Ch As i n the review of last year (90A) the literature on chemical rate processes is surveyed i n four major topics. Each of these topics is reviewed by a member of the faculty of Princeton University. Rate process principles and homogeneous reactions in the gas phase form the first subject. A review of recent developments in heterogeneous catalysis follows. The topic i n the third section is transport properties of gases rend liquid and the final section deals with transport properties i n the solid state as represented i n diffusion and oxidation processes of metals. The period of the reviews is the calendar year 1953, with the cxception of references i n certain foreign periodicals that are available only with considerable delay. An attempt is made to provide continuity with the previous review.
R. H. WILHELM Princeton University, Princeton, N. J.
HIS review includes books and papers concerning mechanisms of chemical reactions and the form of rate equations, complex reactions, and selected examples of gas phase reactions. Bocks. A review and summary of chemical reaction kinetics as an investigational tool has been presented in an extensive volume. Individual chapters are written by authorities in their fields, the editors being Friess and Weissberger (2364). Sections include topics on rate theory, experimental techniques and interpretation of rate data, homogeneous gas reactions, reactions in the liquid phase, homogeneous catalysis, polymerization reactions, biological reactions, and rapid reactions. A group of symposium papers has been published by the American Institute of Chemical Engineers with Van Antwerpen (14.4) as editor. Topics iiiclude heat and mass transfer in chemical reactors and detailed kinetic studies, many in flow systems. Included arc: dehydration of 1-butanol, methane from carbon monoxide and hj-drogen, ethyl acetate formation on cation exchange resin, alcoholyyis and diffusion, hydration of ethylene oxide, and oxidation of nitric oxide on silica gel and on activated carbon, and the condensation of formaldehyde with sodium-paraphenol-sulfonate. The proceedings of the Fourth Symposium on Combustion and Detonation Waves have been published ( H A ) . More than one hundred papers are included in the volume. A feature is a series of nine survey papers in major areas of flame science. A treatise on flames, t,heir structure, radiation and temperature by Gaydon (d7A) has been published. A memorial volume dedicated to L. Farkas (??la)contains among otheri., some fourteen contributed papers on chemical kinetic topics by active workers throughout the world. Topics include fast reactions, elementary reactions, heterogeneous catalysis, free radical reactions, and mechanisms of a number of reactions. Reaction Rate Theory. I n the third paper of a series, Smith and Eyring (76A) discuss the effect on relative reaction rates in simple aliphatic molecules of charge shifts due to induction. Previously calculated charges (76A) on molecules that are subEtituted by an electronegative substituent are shown to be direct'ly related to several stabilization energies. Papers in the series provide quantitative rate expressions for reactions of organic compounds starting with charge distributions on t,he molecules as points of intermediate knowledge in contrast to the more formidable absolute rate calculations approach. Ak detailed formulation of kinetic processes in unimolecular and 880
bimolecular reactions is presented by Benson and Axworthy ( 6 8 , 7 A ) . The activation process, the nature of intermediak reaction complexes, and the assumption of equilibrium in regard to the concentration of these critically energized species are analyzed in detail. The thcory of unimolecular gas reactions is extended by Slater (74-4) to det'erniine the decrease in reaction rate due to lower pressures and degenerah vibrations. The gas molecule is pict'ured as an array of point-atoms vibrating about equilibrium positions with their interatomic and angular separations described by a set of internal coordinates that vary according to the characteristic modes of vibration. If a particular coordinate attains a critically high value, dissociation occurs. A formula is derived which expresses the general dissociation rate. As an example, Slater (73A) calcul~testhe theoretical rate of isomerization of cyclopropane to propylene. Isomerization is assumed t o occur when the vibrations carry any hydrogen at,om too near a carbon of another methylene group. The frequency factor found for the high pressure rate is comparable to the experimental value. The general theory of unimolecular reactions is reexamined by Kassel (48A)to determine what type of information about rate constants for specific activated states may be determined from experimental reaction rate-pressure curves. Possibilities in this respect are limited. Bauer and Wu (QA) present a quantum-mechanical analysis of a reaction Hs X = I-IX $. H There X is chloririe or bromine. The probability factora are calculated numerically. The temperahre independent factor in the relative rates of isotopic three-center reactions is shorn by Bigeleisen and Wolfsberg ( 8 A )to be essentially independent of whether the barrier crossing is treated as a translation or vibration. Calculations are presented for several cases involving the isotopes of carbon where there is a simultaneous bond rupture and bond formation. Thermodynamics of irreversible processes, transport processes in chemically reacting systems, and related eubjects have received considerable attention during the year. Kirkwood and Crawford (6OA) formulate, on the basis of partial local thermodynamic equilibrium, the equations of continuity, motion, and of energy and entropy transport in niulticomponent chemically reacting fluid mixtures. A combination of relations between viscous stresses! heat current, diffusion currents, rate of strain, temperature, and chemical potential gradients with equations of transport leads t o a system of partial differential equations that determines
