolation of the two linear plots yields theoretical values for tj7" and ij7, at room temperature (298 K). Thus, provided that 6,(H) - 8,(D) can be measured, the mole fraction y can be calculated.
Equation [I] shows, as expected, that the sen- sitivity of the method of determining (x - y) is a function of (87" - 67t) i.e. of the 13C nmr chemical shift difference, for the chosen carbon, between conformation 1 and conformation 2. Car- bon 7 was chosen for reasons already indicated, but two other carbons were considered, at C-1 and C-8. Carbon 8 was not useful because (ij8" - ti8,) is only 0.8 ppm, and although (S1. - tirr) is as great as 5.9 ppm, there is in this case the possibility of a direct isotope shift across 5 bonds.
The chemical shift difference S7(H) - 67(D) was determined from the 13C nmr spectrum of a solution containing a mixture of cis-1-ethyl-4-methylcyclo- hexane 1 2 and ~is-l-ethyl-[4-Me-~H,]-4- methylcyclohexane 3 Z 4. It was also essential to incorporate in this mixture the trans-isomers 5 and 6. This allowed us to establish, under identical ex- perimental conditions and for a similar structure, 8"
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2716 CAN. J. CHEM. V 'OL. 58, 1980
that intrinsic isotope shifts do not extend across 6 bonds, and also to measure accurately the intrinsic isotope shifts observed across a smaller number of bonds.
In the mixture containing 1 e 2 , 3 = 4 , 5 and 6, the ratio of cis-molecules to trans-molecules was approximately 2:l for both nondeuterated and deuterated species, whereas the ratio of nondeut- erated to deuterated species was 1: 1 for both cis- and trans-molecules, i.e.
Although the use of a molar ratio of 1:l for non- deuterated to deuterated species optimized the conditions for resolution of signals separated by small isotope shifts, it prevented assignment of the signals. Consequently the crucial experiment was exactly repeated after increasing the proportion of deuterated species from 50% to 55%.
In the 13C nmr spectrumof the mixture, recorded at 62.901 MHz, the signals for C-7 in 1 = 2, and for C-7 in 3 e 4, were well resolved; the separation was 2.21 Hz (0.035 ppm), the signal for the deuterated molecule 3 e 4 being at lower field. On the other hand the signals for C-7"' in the trans-molecules 5 and 6 were not resolved. Therefore we attribute the difference in chemical shift for C-7 in 1 = 2 and 3 = 4 as arising solely from an alteration in the position of conformational equilibrium caused by replace- ment of CH, by C2H3. 13C Chemical shifts for car- bons in 1 = 2 , 3 e 4,5 and 6 are recorded in Tables 1 and 2. Direct, or intrinsic isotope effects accom- panying the change 5 -+ 6 were observed for car- bons 9,4,3(5), and 1. It is important to note that all the intrinsic isotope shifts accompanying the change lH -+ 2H are upjield. Consequently it was
TABLE 1. I3C chemical shiftsa at 62.901 MHz (6 values, ppm down- field from Me4Si) for carbons in
1*2and3*4
Carbons 1 S 2 3 e 4
1 37.580 37.612 2,6 28.718 28.718 3,s 31.209 31.153 4 30.519 30.259 7 27.231 27.266 8 11.930 11.930 9 20.298 19.342b
'Measured at 298 K on a mixture of 1 P 2, 3 = 4, 5 and 6 using 32K data points over 3012Hz, givingapossibleerrordueto digiliza- lion of -10.092 Hz or f 0.001463 ppm.
bSeptet, with 'J("C-'H) = 18.94 Hz.
particularly reassuring that the observed shift for C-7 in 3 S 4 was downjield of that in 1 e 2. In fact this downfield shift, indicating that 6,(4) - 6,(D) is negative, establishes conclusively that mole frac- tion y is greater than mole fractionx, for (67" - 67j) is positive. Consequently, it is clear that the sub- stituent C2H3 has a greater preference for the axial orientation than CH3. The extent of this preference was expressed as an energy difference between AG0(C2H3) and AG0(CH3) of 11.89 + 1.46 cal mol-I (49.79 k 6.11 J mol-I). The principal errors arise from the extrapolation needed to de- termine (a7" - 67r) at room temperature, and from the digitization of the spectrum (k0.092 Hz). It was estimated that the possible error in the extrapola- tion was k15.725 Hz. However, since (67" - 67,) is 441.635 Hz, the proportional error arising from the extrapolation is rather less than that in 6,(H) - 6,(D) due to digitization.
