NOTES
G(C7H&l) = 0.2. There appears to be no dependence of chlorotoluene yields on dose (with the doubtful exception of the single run 19), temperature, or ethylene concentration. There seems to be a direct dependence of yield on dose rate, but lhis is not considered reliable. The CgH1,yields are so small that few conclusions can be drawn. They disappear a t room temperature and when CCL is present. It may be possible to distinguish two processes : one which yields o-ethyltoluene and n-propylbenzene and which is suppressed by 0.78% SnC14, and another which yields m- and/or p-ethyltoluene and n-propylbenzene and which is only partially suppressed by 10% SnCle. iZ very marked contrast is seen between the SnC14 and CCl, results. The latter show considerably larger yields and many rnore products. This contrast is reminiscent of that cited by Chang, Yang, and Wagner6 between the radiolysis of olefins (which they consider to go by an ionic mechanism) and that of paraffins. While there is no conclusive evidence that the products determined in these experiments result from ionic intermediates, a number of considerations lead us i o such an opinion. They are: the apparent lack of a temperature coefficient: the small number of products; and the fact that the reaction is not suppressed by the radical scavengers C,H4 and NO. A G-value of approximately 0.2 for the formation of intermediates is indicated; apparent1.y they react with SnCl4with a rate constanl only slightly larger (at most one power of ten) then that of competing reactioos. If these intermediates are ionic, it seems plausible to identify them with delta-ray ion pairs. An alternative hypothesis would be that the observed reactions result from energy dissipated directly in the solute, but the trend toward a maximum yield a t high solute concentrations tends to negate this hypothesis. A striking feature of the results is the very low yield of alkylation products. This leads to the conclusion that the formation of conventional carbonium ion intermediates is probably very rare. After completing this work, we have learned of two papers in which confirmatory results are reported. Allen and Hummell’ have estimated the yield of separated ion pairs produced by 1.5-Nev. X-rays in liquid hexane as 0.09 to 0.13 ion pair per 100 e.v. Busler, Martin, and Williams12 have studied the ionic radia.tion-induced polymerization of cyclopentadiene and tentatively estimate a yield of 0.26 initiator per 100 e.v. (11) A. 0. Allen and A. Hummel, Discussions Faraday Soc., in press. (12) W R Busler, D H Martin, and Ff. Wllhams, i b i d , in press.
651
Solvent Effects in the Racemization of 1,l’-Binaphthyl. A Note on the Influence of Internal Pressure on Reaction Rates1
by Allan K. Colter and Lawence 11. Clemens Department of Chemistry, Carnegie Institute of Technology, Pittsburgh 15, Pennsylvania (Received September 27, 1969)
In the course of an investigation of the effects of charge-transfer complexing on the rates of racemization of optically active 1,l’-binaphthy12 we were surprised to observe substantial kinetic solvent effects, even among a series of relatively nonpolar solvents. Since the racemization process has a rather well defined activated complex3 and involves little redistribution of charge, it seemed ideally suited for an investigation of solvent effects not inrolving strong specific reactansolvent interactions. d number of authors have *developed a common approach to the problem of kinetic solvent effects in nonpolar reactions, using transition state theory and the theory of regular solutions.* For a reaction A B -+ products, the specific rate in a dilute nonideal solution, ICl, is related to that in some standard state, ko, by the expression
+
where EA, EB,El, and E , are molar energies of vaporization of A, B, the solvent, and the activated complex, respectively, and VA, VB, VI, and I;-+ are the corresponding molar volumes. The quantities ( E I V )are called ~
~
~
~~~
(1) Abstracted in part from a thesis submitted by L. M.Clemens in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Carnegie I n d t u t e of Technology, June, 1963. (2) L. M. Clemens, unpublished work. (3) F. H. Westheimer in M.S. Newman, “Steric Effects in Organic Chemistry,” John Wiley and Sons, Inc., S e w York, K. Y . . 1956, Chapter 12.
