Nov., 1963
EFFECT OF PRESSURE ON EQUILIBRATION OF AZIDES
245 1
TIHE EFFECT OF PRESSURE ON THE EQUILIBRATION OF 01- AND r-METHYLALLYL AZIDE:l BYW. J. LE NOBLE Department of Chemistry, State Universaty of New York at Stony Brook, Stony Brook, New York Received June 7 , 1963 The interconversion of a- and r-methylallyl azide in methylene chloride has been studied as a function of pressure over a range of 6700 atm. The reaction, which presumably goes through a nonpolar, cyclic transition stai,e, has am activation volume of - 9.5 cm.s/mole if approached from the a-direction, - 7.9 cm.*/mole if approached from the pure 7-isomer. The ratio of densities of the azides calculated from these numbers agrees well with the directly observed value. Thus, a volume diminution of about 10 ml./mole is one of the consequences of the formation of a cyclic transition state.
I n the past 10 years equipment has become commercially available by means of which high pressures (-10,000 atm.) can routinely be generated and contained for prolonged periods of time. This fact has enabled chemists to turn to the application of pressure as a tool in elucidating reaction mechanisms.2 It is now known 1,hat very important (if not the most important) changes in rate occur when pressure is applied to a system in which ionization or neutralization of charge is involved in the rate-determining step.a Another important feature often postulated in mechanistic studies is the opening or closure of a ring. Several author^^^-^ have estimated the corresponding part of AV* on the basis of known densities of stable linear and cyclic molecules; however, there appear to be no literature reports of studies undertaken with the specific objective of determining the effect of pressure on reactions in which ring opening or closure is invohed in the transition state and in which furthermore charge separation or neutralization is a t most minor. It was recently reported by Gagneux, Winstein, and Young5 that CY- and y-methylallyl azide rapidly form an equilibrium mixture of the two. They measured both the rate and equilibrium constants of this reaction. It was noted that these quantities were remarkably insensitive t o changes in solvent as well as to methyl substitution. For instance, the rate of equilibration in ethanol is only four times as great as in n-pentane, and in either solvent the rate of eyuilibrcltion of a,a-and r,y-dimethylallyl azide is only three times as large as that of the butenyl azides. These observations are indicative of very little charge separation in the transition state. Although the exact geometry of Lhe transition state is not known, it seems very likely that a six-membered ring is involved. For these reasoIis the isomerization seemed an excelleiit model for this study.
Experimental Preparation of LY- and r-Methylallyl Azides.6-A sample of 18 g. of trans-crotyl chloride (commercial material purified by fractional distillation) was Rdded to a filtered solution of sodium azide in a mixture of 1.5 1. of acetone and 0.5 1. of water. After 24 hr., (1) Presented a t the 144th National Meeting of the American Chemical Society, Los Angeles, California, 4pri1, 1963. (2) See, e.g., 5 . D. Hamann. “Physlco-Chemical Effects of Pressure,’’ Academic Press, Inc., New Y ork, N. Y., 1957, Chapters VI11 and IX. (3) H. G. Da\rd and S. D. Hamann, Trans. F a ~ a d a ySoc., 60, 1188 (1954). (4) (a) C . Walling and J. Peisach. J. Am. Chem. Soc., 81, 5819 (1959); (b) W. J. le Noble, zbzd., 82, 5253 (1960); (e) K. R. Brower, zbzd., 83,4370 (1961); (d) A. R. Osborn and E. Whallev, Trans. F a l a d a y Soc., 68,2144 (1962): (e) C . WalXingand b[. Naiman, J . A m Chem. Soc.. 8 4 , 2628 (1962). (5) A. Gagneux, 5. Winstein, and W.G. Young. zbzd., 82, 5956 (1960). (6) The author is indebted to Professor S. Winstein for providing & nurnher of unpublished d e t d s of this preparation.