The determined value of AG0(C2H3) - AG0(CH3) is very close to the value of 46 J mol-I obtained by Baldry and Robinson (2) from 13C nmr shifts in trans- [l-Me-2H3] 1,3-dimethylcyclohex- ane, although these workers neglected intrinsic isotope effects across 5 bonds. The intrinsic isotope effects measured in the present study are given in Table 2. Wehrli et al. (7) claimed that intrinsic isotope shifts for 13C occurred over as many as 6 bonds in [2JHl] cyclodecanone. How- ever, it is possible that these effects are due in part to the perturbation of a conformational equilibrium (8, 9). In this connection it is perhaps significant that whereas all the isotope-induced 13C shifts of the present study are upfield, several of those ob- served by Wehrli et al. are downfield. Anet and Dekmezian (9) have observed deuterium-induced lH shifts over 5 bonds when an axial hydrogen and an axial CD, were syn-diaxial in a substituted 1,3-
TABLE 2. 13C chemical shiftsa at 62.901 MHz (6 values, ppm downfield from Me4Si) for carbons in 5 and 6, and intrinsic isotope-
induced shifts I
Carbons 5 6 I ( P P ~ )
"Measuredat298Kon amixtureof 1 P 2 . 3 P 4 , Sand6 using 32K data points over 3012 Hz, giving a possible error due to digitization of -10.092 Hz or f 0.001463 ppm.
bSeptet, with 'J("C-'H) = 18.94Hz. <No separation observed.
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BOOTH AND EVERETT. 11. 2717
dioxane. However, the same compound did not reveal deuterium-induced Cbond or 5-bond I3C shifts.
The solvents used in this study were CDC1, and CFC1,-CDCl, (9: 1 vlv). The addition of CFCl, to CDCl, is required to allow measurements at tem- peratures below 200 K, but the volatility of CFCl, poses problems when accumulations are made over long periods at room temperature. Consequently low temperature spectra were determined in CFC1,-CDCl, whereas room temperature spectra employed neat CDCI,. Chemical shift data for sev- eral alkylcyclohexanes have shown that only small changes (generally deshielding) accompany the change from CFC1,-CDCl, to CDC1,. For exam- ple, the I3C nmr chemical shifts (at 302 K) for car- bons in trans-1-ethyl-4-methylcyclohexane, 5, measured on the same instrument, are listed in Table 3 for the two solvents. As anticipated, the largest solvent-induced changes are for carbons on the periphery of the molecule; the changes for ring carbons are insignificant. Bearing in mind that (Zi7" - 8,') for the system 1 * 2 is as great as 7.02 ppm, the error for this parameter in using a value taken from a determination in CFC1,-CDC1, (rather than CDCl,) is negligible.
Experimental Spectra
The 'H nmr spectra were measured at 99.8 MHz on a JEOL JNM-MH-100 spectrometer; 2H nmr spectra were measured in CHCI, on a JEOL JNM-PS-100 spectrometer interfaced to a Nicolet 1085 20 K computer; the reference was CDCI, (6 = 7.17ppm). The 13C nmr spectra were recorded on the JEOL JNM-PS-100 instrument at 25.15 MHz and on a Bruker WM 250 spectrometer at 62.901 MHz. Low temperature 13C nmr spectra were recorded as described previously (5).
Materials The preparations of cis- and trans-1-ethyl-4-methylcyclo-
hexane have been reported elsewhere (6).
TABLE 3. 13C chemical shiftsa at 25.147 MHz (6 values, ppm down- field from Me4Si) for carbons in 5
Solvent
Carbons CFC131CDC13*
"Measured at 302 K using 8K data points over 2500 Hz.
bProponions 9:1 by volume.
