J. Phys. Chem. 1995,99, 9903-9908
9903
Effect of Solvent-Solute and Solute-Solute Interactions on the Rate of a Michael Addition in Supercritical Fluoroform and Ethane Timothy A. Rhodes,? Kevin O’Shea? Gerald Bennett,* Keith P. Johnston,* and Marye Anne Fox**? Departments of Chemistry and Biochemistry and of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712-1167 Received: October 28, 1994; In Final Form: March 23, 1995@
The rate of the Michael addition of piperidine to methyl propiolate in supercritical fluoroform and ethane at 37 “C and pressures between 48.3 and 213.8 bar depends on fluid density. In fluoroform, the rate constant is linearly related to pressure above 82.8 bar, with a smaller nonlinear change being observed at lower pressures and with a minimum at 82.8 bar. In ethane, the rate of reaction is linear with pressure except near the critical point where the rate is significantly enhanced. We attribute the observed rate constant changes to a dependence on solvent dielectric at pressures higher than that at the critical point, as would be consistent with the stabilization of a highly polar transition state. The observed aberrations near the critical point are attributed to solvent-solute clustering in fluoroform ahd to solute-solute clustering in ethane.
Introduction
work on the methanol esterification of phthalic anhydride in supercritical carbon dioxide also shows evidence for solutesolute clustering.20 This study investigates the density dependence of the reaction rate constant of the Michael addition of piperidine to methyl propiolate, a reaction which has been studied earlier in detail by Huisgen and co-workers.21.22 This Michael addition is proposed to proceed through a highly polar zwitterionic intermediate, eq 1, and the large reported solvent effect makes it an
Recently, efforts toward understanding noncovalent association in supercritical fluids have assumed increased importance because of the more frequent use of these fluids as solvents for extraction and chromatography. Supercritical fluids are also of interest because of their unique “tunability” and because several have been suggested as solvents for environmentally benign syntheses.’-3 Supercritical fluids are unique among solvents in that their physical properties (e.g., density, viscosity, dielectric constant, and diffusivity) can be varied simply by changing the pressure and temperature, most notably near the 1 critical point. The ability to “select” solvent parameters for an array of fixed chemical composition is an attractive one, not only for chromatography but also for controlling selectivity among competing chemical reactions by adjusting relative reaction rate constants. Recent work on the nature of the association of a solute with a supercritical fluid suggests that microscopic heterogeneity ideal probe of the nature of local associations in the supercritical within a macroscopicallyhomogeneous environment contributes significantly to their unique behaviors2 Solvent structure plays state and of how molecular interactions can affect reaction rates. an important role in controlling structure and reactivity in The change in polarity induced by a pressure change for a liquids. Both spectroscopy and theoretical work using molecular supercritical fluid (from a nonpolar to a polar medium) would dynamics and Monte Carlo simulation^^-'^ suggest that local dramatically stabilize the zwitterionic intermediate and increase solvent structure may play a more significant role in supercritical the apparent rate constant for the reaction. fluids. Spectroscopic techniques (such as absorbance, fluoresExperimental Section cence, NMR, ESR, and FTIR spectroscopies) have also been used to investigate the microscopic behavior of supercritical Equipment. A high pressure absorbance cell (Figure l), was fluids.I0-l6 All of these studies implicate the existence of built in-house from stainless steel 316 and two sapphire windows intermolecular interactions between either solvent-solute or (Insaco, 0.75 in. thick and 1 in. diameter) which have an solute-solute pairs. Absorbance studies using solvatochromic absorbance cutoff at 200 nm. The Teflon O-ring provides the probes have demonstrated that the fluid density about an pressure seal when the threaded cap is tightened. Two inlets infinitely dilute solute molecule is greater than the bulk density. for high-pressure connections are made using High Pressure Solvent-solute clustering was thus suggested as responsible for Equipment Co. 1/16 in. taper seal connections. The path length a similar shift in the absorption maxima of p-(iV,N-dimethylof the cell (1.63 cm) was determined by measuring the amin0)benzonitrile and ethyl p-(Nfl-dimethylamin~)benzoate,’~.’~absorbance of the cell filled with a solution of known concenand the observed pressure effects on the stereochemistry and tration and extinction coefficient. This procedure was repeated regiochemistry of the photodimerization of i s o p h o r ~ n e ’and ~ several times to reduce experimental error. cyclohexenone similarly require such association. Recent Pressure was measured on a Heise Model 901A pressure
r
’ Departments of Chemistry and Biochemistry.
i Department of Chemical Engineering. @Abstractpublished in Advance ACS Abstracts, May 15, 1995.