this mixture was shaken with 2 1. of water and 2 1. of ether. The ether phase was washed three times with 11. of water, then dried over sodium sulfate. Vacuum distillation by means of a Vigreux column with a Dry Ice reflux condenser yielded a residue the infrared spectrum of which had a strong band a t 2040 em.-’. This mixture was stored at Dry Ice temperature. Samples were separated into the pure isomers by preparative gas chromatography as needed. The separation was accomplished by means of an Aerograph instrument, nhich was fitted with a 3-ft. Silicone-90 column held a t room temperature. The a- and 7-isomers had retention times of 30 and 60 min., respectively, when the pressure of the carrier gas was 10 p.s.i. Up to 50 mg. of the mixture could thus be separated in a single operation. A convenient analytical procedure depends on the fact that the a-isomer has a strong, sharp peak at 10.67 s i n the infrared spectrum (characteristic of vinyl compounds)Tand the r-isomer a t 10.30 p (characteristic of trans olefins). A smooth curve cdnstructed from experimental optical density ratios vs. composition of known mixtures provided a routine and rapid method of analysis of unknown mixtures; the ratio of isomers in a mixture could thus be estimated easily to 3% accuracy over most of the range. Apparatus .-The apparatus has been described earlier The container used was type E described in the same paper; this type is particularly suited for very small samples (0.1 ml. or less). During the generation of pressure there is a considerable temperature rise, so that care must be exercised in rate studies to keep the effect of temperature changes from masking the effect of pressure. Precooling of the reaction mixture, reasonably slow generation of pressure, and choice of the temperature such that the reaction is not too rapid (when compared with the rate of heat exchange through the mdls of the pressure vessel) were used to minimize the problem, but it still was necessary to make a correction for the reaction taking place during the initial phase. Procedures.-A 0.3-ml. test tube, fitted with a small piece of rubber tubing as described earlier,8 was charged with 0.1 ml. of a 4y0 solution of the isomer of interest in methylene chloride. This solution was frozen in liquid nitrogen. The remainder of the vessel then was filled with mercury, care being taken to leave a small air bubble between the mercury and the frozen solution to allow for expansion of the latter as it warmed up. The Teflon stopper was put in place and the vessel was inverted and stored under liquid nitrogen. After the reaction had proceeded for the allotted time, the tubes were again frozen until just before analysis. It was found that temperature equilibrium inside the pressure vessel was reached in about 10 min. Therefore, kinetic runs a t every predsure used included samples withdrawn after 15 min.; the results of these experiments determined the correction to be applied to longer runs. The thermostat was set a t 20.0’. The ratio of densities of the isomers was determined by means of a dilatometric study of the rate of isomerization of pure 7-methylallyl azide; a sensitive, long-stem thermometer was used as the dilatometer. The thermometer was calibrated, the top was cracked off, and the mercury removed. The weight of the mercury and the calibrated scale thus provided a very accurate means of measuring changes in density requiring only 0.1 ml. of liquid.
Restrlts and Discussion The data apply t o reaction 1. (7) L. J. Bellamy, “The Infrared Spectra of Complex Molecules.” John Wiley and Sons, Inc,. New York, PJ. Y., 1954, Chapter 11. (8) W.le Noble, J . Ani. Chem. So:., 86, 1470 (1863).
2452
W. J. LE NOBLE
I
I
I
I
I
Vol. 67
Starting with pure y-isomer, the rate law is
I
In 1/10
+ K)([rlt/hlo)
-K)
= OC,
+
If the right-hand members of these expressions are set equal and the resulting equation is solved for K , one obtains
K
3 Time, hr.
2
1
0
6
5
4
Fig. 1.-First-order plot of the equilibration of a-methylallyl azide in methylene chloride solution a t 20" at various pressures.
- 2.1
TABLE I THERATEOF
-
1.2
d
Y
I%
5
T
2
5. k
h
-2.5
1.0
-2.7
0.8
- 2.9
p
0.6
6 Pressure, 103 atm.
0
3
9
Fig. 2.-Effect of pressure on the rate and equilibrium constants of the equilibration of a- and y-methylallyl azides at 20' in methylene chloride solution; R = 82 cm.3 atm. mole-' O K - ' .
CH3
I
k,
CHz=CH-CH--Na
N,/N,
where N , is the mole fraction of y-isomer in a mixture that started as pure a-isomer and similarly N , is the mole fraction of a-isomer in a mixture that started as pure y-isomer. Hence, by allowing samples of pure a- and y-isomers to react under the same conditions for the same length of time, it was possible to determine the equilibrium constant also without actually allowing them to reach equilibrium. Thus, each run yielded a value of K as well as IC, and k,. I n the rate experiments under pressure, slightly more complicated rate equations were used; those that would obtain if the starting samples of a-isomer were contaminated with some of the y-azide and vice versa. The degree of contamination assumed was that actually found after the heat of compression had been completely dissipated at a given pressure. The results of the measurements of rate and equilibrium constant,s are shown in Table I.