(4) (a) K . J. Laidler and H. Eg-ring, Ann. S . Y . Acad. Sci., 39, 303 (1940); (b) S. Glasstone, K. J. Laidler, and H . Eyring:. “The Theory of Rate Processes.” McGraw-Hill Book Co., Inc., New York, N. Y., 1940, p. 413; (c) K . J. Laidler. “Chemical Kinetics,” McGraw-Hill Book Co., Inc., Xew York, N. Y., 1950, p. 121; (d) A. A . Frost and R. G. Pearaon, “Kinetics and Mechanism,” Second Ed., John Wiley and Sons, Inc., S e w York. Iu.Y., 1961, p. 131.
V o l u m e 68, S u m b e r 3 M a r c h , 1064
NOTES
652
internal pressures or cohesive energy densities5 and are equal to a2, where 6is the solubility parameter.6 Equation 1 has been applied in a qualitative way to account for solvent effects in reactions which are clearly not nonpolar,’ i.e., in reactions in which specific solvation of one or more reactants or the activated complex must surely be important. Its application to such reactions has been criticized by Pearson.8 For a unimolecular reaction, A -+ products, eq. 1 takes the form
parisons of In k or AF* are more meaningful since uncertainties in k are of the order of f1-275.
Table I : Kinetic Dat.a for Racemization of 1,l’-Binaphthyl
lOSk, 33.68”
Solvent
1 Isooctane
. . n-Heptane
A similar expression can be written for a second solvent. Assuming that the molar volume of the activated complex is essentially solvent-independent, the two expressions can be combined to give
In k , / h
=
- 622)
+ B(S1 - 6,)
(3)
where
In previous discussions of the influence of internal pressure on reaction rate^,^^^^^^ the volume of activation has been assumed to be very small, leading to an expression predicting a linear relationship between In k and Thus, Winkler and co-workers found a linear relationship between the Arrhenius activation energy and 6 for the isomerization of cis-azobenzene to transazobenzene in 15 solvents. Assuming 6 = 10.0 tal."' cm.-l’’ (A2 = 100 cal. cm.-9 and V = 200 ~ 1 1 2 . ~ mole-’ for cis-azobenzene, the slope of their straight line requires a value of about 9.25 cal.”z cm.-”’ for 6+. They felt that (6 -. S *) had the correct sign since the internal pressure of trans-azobenzene should be smaller than that of cis-azobenzene and that of the activated complex should be between those of the two isomers. However, a search of the literature reveals that differences in solubility parameter between pairs of geometrical isomers are never larger than about 0.2 tal."% cm.-’”’. It is clear, therefore, that (6 - 6,) for the isomerization of cis-azobenzene cannot be as large as 0.75 cal.’j2~ m . - ~ / ‘ .For the racemization of an optically active biphenyl having no polar barrier groups, both A and B in eq. 3 should be small since AV* and (SA - 6 +) should both be small.
Results The kinetic data obtained in the present work, together with the solubility parameters of the solvents, are listed in Table I. Differences in AH* and A S ” are small and close to experimental uncertainty; comThe Journal of Physical Chemistry
2 3 4 5 6 7 8 9 10 11 12
..
Methylcyclohexane Cyclohexane Carbon tetrachloride Toluene Benzene Methylene chloride 1,2-Dichloroethane Dioxane o-Dichlorobenzene 1,2-Dibromoethane Methylene iodide Dimethylforinarnide
5.35b 6.3gb 5.42 4.61 5.1@ 5.64b 5.04 8.21 9.42 6.68 9.88 9.70 11.1’ 12.4“
AH* AS* (43.90), (43.90), kcal. e.u.
lo%,
mole-‘
mole-’
aa
..
..
...
20.9
21.7
6.9 7.4 7.8 8.2 8.6 8.9 9.2 9.8 9.9 9.9 10.0 10.2 11.8 ..
