KOTES
3894
rise in temperature, the open tetrahedral structureg in the presence of large inorganic ions like K + , Rb+, CS+, C1-, Br-, I-, etc., breaks down whereas this structure-breaking effect is of no importance for ions like Li+ and N a + which have a much larger ion-dipole interaction resulting in appreciable solvation. In forinaniide, this structure is altogether missing and only some molecular association is present. Hence, all the ions in this solvent behave in the same manner irrespective of their sizes. According to Kohlrausch,‘” the faster the ion, the smaller the temperature coefficient of its mobility and all the ions try to attain a transport number as close as possible to 0.5. This general rule is obeyed by KC1 in forniamide although, in aqueous solutions, it is an exception to the rule. It is obvious that the decrease in viscosity with rise in temperature cannot explain the general rule since both the ions will be affected in the same manner. According to Bredig,” due to the difference in the solvation of different ions, their effective volumes (in solution) are different and, generally, the smaller the ion ( i e . , the smaller the crystal radius), the larger its solvated ionic volume, the slower the movement, and the smaller the transport number. The effect of temperature on the transport numbers of cations and anions is, however, difficult to explain since both the increase12-16 and decrease17 in solvation with rise in temperature have *been postulated. Further, relative changes in the sizes of cations and anions, with rise in temperature, are completely unknown. It is usually believed that in electrical conductance, it is only the “primary or chemical” solvation sphere, which is independent of temperature, that moves with the ion, leaving behind the “secondary or physical” solvation part, which is assumed to be temperature-dependent. 1 2 , 1 8 This concept fails to explain the temperature variation of the transport numbers because the moving ionic volume due to “primary” solvation remains unaltered with rise in temperature and hence the transport numbers of cations and anions should be independent of temperature, which is against the experimental facts. Assuming that the “primary” solvation is not affected at all by temperature changes, one is forced to conclude that the “secondary” solvation must be, partly a t least, involved in the transport process, perhaps producing different amounts of drags on different ions when the temperature is raised. Beyond this it will be unsafe to speculate, since the variation of the total solvation (the primary plus secondary) with temperature is, inore or less, an open question at present. According to Eyring’s theory of rate proces~es’~ as applied to the ionic transportlZ0the tangent to the T h e Journal of Physical Chemistry
log t + O / t - O os. 1/T curve gives the difference in the activation energies of K + and C1- ions according to the equation log
t+’ t-0
=
AE(Cl--II+) 2.303RT
I n forniamide this plot is almost a straight line with a negative slope and the difference in the activation energies is about -450 cal., i e . , the activation energy for the transport of K + is larger than for C1- by about 450 cal. This difference will, presuinably, slowly level off at higher temperatures. In water it is positive and srnaller.21 (9) J. D . Bernal and E. H. Fowler, J . Chem. Phys., 1 , 515 (1933). (10) F. Kohlrausch and L. Holborn, “Das Leitvermogen der Elektrolyte,” Teubner, Leipzig, 1916. (11) G. Bredig, “Textbook of Physical Chemistry,” S. Glasstone, Ed., Macmillan and Co., London, 1948, p. 920. (12) F. S. Feates and D. J. G. Ives, J . Chem. SOC.,2809 (1956). (13) S. R. Gupta, G . J. Hills, and D . J. G . Ives. Discussions Faraday Soc., 24, 150 (1957). (14) M . Kaminsky, ibid., 24, 177 (1957). (15) E. Ii. Nightingale, J . P h y s . Chem., 63, 1384 (1959). (16) L. R. Dawson, P. G. Sears, and R. H. Gxaves, J . Am. Chem. Soc., 77, 1989 (1955). (17) J. 0’11.Bockris and B. E. Conway, “Modern Aspects of Electrochemistry,” Butterworths Publications, London, 1954, p. 94. (18) J. O’M. Bockris and B. E. Conway, Quart. Reo. (London), 3, 173 (1949). (19) H. Eyring, J . Chem. Phys., 4 , 283 (1936). (20) H . S. Slater, ibid., 6, 331 (1938). (21) It. W. Allgood. D. J. Le Roy, and R. Gordon, ibid., 8, 418 (1940).
