NOTES
1525
Table 11: Coefficients of Polynomial a t 25" Solvent system
570acetone 10% acetone 10% methanol 20% acetone 20% methanol 20% methanol 20% dioxane 40% methanol 40% acetone 60% methanol
D
75.9 75.9 73.1 74.1 67.6 70,OC 70.0d 60.79 60.94 54.6 51.67
W O '
0.2190 0.2190 0.21565 0.21535 0.20795 0.20881 0.2094 0.20303 0.1968 0.18595 0.1818
Ao (En"))
0.21925 0.21858 0.21601 0.21581 0.20818 0.20846 0.20914 0.20301 0.19682 0,18492 0.18120
Az
AI
0.05700 0.07101 0.05601 0.05732 0.06948 0.08053 0.08039 0.08996 0.09624 0.1317 0.1394
-0.06079 -0.1423 -0.05297 -0.05920 -0.09186 -0.1769 -0.1635 - 0.1473 -0.2395 -0.4818 -0.6878
As
0 0.1388 0 0 0.03742 0.20711 0.1626 0.1016 0.3663 1.3997 2.8260
' Elo is the standard potential obtained by linear extrapolation. These are given here for comparison. See second part of footnote d of Table I. of Table I. See first part of footnote d of Table I.
extrapolation and by the curve-fitting technique. The results show that the agreement between the methods is excellent up to a dielectric constant value of 18. It is of great interest to compare the coefficients of the polynomials used in computing E" values in different mixed solvents. These coefficients are tabulated in Table 11. It is somewhat unfortunate that E" values are not available for any two systems with exactly identical dielectric constants. However, several sets of values of E" are available for different systems with dielectric constant values very close to each other. It is seen that while the dielectric constant for comparable pairs differs by 1-3 units, the first term of the polynomial which is identically equal to E" differs by 0.2-3 mv. The agreement between the coefficients of the subsequent terms is not as good. This is to be expected, because the curvature of the plots of the polynomial is determined by the higher order terms and must be highly sensitive to va.lues of the dielectric constant. We feel sufficiently confident to conclude that the coefficients of the polynomial are determined solely by the dielectric constant of the solvent with regard to the particular process and constitute a standard set of constants. The implication of this conclusion is quite far reaching. It, is, of course, assumed that there are no other interact,ions in the system besides the ion-ion and ion-solvent coulombic interaction as outlined by the Debye-Hiickel theory. Furthermore, there is a direct correlation between the degree of equation which gives the correct extrapolation and the dielectric constant; Table 111gives this correlation.
Conclusions 1. The standard potential of a reversible reaction may be expressed as polynomial in powers of rn'/'. 2. At a constant temperature the dielectric constant
A4
0 0 0 0 0 0 0 0 0
-1.6731 -4.2371
* A" is the same as Eao
Table I11 Range of D
Degree of eq
Above 75
2 or 3 3 4 5
55-75 40-52 la0
is the most important among the factors composing the coefficients of the polynomial. 3. It is expected that the coefficients once determined from experimental emf data corresponding to a particular dielectric constant will form a set standard data. 4. The standard IBM program, IBM 7.0.002, is highly suitable for the evaluation of the polynomial. 5. There is a direct correlation between the dielectric constant of the solvent and the number of terms required to make accurate extrapolation.