H
indicator with a range of 0-344.8 bar & 0.07% full scale. Temperature was monitored and controlled with an Omega temperature controller, and an Omega temperature probe, with
0022-3654/95/2099-9903$09.00/0 0 1995 American Chemical Society
9904 J. Phys. Chem., Vol. 99, No. 24, 1995 A
Rhodes et al. E
0
Front View Side View Figure 1. Front and side view of a high pressure absorbance cell. (A) high pressure inlets, (B) stainless steel cell body, (C) threaded cap for holding sapphire window, (D) sapphire window, (E) hole for temperature probe, (F) hole for heating cartridges, (G) Teflon O-ring, H) Delran O-ring, I) sample compartment.
Gaumer 3/16 in. x 2.5 in. heating cartridges having been inserted into predrilled holes in the stainless steel cell. The desired pressure was generated using a High Pressure Equipment Co. pressure generator 87-6-5. Samples are introduced into the cell either by direct injection by syringe or with a 0.18 pL calibrated injection port inline between the cell and the highpressure generator. Materials. Fluoroform (Wilson Oxygen, 299.0%) and ethane (Big Three Industries, 299.0%) were used as received. The fluoroform and ethane showed no significant background absorbance between 210 and 400 nm. Further purification of solvents by passing through an oxygen scrubber and activated carbon filter showed no change in solvent absorbance or in the addition kinetics. Piperidine (Aldrich, 99%) and methyl propiolate (Aldrich, 99%) were used as received, their purities having been established by gas chromatography. Identical results were obtained with as-supplied and freshly distilled samples. Measurements. Absorption Spectra. The absorption spectra were collected on a Hewlett-Packard 845 1A photodiode array absorption spectrometer. The cell was mounted on a base plate which could be easily and reproducibly placed in the cell chamber of the spectrometer. The high-pressure cell was rinsed with methanol 5 times and dried under an argon purge for 15 min before each run. Methyl propiolate (0.1 pL) was injected with a 1 p L Hamilton syringe No. 7001 equipped with Chaney adapter. The cell having been sealed, 0.18 pL of piperidine was injected into the HPLC valve in the LOAD position. The inlet was then tumed to the FLUSH position, and piperidine was flushed into the cell along with the supercritical fluid by the high pressure generator. The pressure and temperature were then allowed to stabilize for about 2 min before the cell and cell stand were placed in the spectrometer. Spectra (up to 100 per run) were then collected for absorptions between 200 and 400 nm at a predefined interval, either 1 or 5 min. The invariance of the absorption spectrum of the starting materials and adduct upon standing implies that the cell path length does not change measurably during data collection and that phase separation has not taken place. Adherence to Beer's law by the starting materials and adduct shows the independence of spectral features on solvent density and makes the possibility of mixing errors unlikely. Physical Parameters of CHF3 and CzHs. The critical parameters for CHFj are T, = 25.6 "C, P, = 48.46 bar, and Qc
2
4
6
8 IO Density (mol/L)
12
14
16
Figure 2. Determination of density dependence of fluorofom dielectric constant using a modified Clausius-Mosotti e q ~ a t i o n . ? ~
= 7.51 m o m , and those for C2H6 are Tc = 32.2 "C, P, = 48.72 bar, and e, = 6.88 m o m . The densities of the supercritical fluids can be calculated using empirical equations developed for CHFj23 and C Z H ~ An . ~ iterative ~ method was used to calculate the densities at each pressure. All density-dependent data are represented as er,the reduced density, defined as er= @/ec, where is the calculated density and ec is the critical density. The dielectric constants for CHF3 at different densities were obtained using a modified Clausius-Mosotti equationz5(eq 2),
e
(
)
Te-11 -A+B@+C$ TCc+2g where T, is the critical temperature of CHF3 in degrees kelvin, A = 0.064975 M-I, B = 1.5893 x (M-')2, and C = -1.0201 x (M-I)j. The adjustable parameters were obtained by a least-squares fit of literature values of E 25 to eq 2 (Figure 2). The dielectric constants for C2H6 at different densities were obtained using a similar m ~ d i f i c a t i o n(eq ~ ~3), E-11
-- = A
E+2@
+ Be + ce2+ D ln(1 + TJT) + EP
(3)
