J. Phys. Chem. 1980, 84, 679-680 I
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chemisorption and surface diffusion. The relative1 magnitudes of the two rate processes are dependent oinly on the nature of the surface for a given reaction system, e.g., C-O2 reaction. Consequently, the threshold partial pressure should depend only on the nature of the surface. To consider the problem quantitatively, one needs to solve the two-dimensional diffusion equation. Arkz0has shown an analytical solution for the steady-state case of surface diffusion/reaction with a linear rate of adsorption. This solution represents a special case for the Elovich-type rate of adsorption where the surface concentration is small. We are now measuring the rates of adsorption and desorption of the oxides on carbon, and solving both the steady and unsteady diffusion equations. Acknowledgment. Part of the work was performed at Brookhaven National Laboratory under the auspices of the Chemical Sciences Division, U.S. Department of Energy. Discussions with Dr. F. B. Growcock of Brookhaven and Drs. S. W. Weller and E. Ruckenstein of SUNY at Buffalo are appreciated.,
References and Notes OL-L..--l
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Figure 1. Transient rates for carbon-oxygen reaction. (A) 1 % O2in Ar at 1 atm, the rates at unity are 6.2 X min-' for the 1.27-cm diameter disk (0)and 2.7 X min-' for the particles with sizes 841-1000 p m (A).(6)10% O2 in Ar in 1 atm, the rates at unity are 6.4X lo3 min'-' for the disk (0)and 2.8 X min-' for the particles (A). The dashed line indicates the threshold below which surface diffusion is important in the reaction.
oxygen was ohut off and an equal flow of argon was added to maintain a constant total flow. The most interesting results were the transient rates after the oxygen supply was shut off. The typical results are shown in Figure 1 as the normalized rates which are based on different scales on the ordinate such that the steady rates are shown on the same level. The time for the reactant gas to travel from the mass flow meters (where the oxygen was shut off) to the sample was estimated to be 15 s. From the transient rates, one may estimate the history of the partial pressure of oxygen near the sample by using a known rate expression. Nonetheless, the results showed that,,at 850 "C, the transient rates were identical for the disk and the particles, whereas at 700 " C the rates deviated substantially after a certain time. The deviation signified a region where the larger basal-plane surface contributed to the overall rate. Since it had been shown that the abstraction of carbon atoms from the basal plane was insignificant compared with edge carbon attack, the deviation was attributed to the contribution of surface diffusion to the overall rate. In this region, the basal plane served as a collecting area, and the surface oxygen complex migrated to the edge atoms which were promptly removed with the migrated oxygen. The resultx, showed that the surface diffusion mechanism is significant under relatively mild conditions, i.e., lower temperatures or partial pressures. The threshold partial pressure at 700 " C corresponds to the rate indicated by the dashed line in Figure 1. Below the threshold partial pressure, surface diffusion becomes increasingly important and, at still lower partial pressures, it is predominant in the overall reaction. Under the reaction conditions where surface diffusion is important, two rate processes operate on the basal plane: 0022-3654/80/2084-0679$0 1.OO/O