Methyl cis- and trans-4-Ethylcyclohexanecarboxylate 4-Ethylbenzoic acid (4.4723 g) was hydrogenated over
platinum oxide (0.203 g) in glacial acetic acid (25 cm3) at room temperature and atmospheric pressure. After 18 h the uptake of hydrogen was 2133 cm3 (theoretical 2000 cm3). The mixture was filtered and acetic acid was removed under vacuum. Distillation of the residue gave a mixture of cis- and trans-4-ethylcyclo- hexanecarboxylic acid (3.5714g, 79%) as a colourless oil, bp 88-94°C at 0.3 Torr (ref. 10 gives cis-, bp 127°C at 5 Torr and trans-, mp 49-49.8"C). Thin-layer chromatography on silica gel with CHC1,-MeOH 95:s gave 2 spots with Rf values 0.24 (major) and 0.06. The 'H nmr spectrum in CDCI, showed signals for the 1-hydrogen at 6 2.64 (cis, quintet with separations of about 5 Hz) and 6 2.30 (trans, triplet of triplets with separations of 12 Hz and 3.5 Hz). Mass spectrometry gave M? 156.1120 (C,H1602 requires 156.1150).
The above mixture (2.50g) was refluxed for 4 h with dry methanol (2.3 cm3, 1.80g) and concentrated sulphuric acid (0.15 cm3). After addition of water (10 cm3) the mixture was extracted several times with ether. The combined ether extracts were washed successively with saturated aqueous NaHCO, solution and saturated aqueous NaCl solution. Finally the ether was dried (MgS04), filtered, and distilled, leaving a residue of cis- and trans-4-ethylcyclohexanecarboxylate (2.418 g, 89%). A small sample was distilled as a pale yellow oil with an aniseed- like odour, bp 50°C (bath temp) at 14 Torr; tlc showed two spots, Rf 0.69 (major) and 0.06. The lH nmr spectrum showed the methoxy protons as singlets at 6 3.78 (cis-, major) and 6 3.76 (trans-), and the 1-hydrogen at 6 2.56 (cis-, quintet with separa- tions of about 5 Hz) and 6 2.26 (trans-, triplet of triplets with separations of 12 Hz and 3.5 Hz). Mass spectrometry gave M? 170.1286 (CloHl8O2 requires 170.1307). Microanalysis yielded C 70.25, H 10.35; CloH1802 requires C 70.55, H 10.65%.
cis- and trans-4-Ethylcycl0hexane[a,a-~H~]methanol Lithium aluminium deuteride (0.9741 g, 0.0232 mol) was
stirred in dry redistilled ether (40 cm3) under argon. A solution of methyl cis- and trans-4-ethylcyclohexanecarboxylate (5.4107 g, 0.0318 mol) in dry ether (35 cm3) was added to the slurry of LiA12H4 at a rate sufficient to maintain boiling. After completion of the addition, the mixture was stirred for 10 min, cooled in ice, and quenched by addition of iced water (9 cm3). Two molar H2S04 (45 cm3) was added and the mixture was extracted sev- eral times with ether. Distillation of the dried (K2C03) extracts gave a mixture of cis- and trans-4-ethylcyclohexane[a,a- 2H2]methanol (4.12g, 0.0286 mol, 90%) as a colourless oil, bp 100°C (bath temp) at 0.1 Torr. The 2H nmr spectrum showed a singlet at 6 3.27. Mass spectrometry gave M? - H 2 0 at 126.1366 (Cg1H142H2 requires 126.1378). Microanalysis gave C 74.7, H 13.65; Cg1H,62H20 requires C74.95, H 13.95%.
cis- and trans-4-Ethylcyclohexanemethanol A similar experiment to the above, using a mixture of methyl
cis- and trans-4-ethylcyclohexanecarboxylate (1.70 g) and lithium aluminium hydride (0.3008g) gave cis- and trans-4- ethylcyclohexanemethanol(1.3805 g, 97%), bp 50°C (bath temp) at 0.005 Ton-. The 'H nmr spectrum showed the protons of -CH2-0 as doublets (with separations of 6.5 and 5.8 Hz) at 6 3.56 (cis-, major) and 6 3.45 (trans-), respectively. The mass spectrumgave Mt - H 2 0 at 124.1241 (C,H,, requires 124.1252). Microanalysis yielded C 75.7, H 1235; C,HI8O requires C76.0, H 12.75%.