43.91’
-6.9 .. .. ... 15.2 21.9 -7.1 17.Sb 22.7 - 4 . 1
..
..
16.9
22.2
-5.8
_. ..
.. ..
... ...
21.7
21.6
-7.3
.. ..
..
... ...
..
37.6
,
..
22.4 -3.6 21.5 - 6 . 5
a H. Burrell, Interchem. Rev., 14,3,31(1955); J. H. Hildebrand and R. L. Scott, “Regular Solutions,” Prentice-Hall, Inc., Englewood CIiffs, N. J., 1962. Estimated uncertainty, &1-2%; all other rate constants estimated to have less than 1.170uncertainty. Interpolated from a plot of log k us. 1 / T from the data of M. M. Harris and A. S. Mellor, Chem. Ind. (London), 1082 (1961).
A test of eq. 3 in the form log- k/ko (6 - 60)
-
A’(6
+ 60) + B’ (2 A
=
B’ B
=
2.303)
for the data at 33.68’, where n-heptane (specific rate ko, solubility parameter 60) is taken a6 the standard solvent, is shown in Fig. 1. A least squares analysis” leads to a slope of 2.60 X cal.-l ~ 1 1 1 (std. .~ dev. 2.17 X and intercept -0.478 tal,-'/' cm.”’ (std. dev. 0.361), correlation coefficient 0.327. If isooctane and methylene iodide are excluded, the cor(5) (a) G. Scatchard, Chem. Rev.,E, 321 (1931); (b) J. H. Hildebrand and S. E. Wood, J . Chem. Phgs., 1,817 (1933). ( 6 ) J. H . Hildebrand and R. L. Scott, “Solubility of Non-Electrolytes,” Third Ed., Reinhold Publishing Carp., New York, N. Y., 1950. (7) (a) Reference 4b, p. 414; (b) reference 6, p. 422. (8) R. G. Pearson, J . Chem. Phys., 2 0 , 1478 (1952). (9) J. Halpern, G , W. Brady, and C. A. Winkler, Can. J. Res., 28B, 140 (1950). (IO) If reactants and activated complex form regular solutions, bS*i = AS*o and a linear relationship between In k and 8 amounts to a linear correlation between the Arrhenius activation energy or AH* and 6. (11) L. G. Parratt, “Probability and Experimental Errors in Science,” John Wiley and Sons, Inc., New York, N. Y., 1961.
NOTES
653
-0.100
-
-0.200
15.0
16.0 (6
+
17.0
18.0
19.0
60).
Figure 1. Test of eq. 3: A, all points; B, isooctane and methylene iodide excluded. The numbers are those of Table 1.
relation improves greatly with A’ = 1.098 X IO-’ (std. dev. 0.094 X 10-l) and B’ = -1.85 (std. dev. 0.16), correlation coefficient 0.965. Significantly, choice of methylcyclohexane, cyclohexane, benzene, or even isooctane ais standard solvent leads to very similar results. A plot of (log klllc2)/(61 - 6,) 11s. (a1 tiz) for every combination of two solvents also leads to similar results but with somewhat more scatter-especially where (61 - 62) is small. In contrast, a plot of log k us. 6 is parabolic in shape.
