J. Phys. Chem. 1983, 87. 3520-3525
3520
were analyzed in a range of concentration 2-3 orders of Linear regression analysis applied to the data of Figure magnitude lower than both Raman and ultrasonic spectra, 6, forcing the intercept through the origin gives ? = 0.999, slope = 19.8 X lo3, where c has been expressed in mol ~ m - ' ~ . the only major species present are, for this system, ion pairs. This, however, is hardly the general situation that esu cm. If one takes One then calculates p = 18.0 X one would expect. In this respect it is instructive to draw a rigid-sphere model, p = ea, where e is the charge of the a comparison between the behavior of LiC10, and of cm, the apparent chargeelectron. Then a = 3.8 X LiAsF6which may give some rationalization of their difto-charge separation of the Li+ and AsF6- in the rotating ference in association in the solvent, DME. Assuming the dipole. (A more precise calculation using c2 + c3 from eq general Eigen multistep mechanism, extended to the forVIa instead of c in eq XIV gives by linear regressions of mation of dimer ion pairs to be valid for the present systhe quantity ( e - em1)(2e0 1)/(3e0)vs. c2 + c3, forcing the tems intercept through the origin, ? = 0.999, slope = 21.8 X 103. esu cm and a = 3.9 X The result is p = 18.8 X Li+ B- Li+.-.B- ie LiB cm.) 2LiB s (LiB)* Notice that from conductance K A N 1 X lo5 M-l. By equating KOto the Fuoss-Jagodzinski equation3 with B-the anion, it appears that we are able to detect the formation of quadrupoles or dimers for LiC104in DME K A N KO = KF = ( 4 ~ L a ~ / 3 0 0 0 ) e - ' / ~ e ~ (XV) but only the second step of the first equilibrium for L h F 6 , with no quadrupoles being detectable. This may signify that for LiAsFe the equilibrium of association is more shifted b = e2/(aekr) toward the left and ultimately toward the free ions as one can evaluate a N 6.3 X cm, a figure larger than documented by electrical conductance. The molecular the value estimated above from the dielectric data. This reasons for the above may reside in the poorer donor ability might be due to the mass effect and to the higher conand steric hindrance of AsF6- with respect to Clod- both centration used in the dielectric work, forcing more contact competing with the solvent for the first coordination species to be present. This would lower the average dispositions around Li+. Further research along these lines tance between the ions in the pairs. is needed before further speculations are possible.
+
+
Conclusions Conductance, Raman spectra, and ultrasonic relaxation concur to suggest that the majority of LiAsF6 exist as outer-sphere or solvent-separated ion pairs. It is remarkable that, although the electrical conductivity data
Acknowledgment. We are grateful to the U.S.Army Research Office, Research Triangle Park, NC 27709, for generous support through grant no. DAA6/29/82/K0048. Registry No. LiAsF,, 29935-35-1; 1,2-dimethoxyethane, 110-71-4.
Discriminating Interactions between Chiral Molecules in the Liquid Phase: Effect on Volumetric Propertiest Luclano Leporl,' Istituto di Chimica Ouantistics ed Energetics Mdecdare del C A R . , 56100 Plsa, Italy
Mario Mengherl, and Vlncenzo Molllca Istituto di Chimica F i s h . Unhrerslti, d Fisa, 56100 Hsa, Italy (Received:August 31, 1982; In Final Form: January 31, 1983)
Volume changes on mixing for binary mixtures of optically active liquid compounds have been determined at 25 "C by using a vibrating tube densimeter. Six enantiomeric and six nonenantiomericpairs of chiral molecules have been considered. In all the cases chiral discrimination appeared to produce small but significant effects (0.0024.016 cm3 mol-'). The excess molar volumes, p,of the (+) and (-) isomers of limonene, carvone, 2-methyl-1-butanol,and a-methylbenzylamineshowed negative values, while VE of the enantiomers of a-pinene and 2-odanol gave positive results. Partialmolar volumes, Po, for the investigated chiral solutes in chiral solvents have been obtained from p data. The effecta of chiral discrimination of Pohave been compared with the prediction of a simple statistical approach in which discrimination arises from space-fillingdifferences in contacts between hard surfaces.
Introduction Chiral discrimination has been known for a long time and a large body of experimental evidence proves its exi~tence.'-~It has its microscopic origins in the fact that the two enantiomeric molecules (d and 1) interact differ'Portions of this material were presented at the meeting of the SocietA Chimica Italiana, Florence, Italy,Nov 5,1981, and at W A C Conference on Chemical Thermodynamics, London, UK, Sept 1982. 0022-3654/83/2087-3520$0 1.50/0
ently with a second chiral molecule (of the same species, d or 1, or of another species D or L). The phenomena arising from the discriminatory interactions of chiral molecules, usually called diastereomeric or chirodiastaltic interactions, have been recently reviewed by Craig and Mellor? who also (1) Mason, S. F. Annu. Rep. Chem. Soc., Sect. A 1976, 73, 53-69. (2) Craig, D. P.; Mellor, D. P. Top. Curr. Chem. 1976, 63, 1-48. (3) Wynberg, H.; Feringa, B. Tetrahedron 1976, 32, 2831-4.