The Thermal Decomposition of Methylcyclobutane at Low
by A. F. Pataracchia and W. D. Walters Department of Chemistry, C’nizersity of Rochester, Rochester, N e w York (Receioed J u n e SO, 1864)
The thermal decomposition of cyclobutane near 450’ has been found to be a unimolecular ring cleavage reaction which exhibits a falloff in the first-order rate ~ constant in the pressure region below 20 i ~ l m . Several comparisons of the low-pressure experirnental results with unimolecular reaction rate theory have been inade.3b~c~dThe present study was undertaken to (1) This work was supported by a grant from the National Science Foundation to the University of Rochester. (2) Abstracted from the M.S. Thesis of A. F. Pataracchia, University of Rochester, 1961.
NOTES
determine the influence of a change in structure from cyclobutane to methylcyclobutane upon the fall-off behavior. The effect of methyl substitution has already been studied for the case of the unimolecular isomerization of cy~lopropane.~ The honiogeneous thermal isomerization of niethylcyclopropane which yields four isomeric butenes was studied in the region 440-490" a t ]pressures of 0.6 to 200 mm. A decrease in the over-all first-order rate constant was observed a t about the pressure a t which the same effect occurred in the isomerization of cyclopropane. Thus an investigation of the effect of a methyl substituent upon the fall-off behavior of cyclobutane would be of interest also for comparison with the data for cyclopropane and methylcyclopropane. Earlier results on the pyrolysis of methylcyclobutane indicated that it should be suitable for such a s t ~ d y . ~
Experimental Materials and Apparatus. The methylcyclobutane used in this work was a sample which had been prepared in this laboratory by Das.6 The methylcyclobutane had been obtained by the hydrogenation of methylenecyclobutane over Raney nickel a t 50 p.s.i. with the temperature kept below 60'. Subsequent purification of the sample was carried out by gns chromatography with a 2-ni. Perkin-Elmer column A (diisodecyl phthalate) at 33'. The purified sample after drying over Linde 4A Molecular Sieve had a niinimum purity of 99.9%. The cyclobutane from a previous study3&which was used for some experiments was found to be 99.9% pure by a gas chromatographic analysis on a tetraisobutylene-firebrick column. The reaction vessel and furnace were modifications of the apparatus used for several earlier experiments.s* The reactor mas a 12-1. spherical Pyrex glass bulb with a thermocouple well extending into its center. For temperature uniformity the vessel was enclosed in a spherical aluminum shell 2.5 cm. thick (in the form of two separable hemispheres). The temperature of the reaction vessel was measured with five standardized platinum, platinum-l3% rhodium thermocouples (one at the center of the vessel and four a t various points on the surface of the glass vessel) which were connected to a Gray Model E3040 potentiometer. The average of the five values (with a mean deviation of about 0.25') was taken as the reaction temperature. The grease-free system for measurement, in troduction, and removal of samples was connected to the reaction vessel through a 15-mm. mercury cutoff float valve, and thc various parts were connected by 14mm. tubing to permit rapid transfer of gases and efficient pumping. Before each experiment a pressure of
3895
-
less than nim. was obtained. Prior to a series of experiments t,he surface of the reaction vessel was treated by decomposing the reactant in the vessel. For removal of the reaction mixture a trap adjacent to the first mercury float valve was fitted with a special dewar flask so that the coolant (liquid nitrogen) could be brought to a lower temperature by pumping with a mechanical-type oil pump. The pumping on the nitrogen coolant was begun a t least 30 min. before the time of removal which usually corresponded to 25-37 % decomposition. The pressure in the reaction vessel after product removal was less than nim. Analyses. The reaction mixtures were analyzed on a Perkin-Elmer Model 154D vapor fractometer equipped with a Model 194 printing integrator. The 2.7-m. chromatographic column (5-mm. i d . ) was packed with tetraisobutylene on 60-80 mesh Chromosorb. The column was operated a t a temperature near 26" with a flow rate of 56 cc. of helium/min. To keep the vapor samples (which were expanded into the gas chromatograph) within definite