+
Discussion If eq. 3 represents a correct interpretation of the observed solvent effects, the slope of the plot in Fig. 1 leads to AV* = -36.5 mole-l (all points) or - 154.20 em. mole-’ (isooctane and methylene iodide excluded). Taking a value of 222 C M . ~ mole-’ for VA (density of 1.145 g. and 9.9 cal.”z cm.-a’z for 6 ~ the , intercept leads to 6 , = 10.0 ca1.1’2 cm..-s’z (all points) or 13.3 cal.1’2 cm.-”’ {isooctane arid methylene iodide excluded). Although a value of 6* between, say 10.0 and 10 2 ca1.l” cm.-3’2 would be reasonable, values of A V * obtained from the preceding analysis are completely unreasonable. The principal mode of molecular deformation acting to reduce van der Waals repulsion is expected to be bending of the bonds to the interfering hydrogens. a !Since very little stretching is expected to occur, the volume of activation should be small (probably 2.0 ~ 1 1 1mole-1 .~ or less).’:! It is difficult to see how, without important charge redistribution accompanying the activation process, (6 It - 6.4) could exceed about 0 2 ca1.l‘’ We therefore conclude that eq. 3 does not give an accurate description of the solvent effects observed in this work. While more work
is necessary to evaluate the significance of correlations of kinetic solvent effects and internal pressure, the present results suggest that they may be less meaningful than is generally inferred. Solvent effects in the racemization of I,l’-binaphthyl could arise from at least two sources in addition to those predicted by eq. 3. Changes in the barrier to internal rotation could arise from solvent effects on the important bond stretching and bending force constants. Such effects should be small, h ~ w e v e r . ~Solvent effects could also arise from changes in the van der Waals potential function, especially since very close approach of interfering groups could result in some redistribution of charge. It is interesting to compare the present results with those of Lefflor and eo-workers,l3 who have made a study of solvent effects on the rates of racemization of biphenyls having polar barrier groups. Their results were interpreted in terms of changes in specific solvation of the polar groups between initial state and activated complex. However, where comparison of common solvents can be made, the solvent effects in Leffler’s studies are Fimilar in magnitude to those observed in the present work.
Experimental Solvents. Baker Analyzed reagent grade benzene, Fisher “Certified” reagent grade toluene, and Fisher highest purity (99+yo) o-dichlorobenzene were fractionally distilled before use. Fisher “Spectranalyzed” reagent grade cyclohexane and n-heptane were further purified by stirring for several days with a mixture of concentrated nitric and sulfuric acids, washing with water and dilute sodium hydroxide, passing through a silica gel column, and fractionally distilling. Fisher “Certified” reagent grade methylene chloride, Fisher “Spectranalyzed” reagent grade isooctane, Eastman White Label methylcyclohexane, Fisher “Spectranalyzed” reagent grade ethylene chloride, and Fisher “Certified” reagent grade ethylene bromide were further purified as follows. The solvent was stirred for 1 day over concentrated sulfuric acid, washed free of acid with water or aqueous carbonate, and fractionated over phosphorus pentoxide. Fisher “Spectranalyzed” reagent grade carbon tetrachloride was refluxed with 10% sodium hydroxide for 2 days, washed with mater, stirred for several hours with concentrated sulfuric acid, washed with water again, and fractionally distilled over phosphorus pentoxide. Fisher c ‘Purified” (12) D. R. McKelrey and K. R. Brower, J . Phus Chem., 64, 1958 (1960). (13) (a) J . E. LefRer and W. H. Graham, ibid., 63, 687 (1959), (b) B. M. Graybill and J. E. LefRer, ibid., 63, 1461 (1959).
V o l u m e 68, N u m b e r S i%faTeh,1064
NOTES
654
reagent grade methylene iodide was distilled under reduced pressure before use. Fisher “Purified” reagent grade 1,Cdioxane was further purified by Fieser’s method (procedure a).l4 (+)-1,l’-Binaphthyl was prepared by the method of Harris and lIellor,lz Details, including minor modifications of their procedure, will be published elsewhere. The optically active binaphthyl mas obtained as white crystals varying in physical properties from m.p. 156-159’ (uncor.), [ a ] +154’ ~ (benzene) to m.p. 157-160’ (uncor.), [ a ] +192O: ~ reportedlj m.p. 157-159’, [a],,,, + 2 4 5 O . Kmetzc PI*OC&IV.A solution of (+)-1,1‘-binaph31) was transferred to a thy1 (generally ea. 3 x 2-dm. jacketed polarimeter tube maintained at constant temperature by circulation of water from a constant temperature bath. After allowing 10 min. for thermal equilibration, 80 to 100 readings were taken, starting alternately from higher and lower angles of rotation. The reaction was found to follow strict first-order kinetics through three half-lives although in some cases the reaction was followed to only 60-70% completion. Initial readings were in the range 2.1 to 1.7”, depending on the rate of the reaction and the initial purity of the binaphthyl. The data were analyzed graphically by plotting log (at - a,) us. time. Errors in the choice of the best fit straight line are estimated to be less than +1yG in slope or rate constant, except as indicated (Table 1).