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FUNDAMENTALS REVIEW the velocity field and the local thermodynamic state of the fluid in terms of initial and boundary conditions. Chemical reactions are treated in terms of a relaxation-time spectrum that characterizes the lag behind equilibrium. Franck ( M A ) and Meixner (69.4) likewise consider heat transmission in chemically reacting gases with the aid of the thermodynamics of irreversible processes. Serruys j 7 I A ) compares the g;ts flow profile in a tube subject t o hest transfer or chemical reaction and the profile in a gas of constant composition expanded isentropically. Shtandel (7WA) discusses reactions, as in flames, subject to heat and mass transfer in which equilibrium among internal and external degrees of freedom is not established. Freedman ( % A ) derives an equation for the use of ultrasonic absorption to measure the gross reaction rate a t equilibrium for very rapid reactions in the liquid phase for which thermodynamic data are available. Perturbations from equilibrium by sound waves were investigated by Damkohler ( I 7 A )in his study of rapid reactions in gases. The present paper includes an interesting statement that ordinary flow methods for studying very rapid reactions in solutions may not be useful for halflives of less than about 10-4 seconds, because diffusion becomes the rate controlling step rather than the reaction. Complex Reactions. Reactions systems may be complex because of multiple chemical steps or because of the manner in which the reactions are carried out-for example, in continuous or staged operations-by steady state or nonsteady state techniques. Papers in both areas were published during the year. Complex sequential reactions are analyzed by Szabo (81A). Very complicated systems of differential equations result when all the elementary steps of a complex reaction are t o be taken into account and treated with equal importance. The author divides individual reactions within a complex reaction into four classes; starting, propagating, branching, and rupturing. Simplification results through the assumption that one of these classes of reaction is rate controlling. The two differential equations that remain as a result of the simplification express the conversion of the initial substance and of the rate of change of the concentrations of quasi-steady state intermediates. Numerical integration is necessary for solution in most cases. Huhn (%A) compares the above treatment of complex rate equations by Saabo with that of Semenov; the former is a modification of the latter. Lautout, Wyllie, and Magat ( 6 S A ) examine the conditions under which quasi-steady state intermediates will and will not be formed in a complex three-step system of reactions: A B + C, B C = E, C C +. F. Higgins and Williams (S5A) have derived equations for the ratio of rate constants of two consecutive, irreversible second-order reactions between a symmetrkal bifunctional molecule and a unifunctional molecule. They (34.4)now extend the analysis to cases in which the reicting positions in the bifunctional group are not equivalent. A coupling reaction between histadine and p-diazoaminobenzenesulfonic acid is used to verify one special case among the possible solutions. General conditions for kinetics in a system of simultaneous reactions are derived by Halla ( H A ) . Differential equations for chemical kinetics with simultaneous linear gas absorption were solved with a digital computer by Perry and Pigford (6‘4A) for cases involving second-order chemical kinetics. Chemical reactions that vary periodically in time have assumed increasing interest among kineticists since Lotka (66A) in 1920 suggested that oscillatory reactions may occur in chemical as well as in biological systems. Lotka first considered the mathematical development in connection with the theory for the struggle for existence between two kinds of animals that devour each other. The most immediate application in chemistry has been in the theory of flames ( % $ A ) .Karsulin (47A) now reviews and discusses autoperiodic chemical reactions that involve periodic alterations of the electrochemical potential. Hearon (SWA) provides 8 critical analysis for reactions governed by a set of coupled first-order reactions. He concludes that periodic reactions cannot occur in a closed system described by linear rate
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May 1954
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equations. The treatment is extended to open systems with the result that if the matrix of diffusion coefficients is diagonal, periodicities cannot occur. Processes of mixing and fluid velocity distributions both affect the distribution of reaction times in chemical reactions. Danckwerts (19A)contributes to the subject by publishing a mathematical analysis of residence time distributions of material flowing through various kinds of systems. Panchenkov ( 6 S A )discusses formulation of equations for reaction in a tubular reactor assuming plug flow. He is particularly concerned with the form of the chemical rate equation t o be used in constant pressure operation. Kodama, Fukui, and Mazume (62A)derive general relationships for space velocity-space time yield curves in an isothermal reactor in which neither consecutive nor side reactions occur. Adiabatic reactors also are analyzed. The equations are useful in