limits attachments of different sizes were used with the gas sampling valve. Major peaks for ethylene, propylene, and methylcyclobutane were observed. From the size of the ethylene peak the proper attenuation could be selected to give the optimum size for the propylene peak for the comparison of its area with the area under the methylcyclobutane peak. A technique was developed in order to obtain for each reaction mixture a number of such area ratios which upon averaging would give a more reliable value than that from a single determination. The peaks for ethylene (1.5 min.) and propylene (3.7 min.) appeared during the first 4 inin., but the peak for methylcyclobutane did not appear until about 40 min. later. With standard mixtures it was found that additional portions of the mixture could be expanded into the gas chromatograph after the ethylene and propylene had been detected and before the first methylcyclobutane peak was recorded. The successive expansions (2 to 7 ) gave a series of pairs of ethylene and propylene peaks followed by a series of methylcyclobutane peaks. The area under each propylene (or ethylene) peak was then coinpared with the area under the corresponding methyl(3) (a) C. T. Genaux,
IF. Kern, and W. D. Walters, J . Am. Chem.
Soc., 75, 6196 (1953) ; F. Kern and W. D. Walters, Proc. Natl. Acad.
Sci. U . S., 38, 937 (1952); (b) H. 0. Pritchard, R. G. Sowden, arid A. F. Trotman-Dickenson, Proc. Roy. Soc. (London), A218, 416 (1953); (c) J. N. Butler and R. B. Ogawa, J . Am. Chem. SOC.,85, 3346 (1963); (d) R. W. Vreeland and D. F. Swinehart, ibid.,85,3349 (1963); R. W. Vreeland, Ph.D. Thesis, University of Oregon, 1961. (4) J. P. Chesick, J . Am. Chem. Soc., 82, 3277 (1960). (5) M. N.Das and W. I). Walters, Z . phyailc. Chem. (Frankfurt), 15, 22 (1958).
Volume 68, Number 1.9
December, 1964
SOTES
3896
cyclobutane peak. With proper attenuation there was no trend in the variation of the area ratio for the successively expanded portions. The average ratio for each reaction mixture was compared with a calibration curve prepared from samples of known compositions. When the peaks were not suitable for accurate measurement by the integrator, areas were determined in other ways and coinpared with standard samples measured in the same manner. Since C5Hlo-+ CzH4 C3He, the gas chroinatographic ratios could be used to obtain the percentages of decomposition. On the assumption that two molecules of products are forined from one reactant molecule, the per cent decomposition was calculated also from a comparison of the total moles removed from the reaction vessel and the moles introduced. For 27 of the 30 experiments in which both P V T and g.c. results were available, the values from the P V T data (after 30% decomposition) averaged slightly higher than the g.c. values by an amount corresponding to +0.9% decomposition. The agreement seems satisfactory; it is to be noted that the per cent decomposition from P V T results will reflect the presence of all types of product molecules. The first-order rate constants were calculated from the propylene formed with the exception that the point at the lowest pressure in Fig. 2 was obtained froin P V T results and the next point was based on the average for propylene and ethylene. I n the calculations of the rate constants in this work the effect of a small dead space (0.3YG)was taken into account and a small correction was applied for the time of removal of the reaction mixture. In the present study prior to the work on methylcyclobutane, experinients were carried out with cyclobutane a t initial pressures froin 0.32 to 0.016 min. near 449' in the sanie apparatus. A qualitative g.c. analysis of the products showed that ethylene was essentially the only product formed. Three preliniinary experiinents with Po = 0.02 mni. gave an average value of 2.05 for the ( P m / P o ratio ) indicating the formation of two product molecules. The gas noncondensable in pumped liquid nitrogen was found to be only -0.03% of the final products (after 24 hr.). Since the stoichiometry corresponded to that found at higher pressures (C4H8 + 2CzH4), the per cent decomposition was determined from the ratio (moles removed from reaction bulb/nioles introduced). The rate constants will be presented in the Results section, but after the report of the comprehensive low-pressure study of cyclobutane by Vreeland and Swinehart work with cyclobutane was discontinued.