where P is the pressure in MPa, A = 0.111421 x 10-I M-I, B = 0.206 622 x lop4 (M-I)*, C = -0.135 982 x (M-1)3, D = 0.630 432 x M-I, and E = -0.145683 x M-I MPa-I. Kinetics. The independence of the extinction coefficient of the adduct, (18 100 cm-I M-' at 276 nm) on pressure in both supercritical fluids was determined by loading the cell with known volumes of the compound and pressurizing the cell. No change in the extinction coefficient could be observed, within experimental error, at pressures between 48.3 and 213.8 bar at 37 "C. The progress of the addition reaction was monitored by absorption spectroscopy at the product absorption maximum (about 276 nm) with a kinetic analysis of the experimental data being accomplished as described in the text. At this wavelength, absorption by the precursor was negligible. The data obtained in supercritical fluoroform were fit to a bimolecular rate equation by converting the observed product absorbance to concentration. The concentration data were then fit using a linear least-squares method to the bimolecular rate equation, eq 4,
kt =
1 AB0 A , - Bo In[@] ~
(4)
J. Phys. Chem., Vol. 99, No. 24, 1995 9905
Rate of a Michael Addition in Fluoroform and Ethane
0 0.12
2
0
Y
'
1
4
~
1.5
-E5: D
d
l
0.5
0 200
220
240
260
280 300 320 Wavelength (nm)
340
360
380
400
Figure 3. Spectral changes observed during the addition of piperidine(7.2 x M) to methyl propiolate (3.6 x M) in fluorofom, 69.0 bar and 37 "C at 10 min intervals after mixing, with the initial spectrum shown at the bottom.
0.00
" ap.
q
~
P'P,
-
f(t) = 5.862073x10~2t 3.486405
Rz =9.995127xlO-l
300
Z" 2" A S e q - ? - %
Figure 5. Dependence on reduced density of the bimolecular rate constant for the addition of piperidine to methyl propiolate in fluorofom.
-
/$a C
0.3 A
0
lo
20
30
40 io 80
70
80
sb 160
Time (min)
Figure 4. Kinetic analysis of the addition of piperidine (7.2 x M) to methyl propiolate (3.6 x lov4M) in fluoroform at 69.0 bar and 37 O C .
where A0 and Bo are the initial concentrations and A and B are the concentrations at time t. The data collected in supercritical ethane were analyzed similarly. (See Discussion for further details.)
Results Addition in Supercritical Fluoroform. Typical absorbance changes observed during the addition of piperidine to methyl propiolate in supercritical fluoroform are shown in Figure 3. The adduct absorbs at 276 nm, with the observed intensity of this band being referenced to air. Because the background absorbance of the cell and supercritical fluoroform at a given pressure were constant, a prerecorded background spectrum could be subtracted during the kinetic experiment. To determine whether a particular experiment might be susceptible to base line drift, a base line was determined for each spectrum and a statistical analysis was employed to establish a standard error. With no significant error having been obtained, the average base line was subtracted from all absorbance spectra before the concentration was calculated. The bimolecular rate constant was then determined from the concentration-time profile, using the analytical bimolecular rate equation, eq 4. A typical linear least squares fit for the addition reaction in supercritical fluoroform (Figure 4), exactly overlays the data points. Any absorbance greater than 2.0 was discounted because of deviations from Beer's law attributable to instrumental accuracy limitations.26
KI
Wavelength (nm)
Figure 6. Spectral changes observed during the addition of piperidine (8.0 x M) to methyl propiolate (1.8 x M) in ethane at 82.8 bar and 37 "C at 40 min intervals after mixing, with the initial spectrum shown at the bottom.
Rate constants for the addition in supercritical fluorofom at 37 "C and at pressures ranging from 48.3 to 213.8 bar (solvent densities between 3.3 and 15 M) were determined (Figure 5 ) . The average rate constant and the standard deviation were calculated from three independent determinations of the rate constant made at each pressure studied. Addition in SupercriticalEthane. The progress of the same addition in ethane was similarly followed. A representative kinetic experiment in ethane (Figure 6), reveals the lower reactivity in ethane. Figure 7 depicts two typical kinetic analyses of the addition in supercritical ethane, collected at 55.2 bar and 37 "C (near the critical point) and at 144.8 bar and 37 "C (significantly removed from the critical point). Addition in Liquid Pentane. The addition reaction kinetics were also followed in pentane at atmospheric pressure and 37 "C using the same experimental procedure as in supercritical fluoroform and ethane. The addition exhibited the expected linear bimolecular kinetics. The product distribution was identical to that observed in supercritical ethane and to that reported earlier by Huisgen et al."