1.4
& -2.3
=
J_ CH3-CH=CH-CHr-K3
EQUILIBRATION
Pressure, atm.
CONSTANT FUNCTION OF PRESSURE
AND THE EQUILIBRIUM
OF a- AXD y-METHYLALLYL AZIDEAS A
(ha -t- ~c),
K=
Kb
x
104,
seo.-1'
1 1.80 f O.lO(5) 1.77 f 0.06 0.83 f 0.06(13) 1100 1 . 9 0 f .20(5) 1 . 8 6 f .06 1 . 1 9 f .10(8) 2200 2 . 0 0 1 .10(3) 2 . 0 0 f . 06 1 . 8 3 f . 0 6 ( 4 ) 3300 2 . 1 2 1 .10(3) 2 . 1 1 1 .06 2.17zk . 0 9 ( 4 ) 4400 2 . 2 O f .05(3) 2 . 1 8 f .06 2 . 9 7 f .20(4) 5500 2.21 rrt 05(3) 2 . 2 0 f .06 2 . 9 4 f .20(5) 6700 2 . 3 3 f .06 3 . 9 4 h .40(3) a The values of K listed in this column were obtained by the kinetic method described in the text and are shonn here with the average error and the number of determinations. The values of K listed in this column were determined from the identical spectra obtained from solutions of CY- and ?-isomers kept at high pressure, as well as of mixtures pre-equilibrated a t 1 atm. and then stored at high pressure; the average error is estimated to be zk0.06. Only the values listed in this column were used in the calculations. The deviations listed here are also average errors and the number of measurements is shown in parentheses. The decrease in precision reflects the effect of heats of compression.
kr
(1) This reaction is first order, as shown by Gagneux, Winstein, and Young6 and by the present work; Fig. 1 shows the first-order plots of the reaction of the aisomer a t various pressures. The equilibrium constants were determined by allowing samples of either isomer as well as of mixtures already equilibrated a t atmospheric pressure to remain under pressure for relatively long periods of time; at each pressure, all these solutions had identical infrared spectra. The constants thus obtained agreed well with the values calculated from the relative rates a t which the pure aand y-isomers approached equilibrium (see below). Starting with pure a-methylallyl azide, the following rate expression applies a!
~n K / ( ( I
Y
+ ~ > ( [ a I ~ / [ a-I oI ])
=
(IC,
+ k.,N
When RT In K and RT ln k are plotted us. p (see Fig. 2), the slopes of the resulting curves are equal to - A V and -AB*, respectively. The curves represent the least squares expressions
-RT In IC,
=
236,000 - 9 . 5 ~-I- 0.56 X IOF3p2
-RTIn le, = 250,000
-RT In K
=
- 7 . 9 ~+ 0.47 X
10-3p2
-13,700 - 1 . 4 8 ~-I- 0.077 X 10M3p2
Thus, a t 0 atm., AV*a = -9.5 ~ m . ~ / m o l eAB*? , = -7.9 ~ m . ~ / m o l and e , AB = -1.5 cm.3/mole. There appears to be some disagreement on the reliability of AV terms so obtained.9 For this reason, it is of interest to note that the ratio of densities d,/d, = 1.015 when calculated from the density (0.91 a t 20') (9) (a) 9. W.Bensonand J. A. Berson, J. Am. Chem Snc., 84, 152 (1962); (b) C. Wallingand D. D. Tanner,abzd., 85, 612 (1963).
Nov., 1963
ELECTRICAL CONDUCTAXCES
of the equilibrium mixture and from A V (as determined by the pressure dependence of K ) ; this value agrees closely with that obtained from the dilatometric experiment, 1.018. It is believed, therefore, that the AV* terms are awurate to about 1 cm.3/mole. In the study of a mechanism of a reaction, there are several questions which knowledge of pressure effects on the rate constant may help to answer; among these are the extent of charge separation or neutralization, of charge dispersal or concentration, of homolytic bond formatilon or cleavage, and the effect of conformational changes such as the assumption of cyclic or extended shapes. Unfortunately, the latter type of change cannot be studied in the absence of all others by means of high pressure techniques, since a mere conformational change cannot provide all the
O F ~LQUEOUSS O L U T I O N S
2463
activation needed for reactions occurring at convenient rates at room temperature. Thus, attempts to determine the effect of cyclization on AV* should be limited to reactions in which the other effects can be estimated. As remarked earlier, the traiisition state in the isomerization of the butenyl azides is not much more polar than the reactant. Furthermore, it seems safe to assume that homolytic bond cleavage cannot be much more extensive than bond formation, since it would be difficult to explain the stability of the isomers to nitrogen formation if the N3- group were free at any time. The conclusion is that if ring formation is a feature in the formation of the transition state, the corresponding diminution in volume is not greater than 8-10 ~ m . ~ / m o l ethis ; value agrees quite well with those reported in ref. 4c and 4e.