0 1983 Amerlcan Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983 3521
Discriminating Interactions between Chiral Molecules
TABLE I: Physical Properties of Examined Compounds compd ( + )-limonene
(-)-l.imonene ( + )-a-pinene (-)-a-pinene (+)- 2-methyl-1-butanol (-)-2-methyl-l-butanol (+)-2-octanol (-)-2-octanol ( + )-carvone (-)-carvone ( + )-or-methylbenzylamine ( - ) - a -methylbenz ylamine (-)-bornyl acetate
GLC purity 0.993 0.993 0.992 0.99 0.997‘ 0.995c 0.992 0.997 0.999 0.999 0.994 0.996 0.99
p,”
g cm-3
0.838 70 0.839 53 0.854 07 0.854 6 5 0.81546 0.815 77 0.821 20 0.817 85 0.955 93 0.956 1 3 0.949 1 3 0.948 22 0.981 47
IDa,
deg cmz dag-’
OPb
+ 120.9 -94.6 + 47.4
0.97 0.76 0.91 0.84 0.0 0.97 0.93 0.93 0.90 0.98 0.94 0.94 0.95
-42.4 0.0 - 5.6 c9.2 -9.2 t 52.8 -61.0 + 38.4 -39.3 -42.4
a Mean value of the density (at 25 “C) of the different samples used in the measurements or averaged value of the density of the same sample measured at different times. Optical purity as estimated from the specific rotations of pure enantiomers reported in the literature (ref 6). ‘ Containing 3% of 3-methyl-1-butanol as detected by NMR analysis.
give a detailed theoretical treatment of their origin and nature. The most evident manifestations of chiral discrimination are (i) the existence of pairs of solid diastereomeric substances having different physical properties; (ii) the socalled enantiomeric recognition in chemical reactions, which is the basis of resolution of racemates, of asymmetric syntheses, and of biochemical selectivity between enantiomers in life processes, where the discrimination appears in the extreme form. Also in liquid phase, although to a lesser extent than in the solid phase, diastereomeric interactions are effective. Let us mention as an example the polarimetric, NMR, and enthalpic effects observed by Horeau and G ~ e t t 6 . ~ A larger knowledge of the thermodynamic properties of solutions involving optically active molecules is essential to understand the mechanism by which chiral molecules distinguish between enantiomers. In this work, volumetric properties of liquid binary mixtures of common chiral substances have been investigated with the aim of revealing volume effects caused by diastereomeric interactions in liquid phase. Measurements have been carried out of volume changes on mixing, VE, for (i) optical antipodes and (ii) nonenantiomeric pairs of chiral compounds. Moreover, both partial molar volumes of a chiral solute in enantiomericsolvents and partial molar volumes of enantiomeric solutes in a chiral solvent have been obtained from VE data. Density measurements on solutions involving optically active compounds were carried out long ago: but both the imprecision of measurements and the inadequate purity of samples yielded contradictory results. During the draft of this paper, Atik, Ewing, and McGlashan5 published VE data for three pairs of liquid enantiomers. The reliability of those results was questioned by the authors themselves, who also express the hope that others might challenge them.
Experimental Section Materials. All chemicals were commercial products, from Fluka or Aldrich, of the best grade available. Each enantiomer of limonene (l-methyl-4-(l-methylethenyl)cyclohexene), a-pinene (2,6,6-trimethylbicyclo[ 3.1.11hept-2-ene)) and carvone (2-methyl-5-(l-methylethenyl)-2-cyclohexen-l-one) as well as (-)-2-methyl-1butanol and (*)-2-methyl-l-butanol were purified by fractional distillation under nitrogen at reduced pressure. (4)Horeau, A.; Guett6, J. P. Tetrahedron 1974,30, 1923-31. (5)Atik, Z.;Ewing, M. B.; McGlashan, M. L. J . Phys. Chem. 1981,85, 3300-3.