+
The Journal of Physical Chemistru
Results Experiments were performed to find out whether the deconiposition at low pressures proceeds according to the equation CHS--CH--C
I
Hz
l -
CH3-C H z C H 2
CH2 -CH2
(1)
CHZzCHZ
which represented 98-997, of the pyrolysis at 7-417 inm. and 410-450°.5 The course of the reaction at pressures of 0.0026-0.45 imn. was indicated by the following results. With 0.3 mm. initial pressure at 450' the ratio of P m / P owas observed to be 2.02. In a test for side or subsequent reactions, the aniount of gas noncondensable at --210' from an experiment with 0.28 mm. initial pressure carried to 23y0 reaction mm. From the was found to be less than 2.5 X chromatographic analyses of the reaction mixtures it was possible to compare the amounts of ethylene and propylene in experiments at various pressures. The data summarized in Table I indicate that over the pres-
Table I : Comparison of the Amounts of Ethylene and Propylene Formed in the Pyrolysis of Methylcyclobutane a t Low Pressures" Pressure iange, mm
0 0 0 0 a
2-0 45 05-0 20 01-0 05 0027-0 01
Temp 400-440';
N u m b e r of experiments
8 8 7 6
Pc,H~/Pc~H,
1 004 1 016 1 005 0 980
f0 f0 f0 f0
006 014 023 020
decomposition, 25-36%.
sure range studied the ethylene and propylene are present in equivalent amounts. These findings provide evidence that under the conditions of this study the stoichionietry of the decomposition is in agreement with eq. 1. The chromatograms for experiments at the lowest pressures (-0.003 mm.) revealed three very small peaks at 2.2, 2.5 (between CzHl and GHs), and 4.8 min. (after C3H,). The substances were not identified, but the total of their areas amounted to only 0.03 f 0.01 times the combined areas under the ethylene and propylene peaks. Of lesser iniportance was a sinal1 shoulder (sometimes a peak) near the beginning of the ethylene peak. In experiments at pressures of 0.3-0.4 mm. all of these minor features became less distinct (the curve between 2.2 and 2.5 min. being only slightly different from zero) and a maxiniuni estimate
Noms
3897
for them would be 0.001-0.008 times the combined areas of ethylene and propylene. Under the conditions used in this work, reactions other than (1) dlo not seem to oiccur to an extent that will significantly affect the rate constants calculated for (1). The absence of a peak near that of methylcyclobutane indicates that no appreciable isomerization takes place. The decrease in the first-order rate constant as thle initial pressure of methylcyclobutane is lowered to 0.0027 mm. at 420' is shown in Fig. 1, in which log tk is plotted against log Po. The data at 430' are shown in the form of a log (k/k,) us, log Po plot. The values of k , a t 420 and 430' were taken to be 1.27 X and 2.38 X see.-', respectively. I n each case k , was evalualed by the use of plots of k-' us. Po-' and k-1 us. PO-O.6for the present data plus some experiments from the earlier work.
-4.00 I
3
I
22" I
5
-4.25
-4.50 -2.80
-2.0
- 1.0
0.0
1.0
1.2
Log Po, mm.
Figure 1. Change of first-order rate constant for methylcyclobutane with decreasigg initial pressure a t 420": 0, this !study; e, data of Das.6 Curves calculated from quantum form of Kassel theory: curve 1, s = 28; curve 2, s = 27; u = 5.9 A,, E = 62 kcal./mole, A = 4.46 X 1015 set.-', v = 2.96 X 10'8 sec.-l.