9906 J. Phys. Chem., Vol. 99, No. 24, I995
Rhodes et al. ... .
z-
0.12
-
0.10
-
0.08-
M
e
$
0.061
0
20
40
60
80
100 120 Time (min)
140
160
180 200
Figure 7. Kinetic analysis of addition of piperidine (6.5 x M) to methyl propiolate (1.2 x M) in ethane at 55.2 bar (A) and 144.8 bar (0)at 37 "C.
O'O4I 0.02
0.00
1 0
5
10
15
20
25
30
3.5
E
Figure 9. Dependence on dielectric constant of bimolecular rate constants for the addition of piperidine to methyl propiolate in
7
fluorofom.
PiPC
Figure 8. Dependence on reduced density (@/ec) of the fluid dielectric constant ( E ) of fluorofom (0)and of ethane (0)at 37 "C.
Discussion A comparison of Figures 4 and 7 shows that the kinetics of the Michael addition of piperidine and methyl propiolate in supercritical fluoroform and ethane are distinctly different. The principal pressure-induced difference between these two solvents Figure 8, is that the dielectric constant in fluoroform shows a strong density dependence, whereas that in ethane is small and essentially constant over the range of densities studied. Transition state stabilization and solubility are strongly influenced by a change in solvent polarity. The degree of stabilization of the transition state relative to that of the ground state is determined by the respective dipole moments of the ground and transition states. The larger dipole is stabilized to a greater extent by an increase in solvent polarity, resulting in a decrease in the activation energy, AG*. The solubilities of the two reactants in the solvent are determined by their relative polarities. Reactants and solvents mix readily to form a homogeneous solution when all species have similar properties, such as polarity or hydrogen-bonding ability. When the reactants and solvent differ in these properties, they can separate into two or more phases: either as entirely independent phases or as micelles or emulsions. In all experiments described here, concentration ranges were employed such that complete mixing (and no phase separation) could take place.
As was proposed by Huisgen,21,22the zwitterionic-like transition state for the Michael reaction shown in eq 1 is more stabilized by an increase in solvent polarity than is the ground state, and the rate constants observed in fluoroform show the consequent expected relationship to solvent polarity. Figure 9 illustrates the dependence on dielectric constantz7 of the rate constant for this addition in supercritical fluoroform. At a dielectric constant greater than 8, there is an approximate linear relationship between the rate constant of the reaction and solvent dielectric constant. At lower dielectric constant (near the critical point), however, the observed rate constant diverges substantially from the values predicted by this relationship. The behavior of the rate constant at high densities is as expected from enhanced transition state stabilization, but the behavior observed near the critical point is not so easily explained. Consider the effect of aggregation of a solute in a supercritical fluid near the critical point by solvent-solute clustering or solute-solute Clustering. Solvent-solute clustering consists of a large excess of solvent molecules oriented about a solute molecule, whereas solute-solute clustering is characterized by strong association between two or more solute molecules. Clustering differentiates the supercritical fluid from traditional solvents in that large inhomogeneous concentration gradients can occur in either reactant or solvent. Therefore, a direct relationship between reaction rate constants and solvent properties may not be apparent, as observed in Figure 9. Since changes in either reactant or solvent concentration can increase the apparent reaction rate constant, a determination of whether the enhanced rate constants near the critical point are due to changes in the degree of solvent-solute clustering or in reactant concentrations (solute-solute clustering) remains a challenge. Piperidine, methyl propiolate, and fluoroform are all polar molecules with compatible hydrogen bonding capabilities: they are therefore likely to mix homogeneously. However, experimental and theoretical work by Politzer et al. suggests that, at low densities, solubility is predominantly determined by solutesolute interactions rather than solvent-solute interactions.28This same work would assert that the greater solubility of these reagents in fluoroform than in ethane derives from a significant contribution by solvent-solute interactions. A decrease in solvent density should induce a corresponding decrease in solvation free energy and, therefore, an increase in solute-solute
Rate of a Michael Addition in Fluoroform and Ethane
J. Phys. Chem., Vol. 99, No. 24, 1995 9907
300
I
ir 250
200 L
-
0
m
150
P 100
0
10
20
30 40 Time (min)
50
60
70
Figure 10. Kinetic analysis of the addition of piperidine to methyl propiolate in fluorofom at 48.3 bar and 37 "C. The nonrandom residuals in the linear curve fit suggest a deviation from the purely bimolecular