ELECTRICAL CONDUCTANCES OF AQUEOUS SOLUTIONS AT HIGH TEMPERATURE AND PRESSURE. I. THE CONDUCTANCES OF POTASSIUM SULFATE-WATER SOLUTIONS FROM 26 TO 800' AND A T PRESSURES UP TO 4000 BARS BYARVINS. QUIST, E. U. FRANCK,*~ H. R. J O L L E Y AND , ~WILLIAM ~ L. MARSHALL Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee Received June 7, 1963 The electrical conductances of 0.0005032,0.002199, and 0.004986 m KzS04 solutions in HzO have been measured at temperatures from 25 t o 800" and at pressures from 1 to 4000 bars. Electrical conductance wm observed a t solution densities as low as 0.2 g./cm.$. A t constant temperature the equivalent conductances increased rapidly with increa3in.gdensity and reached maximum values a t densities between 0.5 and 0.7 g./cm.3. Although a t densities below 0.8 g . / ~ m considerable .~ ion association and hydrolysis appear to occur, KzS04is found t o behave as a relatively strong electrolyte between 0.8 and 1.0 g . / ~ m solution .~ density. This is in accordance with the behavior of monovalent salts in supercritical water a3 observed earlier. Thermodynamic dissociation constants for the have been estimated at 100,200, and 300". equilibrium ?&SO4-$ K + f
Introduction The ability of water to act as a n electrolytic solvent is not restricted to temperatures below the critical point, but extends well into the region of supercritical temperatures if it is compressed to high enough densities. This is indicated by the electrical conductance of ordinary electrolytes in supercritical water. At present, information on conductances of electrolytes in water a t elevated temperatures is somewhat limited. The first comprehensive studies up to 306' and a t saturation vapor pressures were performed by A. A. Noyes and c o - ~ o r k e r s . ~Precise conductance measurements of NaCl in water between 378 and 393' and a t pressures up to 300 bars were reported by Fogo, Benson, and Copeland.* More recently, apparatus was developed by one of the authors for making conductance measurements in aqueous solutions a t pressures up to 2500 (1) This paper is based on work performed a t the Oak Ridge National Laboratory, which is operated by Union Carbide Corporation for the U. S. Atomic Energy Commission. (2) (a) Research participant, 1960, Institut far Physikalische Chemie und Electrochemie, Karlsruhe Technische Hochsohule, Karlsruhe, Germany; (b) Summer participant, 1961 and 1962, Department of Chemistry, Loyola University, New Orleans, Louisiana. (3) A. A. Noyes, et al., "The Elsotrical Conductivity of Aqueous Solutions," Publication No. 63, Carnegie Institution of Washington, Washington, D. c . , 1907. (4) J. K. Fogo, S. W. Renson, and C. S.Copeland, J . Chem. Phus., 2Z, 200, 212 (1964).
bars and temperatures up to 750°.5a By the use of this equipment, extensive measurements were made of the conductances of many 1-1 electrolytes as a function of temperature, pressure, and coiicentration from which dissociation constants, entropy changes, and heats of dissociation were calculated and compared to each other.5 Also from these previous data, the relative behavior of the ion product of water was evaluated a t extreme conditions of temperature and pressure. A general review of investigations in this field has been published elsewhere.Kc At this Laboratory an improved apparatus has been developed which again extends the range of accessible temperatures and pressures. Since the influence of corrosion has been reduced, more accurate measurements may be obtained, particularly with acidic solutions. Since in the earlier high temperature measurements only uni-univalent electrolytes were studied, a program has been initiated to investigate electrolytes containing polyvalent ions. In a study on the behavior of sulfate salts, the electrical conductances of KzS04 dissolved in R20 a t three concentrations hare been measured a t temperatures from 25 to 800" and a t pressures from 1 to 4000 bars. Sufficient data have ( 5 ) (a) E.U. Franck,Z. phgsik Chem. (Frankfurt),8, 92 (1956); (b) ibid., 8 , 107, 192 (1966); (c) Angew. Chfm., 78, 309 (1961).