Although the effect of the initial pressure upon the activation energy was not studied in detail, some information was obtained from a few experiments at Po = 0.4 mm. and at Po = 0.06 mm. for the region 400-430' and from four experiments with Po nea,r 0.0028 mm. at 410440°. The activation energy at 0.4 mm. was 62 A= 1 kcal./mole. These preliminary results indicated that the activation energy probably decreases for pressures of 0.06 and 0.0028 mm. by about 3-4 and 5-6 kcal,/mole, respectively. Both the quantum and classical forms of the Kassel theory6 were used for 1 he calculation of fall-off curves. I n Fig. 1 are shown the curves at 420' from the quantum form of the Kassel theory for the number of oscillators s = 27 and s = 28 (and with other parameters
0.0
-0.2 h
*8
-2 2
-0.4
d
-0.6
-0.8
- 2.8
-2.0
- 1.0 Log Po,mm.
0.0
1.0
Figure 2. Comparison of the decrease in the first-order rate constant for methylcyclobutane a t 430" with Kassel classical theory and with fall-off data for cyclobutane. Rate constant for methylcyclobutane a t 430": 0, this work; 0, data of Das.6 Curve 1, s = 24. Curve 2, s = 23, u = 5.9 b.,b = 44.4 ( b = E / R T ) , A = 4.4 X 10'5 set.-'. Curve 3, cyclobutane a t 430" from ref. 3d. Curve 4, cyclobutane a t 449": 8, Vreeland and Swinehartsd corrected to 449'; 8, Kern, ref. 3a; 6,this work.
as given below Fig. 1). These curves are in reasonable accord with the experimental results a t 420' and a similar curve for s = 28 (not shown) agreed with the data a t 430'. With the classical form of the Kassel theory the fall-off curves for s = 24 and s = 23 were obtained with the program of Schlagl for the Bendix G-15 computer (see curves 1 and 2, Fig. 2). The curve for s = 24 is slightly higher than the experimenta,l data, but the curve for s = 23 fits the data well. Thle lower value of s for the classical form* compared to the quantum form would have been anticipated. The effect that methyl substitution on cyclobutane produces upon the fall-off curve can be seen in Fig. 2. Curve 4 shows the decrease in the first-order rate constants obtained for cyclobutane at 449' from various studies. The results for cyclobutane in our apparatus at 449' seem to be in satisfactory agreement with the data of Vreeland and Swinehart at 449OS3d In the lower pressure region our methylcyclobutane fall-off curve at 430' is shifted toward lower pressures by 1 . 1 5 (6) L. 9. Kassel, "The Kinetics of Homogeneous Gas Reactions," Chemical Catalog Co., Rsinhold Puhlishing Corp., New York, N. Y., 1932, pp. 100-103. (7) E. W. Sohlag, B. S. Rahinovitch, and F. W. Schneider, J . Chem. P h y s . , 3 2 , 1599 (1960). (8) The situation with respect t o the classical form has been discussed hy B. S.Rahinovitch and J. I€. Current, ibid.,35, 2250 (1961) ; E. W. Schlag, ibid., 35, 2117 (1961); M. Vestal, A. L. Wahrhaftig, and W. H. Johnston, ibid.,37, 1276 (1962); G. M .Wieder and R. A. Marcus, ibid., 37, 1835 (11962).