(1)J. J. Carberry, "Chemical and Catalytic Reaction Engineering", McGraw-Hill, New York, 1976,Chapter 8. (2) M. Boudart, AIChE J . , 18, 465 (1972). (3)S. W. Weller, Adv. Chem. Ser., No. 148, 26 (1975). (4)J. Gadsby, F. J. Long, P. Sleightholm, and K. W. Sykes, Proc. R . SOC.London, Ser. A , 193, 357 (1948). (5) F. Bonner and J. Turkevich, J. Am. Chem. Soc., 73, 561 11951). (6) P. L. Walker, Jr., F. J. Rusinko, and L. G. Austin, Adv. Catal., 11, 133 (1959). (7) S. Ergun and M. Mentser, Chem. Phys. Carbon, 1, 203 (1965). (8) C. Wagner, Adv. Catal., 21, 323 (1970). (9) N. R. Laine, F. J. Vastola, and P. L. Walker, Jr., J . Phys. Chem., 67, 2030 (1963). (10) P. L. Walker, Jr., F. J. Vastola, and P. J. Hart in "Fundamenitals of Gas-Solid Interactions", H. Saltsburg et ai., Ed., Academic Press, New York, 1967,p 307. (11) H. Marsh and A. D. Foord, Carbon, 11, 421 (1973). (12) R. T. Yang and M. Steinberg, J. Phys. Chem., 81, 1117 (1977). (13) F. S. Feates and P. S. Robinson, "Third Conference on Industrial Carbon and Graphite", Society of Chemlcal Industry, London, 1971, p 233. (14) J. T. Galiagher and H. Harker, Carbon, 2, 163 (1964). (15)D. W. McKee and D. Chatterji, Carbon, 16, 53 (1978). (16) R. T. Yang, J. 8. Fenn, and 0. L. Haller, AIChEJ., 20, 735 (1974). (17) G.R. Hennig, Proc. Carbon Conf., 5th, 1, 143 (1962). (18) E. J. Evans, R. J. M. Griffiiths, and J. M. Thomas, Science, 171, 174
(1971). (19) L. S. Darken and E. T. Turkdogan in "Heterogeneous Kinetics at Elevated Temperatures", G. R. Beiton and W. L. Warreli, Ed., Plenum Press, New York, 1970,p 25. (20) R. Aris, J. Catal., 19, 282 (1971). Depafiment of Chemical Englneering State University of New York at Buffalo Amherst, New York 14260
Ralph T. llang' Chor Wong
Received August 13, 1979; Revised Manuscript Received January 16, 1980
Effect of Deviations from the Lorentz Rule for the1 Additivity of Molecular Sizes on the Surface Tensions of Simple Liquid Mixtures Using a Monolayer Model
Sir: In a previous test' of a monolayer model for the surface tensions of simple liquid mixtures Dickinsonl and McLure obtained reasonably good agreement between prediction and experiment when for each mixture the constant 5 = c l z / ( c l l ~ z z ) l ~ z ,expressing the deviation of the energy cross-term parameter from the Berthelot or geometric-mean combining rule, was derived from fitting the experimental excess Gibbs free energy, using a treatment based on a van der Waals one-fluid model, and the constant p = 2 g l z / ( ~ l l+ azz)- 1, expressing the deviation of 0 1980 American Chemical Society
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J. Phys. Chem. 1980, 84, 680-681
(3) J. S.Rowlinson, "Liquids and Liquid Mixtures", 2d ed, Butterworth, London, 1969. (4) R. Defay, I. Prigoine, A. Bellemans, and D. H. Everett, "Surface Tension and Adsorption", Longmans, London, 1966. (5) F. B. Sprow and J. M. Prausnitz, Trans. Faraday Soc., 82, 1105 (1966). Department of Chemistry The University Sheffield S3 7HF, United Kingdom Centro de Quimica Estrutural Instituto Superior Tecnico Avenida Robisco Pais 1000 Lisbon, Portugal 0
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Ian A. McLure*
Vlrglllo A. M. Soares
Received October 25. 1979
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Publication costs assisted by the US.Department of Energy
Flgure 1. Excess static surface tensions 7,: as a function of mole fraction x , for (i)argon (1) 4- methane (2) at 90.7 K, (ii) carbon monoxide (1) methane (2) at 90.7 K, (iii) nitrogen (1) methane (2) at 90.7 K, and (iv) nitrogen (1) argon (2) at 83.8 K;the upper full line gives the excess static surface tension from the van der Waals model setting p = 0 and the lower full line the excess surface tension from the same model but with both $. and p taking the values which fit the bulk properties, for N2 Ar the two lines are indistinguishable: (0)experiment (ref 5).