kinetics. clustering. However, the particular density at which solutesolute clustering dominates over solvent-solute clustering is most certainly dependent on the properties of the solute and supercritical fluid. Politzer's studies of solubilities in supercritical fluids suggest that the observed rate constant enhancement near the critical point is caused by a combination of solute-solute and solventsolute clustering, but the magnitude, or even the presence, of either type of clustering remains an open question. This question can be answered by considering the significance of the kinetics data and the assumptions implicitly made in their collection. To interpret standard non-zeroth-order kinetic rate equations, two assumptions significant to the present discussion are made: (1) that collisions between reactants are random and (2) that reactants are randomly distributed in a homogeneous environment. Solvent-solute clustering can accommodate these assumptions because, in fact, it is merely an extreme case of standard solution solvation. Solute-solute clustering, however, dramatically disrupts the random placement of reactants and affects their collisions. Standard kinetic rate equations cannot account for this behavior, and the only reliable method capable of solving kinetics for a nonrandom system (such as encountered with solute-solute clustering) is probably computer-based simulation. With these assumptions and their consequences in mind, we again examine the kinetics of the addition. As illustrated by Figure 4, the kinetics of the addition reaction are well-behaved in supercritical fluoroform at 69.0 bar, er = 1.3. Close inspection of the kinetic data at a lower density, Figure 10 (48.3 bar, er = 0.433), reveals slight curvature. This curvature suggests either a change in mechanism or the operation of another phenomenon that alters the observed kinetics. Our product analysis is fully compatible with that reported by Huisgen,*' and we have been unable to find any evidence for the possibility that the mechanism changes in a fixed medium as a function of pressure. Although the subtlety of the deviation in the CHF3 curve might lead one to dismiss it altogether, the presence of parallel strong and reproducible curvature in supercritical ethane suggests that the deviations, even in fluoroform, are real. The deviation from simple linear kinetic behavior is the clearest indication that solute-solute clustering is partially responsible for the unusual rate constant enhancement observed in supercritical fluoroform. However, solvent-solute clustering is still the controlling factor in the rate constant enhancement: that is why the observed deviations are so small in this medium. Extending the present study to lower pressures
would be expected to reveal even greater deviations from linear kinetic behavior because of decreased solvent-solute clustering (and therefore a greater relative significance of solute-solute clustering), but such experiments cannot be conducted because of the low solubility of reactants at sufficiently low pressures. The nonrandom concentrations induced by solute-solute clustering render quantitative analysis of the addition kinetics in supercritical ethane difficult. Attempts to establish a change in mechanism by fitting the concentration-time data to a series of altemative rate equations were fruitless, however. Solutesolute clustering inherently changes the local solvent environment as well as reactant concentration, because solvent molecules are displaced from the local cluster by the excess solute. This additional factor makes the kinetics even more complicated (and less solvable by normal simulation methods. In spite of these limitations, some qualitative comments on the rates of reaction in supercritical ethane are warranted. The observed reaction rates were essentially independent of fluid density, except near the critical point, where they were significantly larger than expected. Also, the reaction rates at high densities exhibit a steady (although nonlinear) decrease with time, whereas the rate near the critical point exhibits apparent fast and slow components (Figure 7). Thus, the Michael addition of piperidine to methyl propiolate in supercritical fluoroform exhibits three distinct behaviors. At high densities, where local clustering is believed to be minimal: the addition reaction rate constant is controlled by transition state stabilization and shows a linear dependence on solvent polarity. At densities near the critical point, the rate constant is controlled primarily by solvent-solute clustering. Effectively, the reaction proceeds in a microenvironment that has different solvent properties than the bulk solution. At densities lower than the critical density, the reaction rate constant begins to show a dependence on solute-solute clustering and larger rates are observed. The addition kinetics show two distinct regions of behavior in supercritical ethane. At high densities, the reaction rate is essentially unaffected by changes in density since solvent polarity is only weakly affected by density in ethane. At densities near the critical point, the reaction rate is dramatically increased by solute-solute clustering. Solvent-solute clustering cannot account for the observed rate increase, because solvent density has no effect on the rate in ethane. This is the first kinetic evidence that establishes simultaneous solvent-solute and solute-solute clustering within the same molecular array. The observed ability to adjust reaction rate by changing pressure in a supercritical fluid and, hence, to favor one interaction type among competing modes for local aggregation provides for a new means of kinetic control of organic reactions.
Acknowledgment. This work was supported by the National Science Foundation.