The other compounds, i.e., (-)-bornyl acetate (l(S)-endo1,7,7-trimethylbicyclo[2.2.l]hept-2-yl acetate) and the optical antipodes of 2-octanol and a-methylbenzylamine (a-methylbenzenemethanamine), were used without further purification. All samples used in the experiments showed a GLC purity 399%. The presence of the same type and about the same amount of impurities was revealed in both enantiomers for most enantiomeric pairs. In the case of the (-) isomer and racemic P-methyl-l-butanol, the suspected presence of 3-methyl-1-butanol, not detected by GLC, was checked by NMR spectroscopy. About 3% 3-methyl-1-butanol was found in both compounds. The specific optical rotatory power, [a], was determined for all chiral substances under investigation and their optical purities, as estimated from the specific rotations of pure enantiomers: were higher than 90%, with the exception of (-)-limonene (76%) and (-)+pinene (81%). In Table I are collected the GLC and optical purities, as well as the density and [a] values of the investigated materials. The water used in the calibration of the densimeter was first deionized and then distilled from an alkaline KMnO, solution. Apparatus. All density measurements were carried out with an A. Paar digital vibrating density meter (Model DMA 602) operated in the static mode and capable of a The . measuring precision of better than 3 X lo4 g ~ m - ~ cell was thermally regulated by circulating water from an ultrathermostat. The temperature inside the cell, as checked by a thermistor, was stable within 0.002 O C . The densities p were calculated from the measured period T of vibration of the hollow tube containing the sample by the equation p = po + k(P - To2) (1) were Tois the oscillation period of the tube filled with a reference substance with known density, pO.’ The in(6) Beilstein ‘Handbuch der Organischen Chemie”;Springer-Verlag: Berlin. (7) For substances with known densities (nitrogen, water, KCl,) or whose densities were measured by us with a hydrostatic differential balance (n-hexaneand ethanol), we found that the p data were better described by the relationship p = po + A ( P - T:) + B(F - To2)*,A and B being constants (standard deviation of the fit sf = 10 X 10” g ~ m - ~ ) . On the contrary, systematic differences of about 50 x 10” g cm-3between experimental densities and those calculated by eq 1 were observed for n-hexaneand ethanol having p values intermediateto the explored density range. This means that the dependence of p on P is not exactly linear over a wide range of density. Nevertheless, eq 1,suggested by the manufacturer of the densimeter and used by us, is applicable with an uncertainty less than 1X 10” g cm-3 when the measured density does not differ more than 0.01 g cmd from pg.
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The Journal of Physical Chemistry, Vol. 87, No. 18, 1983
Lepori et al.
TABLE 11: Volume Changes on Mixing (cm' mol-') for Liquid Optically Active Compounds at 25 "C no. of system 1 2 3
4 5 6 7 8 9 10 11 12
compd 1
compd 2
a
b
( + )-limonene ( + )-a-pinene (+ )-2-methyl-l-butanol ( + )-2-octanol ( + )-carvone ( t )-a-methylbenzylamine
Enantiomeric Mixtures' (-)-limonene -0.0107 (-)-a-pinene 0.0079 (-)- 2-methyl-1-butanol - 0. 0148d (-)- 2-octanol 0.0302 (-)-carvone -0.0199 (-)-a-methylbenzylamine - 0.0189
(-)-bornyl acetate (-)-bornyl acetate (-)-2-methyl-l-butanol (-)- 2-methyl-1-butanol (--)-carvone (-)-carvone
Nonenantiomeric Mixturese 1.4224 (-)-carvone 1.4555 ( + )-carvone 0.6 3 8gC (-)-carvone 0.6 214' ( + )-&-pinene 0.6407 (-)-&-pinene 0.6241 ( + )-carvone
-0.1065 -0.1282 0.5827 0.5668
sfa
VE max
arb
0.0011 0.0004 0.0002 0.0005 0.0005 0.0006
-0.0027 0.0020 -0.0037d 0.0076 -0.0050 -0.0047
-0.0143 0.0103 -0.0629 0.0349 -0.0225 -0.0214
0.0017 0.0015 0.0025 0.0018 0.0051 0.0053
0.3424 0.3480 0.1597 0.1554 0.2385 0.2322
a Standard deviation of the fit, s f 2= c [ VE(calcd) - VE(expt)]'/(N - P), N and P being the number of experimental points Value corrected for the optical purities of the and parameters, respectively. The uncertainty on VEm, is about 0.5sf. Equation 3 was employed t o fit VE data. d Value obtained by using racemic (+)-2-methyl-1constituents (see eq 4). butanol instead of the ( + ) isomer. e Equation 5 was employed to fit VE data, X indicating the mole fraction of constituent 1.