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the size cross-term parameter from the Lorentz or arithmetic-mean combining rule, was set equal to zero. We now report the effect on the surface tension predicted by the same monolayer model of assigning to 4 and p the simultaneous values found by Soares, Nieto de Castro, and Calado to give the best account of all the bulk properties, and particularly the excess volume, of the same mixtures by again using a van der Waals one-fluid modeL2 The results of the present and the previous calculations in terms of the excess static surface tension yap= Tat- xlyl - x2yzare shown in Figure 1. The values of [ found by Soares, Nieto de Castro, and Calado are slightly different from those used by Dickinson and McLure3 and they lead to very small changes in the predicted ystEfor p = 0 in the direction of improved prediction. For Nz Ar at 83.8 K the former [ leads to agreement which is complete with p = 0 and which is unaltered by the introduction of the p which improves the fit of the excess volume. For the remaining mixtures, Ar CH4, CO + CH4, and Nz CHI, all at 90.7 K, y,? previously predicted to be less negative than the measured value moves into closer accord when the deviation from the Lorentz rule is included in the calculation. For all four mixtures the incorporation of the fitted [ and p leads to better reproduction of the skewness of the ye: vs. x isotherm. None of the foregoing affects the earlier conclusions regarding the general applicability of the first-order monolayer model of Prigogine and Defay4 for predicting yapfor simple mixtures. However, our results demonstrate that the success of a theory for surface tensions, just as for excess volumes, cannot be fairly assessed unless deviations from both the Berthelot and the Lorentz combining rules for the cross-term parameters are taken into account.
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Formation of Vinylidenecarbene Intermediates in Multlple Infrared Photon Elimlnatlon Reactions
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References and Notes (1) E. Dickinson and I. A. McLure, J. Phys. Chem., 80, 1880 (1976). (2) V. A. M. Soares, C. A. Nieto de Castro, and J. C. G. Calado, Rev. Port. Quim., 14, 117 (1972).
0022-3654/80/2084-0680$0 1.OO/O
Sir: Multiple infrared photon excitation (MIRPE) of a-chloro olefins (RzC=CHC1) by intense C02laser pulses has been found to lead to elimination of HCl.1-3 Deuterium labeling studies2 have shown that the reaction proceeds mainly via a 3-center elimination. This result suggests that vinylidenecarbene (RzC=C:) may be formed during the dehydrohalogenation. Such species are well-known in s ~ l u t i o nhowever, ;~ the only other gas-phase reaction in which they are formed appears to be mercuryphotosensitized 1,l elimination^.^^^ Carbenes, such as :CF2, have often been observed in laser-induced multiple-photon dissociation.6 In the MIRPE of vinyl chloride (R = H, D), acetylene is the sole hydrocarbon product, suggesting that rearrangement of the carbene is extremely rapid, if not concerted with the elimination. This behavior is consistent with expectation^^,^ that the barrier to the rearrangement HZC=C: --* H C r C H (1) is extremely low. We have extended our previous work2 on these systems to substituted vinyl chlorides (R = CH3, F) in order to see whether the rearrangement could be slowed down sufficiently to permit the vinylidenecarbene to exist as a long-lived intermediate. 1-Chloro-2-methylpropene (Aldrich) and 2-chloro-1,ldifluorethylene (PCR) were used as received except for transfer under reduced pressure to the reaction cell. Infrared spectra prior to MIRPE showed no major impurities to be present. The compounds were photolyzed with the 9.6-km P(16) or P(18) and 10.6-pm R(18) COSlaser lines, respectively, either alone at pressures of 4-5 torr or in the presence of added gases. The gaseous product mixtures were collected and analyzed by GC/MS (H/P 5990 A or Hitachi RMU-61). The MIRPE of (CH,),C=CHCl leads to HC1 (observed in the product infrared spectrum) and butadiene as major products, with smaller amounts of allene, 2-butyne, and diacetylene. Photolysis in the presence of CH,OH, HzO, NH,, H2S, or D2S vapor yielded no additional products. These results suggest that the (CH&$=C: formed by loss of HC1 rearranges extremely rapidly, either by methyl migration across the double bond (eq 2) or by intramolecular insertion (eq 3). Since the acetylenic form is -30-40 kcal/mol more stable than the carbene? the resulting 2-butyne, if formed, would contain a large amount of excess vibrational energy. Some of this could be stabilized by collisional relaxation, 0 1980 American Chemical Society