cis- and trans-4-Ethylcyclohexane[a,a-2H,]methanol 4'- Methylbenzenesulphonate
4-Methylbenzenesulphonyl chloride was purified by dissolu- tion in ether and repeated washing with aqueous sodium carbo-
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271 8 CAN. J . CHEM. VOL. 58, 1
nate (1 M) until the pH of the ether exceeded 6.0. The ether I solution was dried over anhydrous Na2S04, filtered, and evapo-
rated. The crystals of pure sulphonyl chloride were crushed and dried under high vacuum.
The mixture of cis- and trans-4-ethylcyclohexane [a,a- 2H2]methano1 (7.009 g, 0.0486 mol) was dissolved in dry (KOH), redistilled pyridine (15.36g) at 0°C. To the stirred mixture was added 4-methylbenzenesulphonyl chloride (10.2011g, 0.0535 mol) in portions during 30 min. The mixture was stirred for 2 h at 2OC and then for afurther 1.5 h as the temperature was
T (K) T-' (K-') K In K
allowed to rise to 14°C. A mixture of concentrated hydrochloric The data were analyzed as described elsewhere acid (30 cm3) and ice water (100 g) was added to the white, pasty (5). ~~~~i~~ in mind the following experimentally reaction mixture. Several extracts with ether were combined, dried (MgSO,), filtered, and evaporated. The residue of cis- derived parameters for the group: * 0e06 and trans-4-ethvlcvclohexane ra.a-2H,lmethanol 4'-methvl kcd m01-I for -AH0 and 0.64 f 0.35 cal K-I m01-' -- benzenesulphonate~(14.71 g, 102%) was a colourless oil con- for AS0, and on the reasonable assumption of ad- taminated with ether. An attempted distillation of a small por- ditivity, We Obtain the following: tion at 1 Tom caused decom~osition. The zH nmr spectrum gave signals at 6 3.88 (-CD,O-, cis-) and 6 3.65-(-~~,6--, -AH0fC2H,) = 1.79 + 0.07 kcal mnl-I
cis- and trans-4-Ethylcyclohexanemethanol4'-Methylbenzene- sulphonate
An experiment similar to the above, using a mixture of cis- and trans-4-ethylcyclohexanemethanol (1.33 g, 0.00937 mol) and 4-methylbenzenesulphonyl chloride (1.98 g, 0.0103 mol) gave cis- and trans-4-ethylcyclohexanemethanol 4'-methyl- benzenesulphonate (2.5992 g, 0.00878 mol, 94%) as a colourless oil. The 'H nmr spectrum included doublets (separations 7 and 6 Hz) at 6 4.00 (-CH20-, cis-) and 6 3.88 (-CHzO-, trans-), respectively. The mass spectrum gave Mf as 296.1429 (C1,H2,O3S requires 296.1446). Microanalysis yielded C 64.4, H 8.0; Cl,Hz403S requires C 64.85, H 8.15%.
I cis- and trans-l-Ethyl-4[Me-2H3]methylcyclohexane
Lithium aluminium deuteride (2.4618g, 0.0568mol) was stirred in dry, redistilled ether (56cm3) under argon. The mixture of cis- and trans-4-ethylcyclohexane [a,a-2Hz]methanol 4'- methylbenzenesulphonate (14.30g, 0.0480 mol), dissolved in dry, redistilled ether (140 cm3) was added to the slurry of LiAI- 2H, at 20°C. The mixture was heated under reflux, with stirring, for 2.5 h during which time aprecipitate appeared. The reaction mixture was poured into ice water(24 cm3)andaqueous sulphuric acid (210 cm3, 2 M) was added. Several ether extracts were combined, dried (MgSO,), filtered, and distilled, giving amixture of cis- and trans- l-ethyl-4[Me-zH3] methylc yclohexane (4.2642g, 0.0331 mol, 78%) as a colourless oil, bp 140-144°C. Mass spectrometry gave Mf at 129.1574 (C,lHl,ZH, requires 129.1597). A complete separation was achieved by preparative gas-liquid chromatography, as described earlier (6). In the 'H nmr spectrum, cis-l-ethyl-4[Me-zH3]methylcyclohexane gave a triplet, separations 6Hz, at 6 0.88 (CH,); the trans-l-ethyl- 4[Me-2H3]methylcyclohexane gave a triplet, separations 6Hz, at 6 0.86 (CH,). The 2H nmr spectra gave singlets at 6 0.96 (CZH3, cis-) and 6 0.90 (CzH3, trans-).