Hydride Transfer Energetics with Aluminum Bromide Catalysts by G. M. Kramer,Ia B. E. Hudson,lb and M. T. Melchiorlb Esso Research and Engineering Company, Linden, New Jersey (Received August 19, 1986)
Intermolecular hydride transfer with aluminum bromide was originally investigated by Bartlett, Condon, and Schneider.28 The reaction is considered Volume 71, Number 6 AprQ 1887
NOTES
1526
an integral and often rate-controlling step in strong acid-catalyzed isomerizations and alkylations. The present work was undertaken to obtain additional information about the energetics and nature of hydride transfer. This study involved the use of nmr spectroscopy to follow hydride transfer between isobutane and t-butyl cations in solutions of isobutane, 1,2,4trichlorobenzene, and aluminum bromide promoted with water or moist air. It was found that activated aluminum bromide in 1,2,4-trichlorobenzene would support the intermolecular exchange, eq 1, at such a rate as to broaden the nmr spectrum of isobutane. The C
I I C
C-C-H
C
I + +C-C I
C
C
I I
C-Cf
C
C
+ H-C-CI
I
(1)
C
broadening provides a measure of the exchange rate and of the average lifetime of an isobutane molecule in the system. 2b Aluminum bromide catalysts with reproducible activity were difficult to prepare but it was always possible to obtain sufficient activity to yield broadened spectra. The temperature dependence of exchange rate over several active systems was investigated in an attempt to determine the apparent activation energy at the reaction. Results from two sets of experiments over active systems are discussed below. Experimental Section The aluminum bromide catalysts used in these experiments were activated by the addition of water or by exposure to moist air. Pure aluminum bromide caused no detectable reaction. The activated catalysts were difficult to prepare with reproducible activity but could always be prepared with sufficient activity to afford broadened spectra. Well-resolved spectra of isobutane could be obtained after exchange had proceeded for some time by quenching the catalyst with excess water. The reagents used in these experiments include Phillips Research grade isobutane which was treated with molecular sieves t o remove any traces of olefin and water and commercial 1,2,4-trichlorobenzenewhich was treated with 97% HzS04, washed and dried with CaCI2, and then distilled in a vacuum-jacketed packed column. A heart cut boiling at 213” was used as the solvent. Aluminum bromide was distilled in conventional fashion, collected in several glass-stoppered vials, and stored in a drybox under a nitrogen atmosphere until use. Samples for nmr studies were prepared in a drybox. The Journa2 of Physical ChemOtrV
The filled sample tubes were either stoppered with a polyethylene cap or frozen and sealed with a flame. Tubes closed by either procedure were tested for safety at temperatures up to 65” and found to be acceptable. Solutions were prepared by first distilling isobutane into a sample tube cooled by a COz-acetone bath. Trichlorobenzene was then added to the butane with a hypodermic. The trichlorobenzene froze and essentially sealed in the liquefied butane. The cold tube was weighed and pure or air-exposed aluminum bromide added. The system was then capped and allowed to thaw at room temperature. This procedure yielded clear solutions. When water was used as an initiator, it was found convenient to introduce it into the sample tube first and then follow the above procedure. Typical solutions discussed in this work contained 0.256-0.35 cc of isobutane, 0.75-1.0 cc of trichlorobenzene, 0.127 g of aluminum bromide, and 0-2 jt1 of HzO. The solutions were brought to constant temperature in a water bath before the nmr measurement. All nmr spectra were obtained on a Varian A-60 spectrometer with variable-temperature attachments. The Varian instrument was tuned for maximum resolution at each temperature with a standard isobutane solution before the reaction mixture was examined. Results and Discussions Pure, degassed isobutane has a 60-Mc nmr spectrum which is adequately described as AB9with J / 6 = 0.12.8 The methyl proton resonance is a doublet which is broadened by unresolved second-order splittings. The effective half line width is 1.20 f 0.05 cps. The tertiary hydrogen resonance is more completely resolved and each member of the gross multiplet is split by second-order terms into components having halfwidths of -0.3 cps. For the purpose of estimating exchange rates, it has been assumed that the methyl doublet can be considered as a broadened first-order doublet. Determination of the Activation Energy for Hydride Transfer. It has been assumed that the theory developed for the behavior of chemically exchanging first-order spin systems can be applied to the present case if the second-order perturbation of the methyl “doublet” is treated as an inherent part of the natural line width (zero exchange). With this approxima(l! .(a) Central Basic Research Laboratow; (b) Analytical Research
Division. (2) (a) P. D. Bartlett, F. E. Condon, and A. Schneider, J. Am, C h . Soc., 66, 1531 (1944); (b) J. A. Pople, W. G. Schneider, and H. J. Bernstein, “High Resolution Nuclear Magnetic Resonance,” McGraw-Hill Book Co., Inc., 1959, pp 218-224. (3) Reference 2b, p 119.