References and Notes (1) Supercritical Fluid Technology: Reviews in Modern Theory and Applications; Bruno, T. J., Ely, J. F., Eds.; CRC Press: Boston, MA, 1991; p 593. (2) Brennecke, J. F. In Supercritical Fluid Engineering Science; Kiran, E. Brennecke, J. F., Eds.; American Chemical Society: Washington, DC, 1993. (3) Of all the supercritical fluids in common use, only carbon dioxide is under consideration as an environmentally benign solvent for synthesis. However, the use of supercritical fluid solvents can simplify reaction product extraction, reducing the use of organic solvents for purification.
9908 J. Phys. Chem., Vol. 99, No. 24, 1995 (4)Randolph, T. W.; O'Brien, J. A.; Ganapathy, S. J. Phys. Chem. 1994, 98, 4173. ( 5 ) Chialvo, A. A.; Debenedetti, P. G. Ind. Eng. Chem. Res. 1992, 31, 1391. (6) Murray, J. S.; Lane, P.; Brinck, T.; Politzer, P. J. Phys. Chem. 1993, 97, 5144. ( 7 ) Debenedetti, P. G.; Chialvo, A. A. J. Chem. Phys. 1992, 97, 504. (8) Tom, J. W.; Debenedetti, P. G. Ind. Eng. Chem. Res. 1993, 32, 2118. (9) Betts, T. A.; Zagrobelny, J.; Bright, F. V. In Supercritical Fluid Technology; Bright, F. V., McNally, M. E., Eds.; American Chemical Society: Washington, DC, 1992; p 48. (10) Sun. Y.-P.: Bennett. G.: Johnston. K.P.:, Fox., M. A. J. Phvs. Chem. 1992,96, 10001. (1 1) Brennecke, J. F.;Eckert, C. A. In Sumrcritical Fluid Science and Technology;Johnston, K. P., Penninger, J. M.'L., Eds.; American Chemical Society: Washington, DC, 1989; p 14. (12) Hmiez. B. J.: Yazdi. P. T.: Fox. M. A,: Johnston. K. P. J. Am. Chem.'Soc. "1989,111, 1915. (13) Blitz, J. P.: Yonker, C. R.: Smith, R. D. J. Phvs. Chem. 1989. 93. 666 1 . (14) McDonald, A. C.; Fan, F.R. F.;Bard, A. J. J. Phys. Chem. 1986, 90, 196. (15) Lamb, D. M.; Vander Velde, D. G.; Jonas, J. J. Magn. Reson. 1987, 73, 345. (16) Betts, T. A.; Zagrobelny, J.; Bright, F. V. J. Am. Chem. SOC.1992, 114, 8163.
Rhodes et al. (17) Sun, Y.-P.; Fox,M. A,; Johnston, K. P. J. Am. Chem. SOC. 1992, 114, 1187.
(18) Hrnjez, B. J.; Mehta, A. J.; Fox, M. A.; Johnston, K. P. J. Am. Chem. SOC. 1989, 111, 2662. (19) Combes, J. R.; Johnston, K. P.; O'Shea, K. E.; Fox, M. A. In Supercritical Fluid Technology; Bright, F. V., McNally, M. E., Eds.; American Chemical Society: Washington, DC, 1992; p 31. (20) Ellington, J. B.; Park, K. M.; Brennecke, J. F. Ind. Eng. Chem. Res. 1994, 33, 965. (21) Huisgen, R.; Giese, B.: Huber, H. Tetrahedron Lett. 1967, 1883. (22) Giese, B.; Huisgen, R. Tetrahedron Lett. 1967, 1889. (23) Aizpiri, A. G.; Davila, J.; Rubio, R. G.; Zollweg, J. A,; Streett, W. B. J. Phys. Chem. 1991, 95, 3351. (24) Younglove, B. A.; Ely, J. F. J. Phys. Chem. Re$ Data 1987, 16, 577. (25) Downing, R. C. Fluorocarbon Refrigerants Handbook; PrenticeHall: Englewood Cliffs, NJ, 1988; p 402. (26) Willard, H. H.; Merritt, L. L., Jr.; Dean, J. A,; Settle, F. A,, Jr. lnstrumental Methods of Analysis, 6th ed.; Wadsworth Publishing: Belmont, CA, 1981; p 1030. (27) The dielectric constant is calculated from the density using the modified Clausius-Mosotti equation (eq 2). (28) Politzer, P.; Murray, J. S.; Lane, P.; Brinck, T. J. Phys. Chem. 1993, 97, 729. JP9429208