Volume 68, ,Vumber 13 December, 1964
3898
1.2 log Po units compared to curve 3 for the cyclobutane fall-off at 430' observed by Vreeland and Swinehart.3d As would be expected, the difference (at the lower pressures) between the methylcyclobut ane falloff data at 430' and curve 4 for cyclobutane at the higher temperature (449') is somewhat larger (1.251.4 log Po units). The value of s = 23 (Kassel classical) for niethylcyclobutarie may be compared with Vreeland and Swinehart's cyclobutane value of s = 18.3d I n each case s is approximately 60% of the total number of vibrational degrees of freedom and on this basis the vibrational degrees of freedom of the added methyl group appear to participate almost as effectively in the activation process as the rest of the molecule. This finding would seem t o be in accord with the concept of intramolecular energy transfer during the lifetime of the activated molecule. For methylcyclopropane4 the value of s = 19 which gives a suitable Kassel classical fall-off curve represents an increase of 6 or 7 over the s appropriate for cyclopropane. Moreover, Flowers and Freyg found that the curve for s = 23 reproduces their fall-off data for 1,l-dimethylcyclopropane (which has the same number of vibrational degrees of freedom as methylcyclobutane) , Also of interest is that the fall-off curve obtained by Chesick'o for methylenecyclobutane lies between the curves for methylcyclobutane and cyclobutane. In the low pressure work on cyclopropane'' and cyclob~tane,~c.d it has been observed that the curve for the decrease in rate constant tends to level off at pressures in the region nim. and below. The data in Fig. 1 and 2 for methylcyclobutane do not extend to a pressure of mm. and do not exhibit a noticeable leveling off, Acknowledgment. The authors wish to thank Dr. E. W. Schlag for his computer program and Mr. Carl Whiteman for his assistance. (9) M.C. Flowers and H. M . Frey, J . Chem. Soc., 1157 (1962). (10) J. P.Chesick, J . P h y s . Chern., 65, 2170 (1961). (11) A. D. Kennedy and H. 0. Pritchard, ibid., 67, 161 (1963).
Solvent Dipole Competition for Interamide Hydrogen Bonds'
by James S. Frarizen and Barbara C. Franaen Department of Biochemistry and S u t r i t i o n , Graduate School of Public Health, L'nitersity of Pittsburgh, pittsbtkrgh. Pennsgluania (Received J u n e 29, 29/34)
It has been demonstrated that the hydrogen-bonding interaction between amides is weakened by a dipolar T h e Journal of Physical Chemistry
NOTES
solvent.2 This earlier study has now been extended to another solvent system of varying dipolar character. By using either carbon tetrachloride, F = 0.0 D . , or l,l,l-trichloroethane, p = 1.6 D., or mixtures of the two, a range of solvent dielectric constants from 2.25 to 7.0 can be covered. This system is more appropriate than the cis-trans-dichloroethylene system used previously because no type of solvent-solute hydrogen bonding is possible. The extensive studies of Allerhand and Schleyer3 have revealed no evidence for the participation of methyl groups in hydrogen bonding, and, therefore, any competitive effects by the solvent must be due to dipole-dipole interaction. e-Caprolactam was chosen as the hydrogen-bonding solute since it forms dimers ~ n l y ,thus ~ , ~eliminating the need for making assumptions about relative magnitudes of equilibrium constants as is required for multiple equilibrium systems.5 The extent of association was determined from the variation of the apparent extinction coefficient of the first overtone of the free N-H absorption according to the treatment of Lord and P ~ r r o . ~
Experimental The solvents employed were obtained from Fisher Scientific Co. Spectroanalyzed grade carbon tetrachloride was used without further treatment. The trichloroethane, however, exhibited a strong absorption band at about 273 mF which was probably due t o aromatic contamination. This solvent was, therefore, distilled through a 90-cm. electrically heated column packed with Berl saddles. Using a reflux ratio of 8 : 1, the fraction boiling at 72-73' and having no absorption band at 276 nip was used for the hydrogen-bonding experiments. e-Caprolactam from K and K Laboratories was dried overnight in vacuo at room temperature and used directly. The spectral measurements of the unassociated N-H group in the near-infrared region were carried out as described in the earlier paper2 except for a few minor changes. Since the Gary 14-R spectrophotometer was available, the reverse beam feature of this instrument was exploited. Thus instead of passing the entire wave length range of the source through the sample, only monochromatic radiation traversed the solutions. As a result, heating of the sample by the beam was reduced to (1) This work was supported in part by a Public Health Service Research Grant (GM-10133-02) from the Division of General Medical Sciences. (2) J. S.Franzen and R. E. Stephens, Biochemistry, 2, 1321 (1963). (3) A. Allerhand and P. von R. Schleyer, J . Am. Chem. Soc., 85, 1715 (1963). (4) R. C. Lord and T. J. Porro, 2 . Elektrochem.. 64, 672 (1960). (5) > Davies 'I. and D. K . Thomas, J . Phys. Chem., 6 0 , 763 (1956).