NOTES
1527
tion, the doublet line shape is a function of two dimensionless parameters CY
= W/J;
p = JT
where 2W is the half line width at zero exchange, T is the average lifetime of the methine proton, and J is the methyl-methine spin-coupling constant in radians per second. The analysis of the spectra has been carried out in terms of S , the separation of the methyl doublet maxima (cf. Figure 1A). The doublet separation for pure isobutane (zero exchange) is SO= J . The values of W and So obtained from pure isobutane determine (Y as 0.10 (cf. Figure 1B). Thus for finite exchange lifetimes, S can be calculated as a function of p only. For this purpose published tables of line shapes were used.4 The theoretical value of S@)/So is shown in Figure 2 (for (Y E 0.10). Over the range of p values considered, S(p) is quite sensitive to small changes in exchange rate. A sample exhibiting an exchange rate corresponding t o p s 2.5 (cf. Figure 1A) was examined at several temperatures over the range 25-40". There was no apparent change in line shape or trend of doublet separation, S , with temperature. A maximum change in S was conservatively taken as twice the greatest scatter of all measurements (cf. Figure 2). This leads to an upper limit for the apparent activation energy.
E, 5
1
I
l
*
.
p
'
t
t l " ' ; " L
Figure 1. (A) The methyl doublet of isobutane with j3 = 2.5; (B) definition of parameters at zero exchange.
0.750
Although approximations inherent in the use of firstorder theory restrict the accuracy of a single rate measurement, it is felt that relative values of p and consequently the upper limit of E, are quite reliable. A second sample having an exchange rate corresponding to p E 4.2 was examined over a lengthy interval. Between 40 and 50 hr after preparation the temperature was repeatedly cycled between 0 and 37" and spectra were obtained (Table I). The doublet
*
d QP
0.800
lo3 cal/mole
*
5Y 0.700 0.650
i
0.600 0.550 0.500 0.450 2.0
2.5
3.0
3.5
4.0
4.5
8.
Figure 2. Doublet separation in exchanging system. Table I: The Effect of Temperature on Doublet Separation T,OC
Separation, cpa
37 8 8 20
5.80 6.05 5.75 5.30
20 8 37
20
6.00
37
T,O C
0"
Separation, CPS
5.60 5.70 5.77 5.96 5.70
Separation = 5.76 & 0.21 cps a Supersaturated solution. The practical low-temperature limit of this work was set by the time for which a supercooled solution could be maintained.
*
separation remained relatively steady at 5.76 0.21 cps during these cycles but decreased when maintained at 37" for several hours and after lengthy storage. The increased rate after several hours at 37" may be due to a slow and reversible change in the effective catalyst concentration since the original rate is restored by cycling through lower temperatures. After prolonged storage, noticeable quantities of a sludge phase formed in the nmr tube. The exchange rate appears to (4) "Tables of Exchange Broadened Multiplets," Technical Note No. 2, U. 8.Air Force, Weiamann Institute, Rehovoth, Israel, 1961.
Volume 71, Number 6 April 1967
1528
increase in the presence of the sludge, and this phenomenon is under present study. Nature of the Catalyst. The catalysts is perhaps best considered to exist as an ion pair in polar cavity in the low dielectric medium of trichlorobenzene. The ion pair consists of a t-butyl cation and an aluminum bromide-generated anion. In view of the low activation energy of the process, the exchange reaction must occur upon a suitably oriented collision of the t-butyl cation and a neighboring isobutane molecule without much separation of the ionic entities. That is to say that the reaction may proceed either within or at the walls of the polar cavity but probably not outside of the cavity because of the large amount of energy which would be needed to separate the ion pair in the low dielectric medium, D1,2,4*:1D& = 4.3. The low activation energy for transfer in solution raises mechanistic questions when one considers possible rate-determining steps in paraffin isomerization and alkylation reactions. For example, ion formation is generally considered to be slow in the isomerization of the various hexanes to an equilibrium mixture over aluminum halides. This may be true when starting with n-hexane which must first form a secondary ion, but the reaction of 3-methylpentane, 2methylpentane, and 2,3-dimethylbutane may well be limited by one of the ionic rearrangement steps. The low activation energy for hydride transfer in lowdielectric media as determined in this study suggests that this reaction be used as a diagnostic criterion for the presence of low molecular weight aliphatic cations. This would be in accord with the direct observation of hydride transfer and consequently a low activation energy for reactions occurring in the mass spectrometer.s (5) A rough estimation of the effective catalyst concentration, based on collision theory, leads to the conclusion that there is one active site for every l o 3 aluminum bromide molecules. The activesite concentration in a typical experiment is thus about 4 X 10-4 mole/l. (0) F. W. Larnpe and F. H. Field, J. Am. Chem. Soc., 81, 3238 (1959).