'
strument constant, k, was determined daily from accurate calibration with water and nitrogen gas (purity 99.998%). The water density was taken from Ke11,8 that of nitrogen was calculated by the ideal gas law from the value of the atmospheric pressure. Nitrogen instead of room air was employed as calibration fluid, since air density appeared to be notably affeded by the occasional presence of vapors of organic compounds. Small differences in the instrument constant were observed from day to day and the drift during the measurements was estimated to produce density uncertainties lower than 3 X lo+ g ~ m - ~ . The overall apparatus has been checked by measuring the apparent molar volumes of ethanol and KCl in water at 25 "C. The values obtained for the partial molar volumes at infinite dilution, P"(ethano1) = 55.10 f 0.01 cm3 mol-' and VO(KC1) = 26.89 f 0.02 cm3 mol-', are in very good agreement with the literature data.gJO Measurements. The density measurements were taken by reading the period T of the oscillation of the vibrating tube filled with the examined fluid (gas, pure liquid, or mixture) after thermal equilibrium, as revealed by the constancy of both the temperature inside the cell and the period of vibration, was reached. The liquid mixtures to be studied (which were not degassed) were generally made up by adding successively weighed amounts of a pure component to a known amount of the other (3-5 g). This method, which produced results as precise as those obtained by investigating one solution at a time, allowed us to save time and material. In most cases at least ten measurements were carried out in two runs for each system examined, starting alternatively from one component and then the other. For each pair of chiral compounds 1 and 2, the volume change, P,on mixing pure liquids to form 1 mol of mixture has been determined through the equation where p is the density of the mixture, M 1 and M2 are the molecular weights of the two constituents, X I and X 2 their mole fractions, and p 1 and p 2 the densities of the pure liquids. Although p 1 and p 2 are expected to be identical (8) Kell, G. S. J. Chem. Eng. Data 1975,20, 97-105. (9) Cabani, S.; Gianni, P.; Mollica, V.; Lepori, L. J. Solution Chem. 1981,10,563-95, and references therein. (IO) Millero, F. J. "Water and Aqueous Solutions"; Horne, R. A., Ed.; Wiley: New York, 1972; pp 565-95.
I
0 25
I 0 50
1
I 075
Mole F r a c t l o n a i l + l - C a r u o n e
Figure 1. Excess molar volumes for the (+)-cawone system at 25 O C .
+ (-)-cawone
for any pair of optical antipodes, their measured values differed up to 0.001 g cm-3 owing to the presence of impurities. This fact did not affect excessively the VE values, as explained in the Appendix.
Results and Discussion In the first and second part of this section the excess volumes for enantiomeric and nonenantiomeric mixtures, respectively, are examined. The third part deals with partial molar volumes of chiral solutes in chiral solvents. These quantities, although closely related to excess volumes and directly derived from them, are considered separately since they are easier to rationalize. In the Appendix, finally, the possible sources of errors in the measurements are examined and an estimate of the accuracy of the results is made. In particular, it is shown that the observed effects are scarcely affected by the presence of impurities in the samples used. VE for Enantiomeric Mixtures. Each system was investigated over the whole mole fraction range and the excess molar volumes appeared, as expected, symmetrical about X = 0.5 for all six pairs of antipodes examined. As an example, Figure 1 shows the plot of VE vs. X for the system (+)-cawone + (-)-carvone. The VE data were fitted to the one-parameter equation'l VE = a X ( 1 - X ) (3) by a method of least squares, X being the mole fraction of any one of the two components. The mole fractions employed in this calculation procedure were obtained from the amounts of substance actually used without taking into account the optical purities of the enantiomers. The upper part of Table I1 summarizes a and VE,, values for the enantiomeric pairs examined, VE,, being the maximum volume change on mixing corresponding to
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983 3523
Discriminating Interactions between Chiral Molecules
X = 0.5. The values of the standard deviation of the fit, sf,are also reported. The only VE data for liquid mixtures of optical antipodes which may be compared with our data are those by Atik et al.5 obtained by dilatometric measurements. These authors report VE = -0.0014 cm3 mol-’ for limonene and p = -0.0018 cm3 mol-l for a-methylbenzylamine at X = 0.5. The last column in Table I1 collects a’ values, i.e., a values corrected for the optical purities (OP1 and 0P2) of enantiomers through the equation a’ = 4a/(OP1
+ 0P2)z
(4)
The corrections are always positive and increasing with decreasing optical purity of samples used (cf. systems 1 and 2 in Table 11). In system 3, the a’ value appears more than four times larger than the a value. This is due to the fact that instead of (+)-2-methyl-l-butanol,not commercially available, the racemic (*)-2-methyl-l-butanol (OP1 = 0) has been employed. It is evident from Table I1 that the volume changes on mixing for the examined pairs of enantiomers are very small in magnitude ( 0 the contrary occurs. Our results on VE agree qualitatively with the scanty enthalpy changes on mixing for liquid mixtures involving enantiomers?l2 which appears to be very small (