Calculation of Thermodynamic Parameters (a) Low Temperature Area Method
Low temperature 13C nmr spectra were recorded , for ~is-l-ethyl-4[Me-~H~] methylcyclohexane 3 S
4 as indicated previously (5) for the corresponding nondeuterated compound. The results are sum- marized below (equilibrium constant K = [411[3]).
(curve fit method)
Averaged value for -AH0(C2H3) = 1.82 f 0.07 kcal mol-I.
AS0(C2H,) = -0.10 + 0.32 cal K-I mol-I
(plot)
AS0(C2H3) = -0.45 f 0.39 cal K-I mol-I (curve fit)
Averaged value for AS0(C2H3) = -0.28 0.40 cal K-I mol-I.
(6) Room Temperature Chemical Shift Method Measurements gave
at 62.901 MHz and 298 K. Thus
67(H) - 67(D) = -0.035 134 ppm
Graph extrapolation gave
z7" - z7' = 7.021 1125 ppm
at 298 K. From [1], x - y = -0.0050041. From the previously determined (5) values of AG0(CH3), AS0(CH3), AGO(Et), and ASO(Et), we deduce that mole fraction x = 0.5209961 at 298 K, and equilib- rium constant K for 1 6 2 is 0.91940 at 298 K.
Hence mole fraction y = 0.5260002 at 298 K and equilibrium constant K for 3 = 4 is 0.90114 at 298 K. Thus
AG0(C2H3) - AGO(Et) = RT In 0.901 14 = 61.554181 cal mol-I
at 298 K
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BOOTH AND EVERETT. 11. 2719
NOW 1 . H. BOOTH and J. R. EVERETT. Can. J. Chem. 58, 2709 (1980).
AG"(CH,) - AG"(Et) = 49.660000 cal mot1 2. K. W. BALDRY and M. J. T. ROBINSON. Tetrahedron, 33, 1663 (1977). at 298 3. S.-F. LEE, G . BARTH, K. KIESLICH, and C. DJERASSI. J. Am. Chem. Soc. 100.3965 (19781.
Hence 4. S.-F. LEE, G. BARTH', and C. DJERASSI. J. Am. Chem. Soc. 100,8010 (1978).
Ae(C2HJ - AGO(CHJ = 11.894181 cal m0l-l 5 . H. BOOTH and J. R. EVERETT. J. Chem. Soc. Perkin Trans. 11,255 (1980). at 298
6. H. BOOTH, J. R. EVERETT, and R. A. FLEMING. Org. Magn. Reson. 12,63 (1979).
Since possible errors are k0.001463 ppm in digiti- 7. F. W. WEHRLI, D. JEREMIC, M. MIHAILOVIC, and S. zation and f 0.25 ppm in the extrapolation to find MILOSAVUEVIC. J. Chem. Soc. Chem. ~ o m m u n . 302
(a7" - a,,), the final result may be expressed as (1978). 8. F. A. L. ANET, A. K. CHENG, and D. KRANE. J. Am.
Chem. Soc. 95,7877 (1973). AG0(C2Hd - AGO(CHJ 9. F. A. L. ANET and A. H. DEKMEZIAN. J. Am. Chem. Soc.
101,5449 (1979). = ' mol-' 10. N. L. ALLINGER and C. A. FREIBURG. J. Org. Chem. 31, or49.79 k 6.1 1 J mol-I 894(1979).
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