Acknowledgment. We wish to thank the Kational Science Foundation for a grant in support of this research. (14) L F. Fieser, “Experiments in Organic ChemistrJ ,” Third E d , D. C Heath and Company, Boston, 1955, p 225 (15) ;I?M Harris and A S Mellor, Chem Ind (London), 1082 (1961)
of the literature revealed only an estimate of 2.0 for the molar refractivity,2 corresponding to an index of refraction of 1.10. Since an experimental value for the refractive index of anhydrous liquid HF is of interest, this note reports its determination.
Experimental A s the anhydrous H F had t o be kept in a closed unreactive system. the refractive index measurements were made using a hollow prism and spectrometer similar to that used by Stein, T’ogel, and L ~ d e w i g . ~ The prism was made of nickel with replaceable sapphire 15indows sealed with Teflon gaskets. 111 addition to the sample space, passages for the circulation of constant’ temperature water were drilled in the prism providing temperature regulation to within * 0.05’. Following Tilton’s4analysis of the Frauenhofer method of minimum deviation for the determination of indices of refraction, the hollow prism had a refracting angle of 80’. For an error of +0.0001 in refractive index, this angle allows a tolerance of 1.0 min. of arc for n = 1.3 and 3.0 min. of arc for n = 1.1 in the measurement of refracting angle and tolerances of 1.25 to 1.7 min. of arc for n = 1.1 to 1.3, respectively, in the measurement of twice the angle of minimum deviation. The spectrometer employed was a Spencer hlodel 10025 with a vernier reading to 1 min. of arc. I n order to minimize errors, since the circle was uncalibrated, angle measurements were carried out as prescribed by T i l t ~ n .A ~ General Electric sodium Lab-Arc was used as the source of the sodium D-line, and Beckman hydrogen and mercury lamps with appropriate interference filters were used 3 s sources for wave lengths of 6562, 4861, and 4358 A. in the measurements of dispersion. The anhydrous HF was prepared by fractional distillation in the still described by Katz and Sheft.6 Two diff erent samples were used, each having a specific conductivity of 2 X mho.
Discussion of Results The Refractive Index of Anhydrous Hydrogen Fluoride1&
by 9..J. PerkinsIb Argonne S a t i o n a l Laboratory Argonne, IlEinoia (Receiwd Octobcr 7 , 1968)
The value of the refractive index of anhydrous hydrogen fluoride was needed in connection with studies of the Ranian spectra of HF-BrFb solutions. A search The Joz~rnalof Physical Chemistry
The refractive indices of anhydrous H F a t 2.5’ for four different wave lengths are given in Table I. The indices of the two different samples agreed with each other to f.0.0001. The molar refractivity calculated ~~~~~~~
(1) (a) Based on work performed under the auspices of the U. S. Atomic Energy Commission. (b) University of Illinois, College of Pharmacy, Chicago, II1. (2) C. P. Smyth, “Dielectric Constants and Molecular Structure,” Chemical Catalog Co.. New York 19, N. Y. (3) L. Stein, R. C. T-ogel, and W. H. Ludewig, J . Am. Chem. Soc., 76,4287 (1954). (4) L. R. Tilton, J . Res. Sat2. B u r . Std., 2 , 923 (1929). ( 5 ) J. J. Katz and I. Sheft, Chem. Eng., 223 (1961).