Surface Catalytic Effects in Nitrous Oxide Radiation Dosimetry1a by F. w. Lampe,lb L. Kevan,lc E. R. Weiner,ld and W. H. Johnston William H . Johnaton Laboratorha, Inc., Baltimre, 81816 (Received August 26,1066)
Maryland
used as a gas-phase Nitrous oxide has been radiation dosimeter.2 A critical review of the experiThe Journal o j Phyaical Chem$a&t
NOTES
mental conditions under which this dosimeter gives valid results allows one to conclude2@that G(N2) = 10.2 f 0.4 from N2O at doses up to 5 Mrads in the pressure range of 0.3-2 atm at 25". We would like to report here that complications from metalsurface catalysis may arise in certain applications of this dosimeter. Nitrous oxide, ethylene, and methane have all been tested as dosimeters for a strontium P-irradiator developed in our laboratory. This irradiator contains 600 curies of SrgO-YNin the base of a 4.2-1. stainless steel reaction chamber. The entire reaction chamber is filled through a valve system with the gas or gaseous mixture to be irradiated; the gas is continuously circulated through a bellows pump to ensure dose uniformity. Total pressure is continuously monitored by a Wallace-Tiernan gauge. Temperature can be varied from 20 to 100". Gaseous samples can be withdrawn through the valve system directly into a gas chromatograph for analysis. The entire system was observed to hold a constant vacuum of less than torr for periods of time much greater than the reactive times. The gases were purified by degassing and trap-to-trap distillation before irradiation. N2, H2, and C2Hawere determined by gas chromatography on molecular sieve and silica gel columns. H2 was also determined by mass spectrometry. For comparative results some irradiations at high dose rates with 0.4Mev electrons from a Van de Graaff generator (High Voltage Engineering, Inc.) were performed. Ethylene (500 torr) dosimetry based on G(H2) = U3and methane (500 torr) dosimetry based on G(H2) = 5.74 and G(C2He) = 2.14 gives a dose rate of 0.47 0.02 Mrads/hr for the strontium p-irradiator a t 26". In contrast, N20 dosimetry produces N2 yields which are an order of magnitude greater than expected from radiation decomposition. Furthermore, the N2 yields are independent of N20 pressure at 50-700 torr and are proportional to the time spent in the irradiator. These results are shown in Figure 1. The pressure-independent yields demonstrate that a mechanism other than radiation decomposition predominates. We suggest that a surface catalytic mechanism may be operative; it may be formulated as
*
(1) (a) This research was supported by the Division of Isotopes Development of the U. S. Atomic Energy Commission under Contract AT(30-1)-2901 with William H. Johnston Laboratories, Inc.; (b) Pennsylvania State University and Johnston Laboratories, Inc. ; (0) University of Kansas and Johnston Laboratories, Inc. ; (d) University of Denver, Denver, Colo. (2) For recent reviews see (a) AEC Report No. JLI-2901-75 (1906); (b) F. T. Jones and T. J. Sworski, J . Phys. Chem., 70, 1640 (1966). (3) K. Yang and P. L.Gant, ibid., 65, 1861 (1961). (4) F. w. Lampe, J . Am. Chem. SOC.,79, 1055 (1957).