determining optimum reaction conditions. The procedure of reacting in a steady state cascade is reviewed by Weber (88A)who suggests a method for calculating chemical conversion in such a system. Chemical reaction in a tubular reactor considering a mean fluid velocity and mean axial diffusivity is discussed by Yagi and Miyauchi (92A). Activation of Reactions. Methods for activation of chemical reactions by means other than common ones, such as heat and light, continue to attract interest. Reported are investigations on molecular rays, shock wave technique, and the use of ultrasonic energy. Martin and Meyer (67A) describe in detail the use of molecular rays to excite reaction. Molecular rays of iodine and of trichlotrifluorethane are used to bombard and dissociate chlorine dioxide. The shock tube is used by Carrington and Davidson ( 1SA) to measure dissociation of nitrogen tetroxide (N204). The rate of reaction was studied photoelectrically through change in light absorption. Theory regarding activation of certain chemical reactions by ultrasonic energy generally is in terms of a cavitation mechanism in liquids. No major advances in this regard appeared this year, but several new reactions have been studied. Prudhomme, Picard, and Busnel (69A) and Busnel and Picard (11A)re-examined previous measurement on the oxidation of potassium iodide, particularly in regard to small differences in experimental arrangement and their effects on the reaction. Consittency of experimental results also is the topic of a paper b y Dognon and Simonot (ZOA). Rust (7OA) provides a review of the field. Lindstrom and Lamm (56A)polymerized acrylonitrile by ultrasonic waves and ascribed the results t o an initial dissociation of water to form hydrogen and hydroxyl radicals that then cause the chemical effects. The inhibition of ultrasonic cavitation by high molecular weight compounds was studied in oxidation studies by Virtanen and Ellfolk (87A). Homologous series of aliphatic acids, aldehydes, alcohols, hydrocarbons, and amines were added in small concentration. The inhibition of reaction appears to parallel decrease in surface tension of the solution which suggest to the authors energy changes in cavitation. Myagawa, Koshino, and Inoue (6OA) found gas forming reactions to be accelerated by ultrasonic waves. Examples are sodium nitrate and sodium d f a t e with acetic acid. Free Radicals. (‘Within the last five years there has been a sharp shift in emphasis, with attention being focused on the rates of free radical reactions themselves, rather than on over-all reactions with the elementary steps regarded as merely incidental stages,” to quote from the introductory remarks of E. W. R. Steacie in the Discussions of the Faraday Society on the “The Reactivity of Free RadicJs” which was published during the year. This series of papers is required reading for all who are interested in reactions involving free radicals. Some 23 papers are presented on subjects ranging from the production of free radicals, their measurement as well as the mechanisms of various more or less elementary reactions. The papers in the Discussion will not be mentioned individually in this review. TrotmanDickenson (86A) review the reactions of methyl radicals and Ivin, Wijnen, and Steacie ( @ A ) review those of ethyl radicals.
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ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT Whittle and Steacie (89A) measure the rates of methyl and deuteromethyl radicals from acetone with hydrogen isotopes. T h e rate of recombination of methyl radicals prepared from dimethylmercury is measured by Ingold and Lossing (42A); analysis of products is performed with a mass spectrometer. Porter and Benson ( 6 6 A )report on the reaction of methyl radicals with carbon monoxide. The oxidation of methyl and acetyl radicals from photolysis of acetone is investigated by Hentz ( S S A ) . Hoare (37A) also explores the photochemical reactions of acetone b u t considers the experimental system, acetone, formaldehyde, and oxygen in three two-component mixtures. Trick and Winkler (84A)subject propylene to reaction with active nitrogen. Avramenko and Lorentso ( S A ) react formaldehyde and acetaldehyde TTith atomic oxygen. Mechanisms are proposed in each instance t o account for the distribution of products obtained. Kistiakowsky and Sternberg (51A) in a kinetic investigation of the photobromination of ethylene a t different wave lengths of light interpret the results to mean that the photochemically effective transitions of the bromine molecules in radiation of wave lengths longer than the convergence limit, 5170 A., lead to the continuum of the 3~ 11 state, which then dissociates in one elementary act t o form two normal atoms. The kinetics of the photooxidation of benzaldehyde are reported by Ingles and hlelville ( S Q A ) . The rate was found t o be proportional to the first power of the concentration of the aldehyde and the square root of the intensity of absorbed light. The rate is independent of oxygen pressure. The dehydrogenation of the aldehyde by the peroxy radical is the rate determining step in propagation. The termination step involves the interaction of two peroxy radicals. Benson (6A) explores in a theoretical paper the conditions that must be imposed upon the various specific rate constants involved in the steps of a chain reaction in order to fulfill the requirements of a stationary state and the chain induction period also is described quantitatively. Szabo (80.4) proposes that radicals having odd numbers of electrons may combine with other paramagnetic substances, notably oxygen to give relatively stable intermediate radicals. Decomposition Reactions. The class of unimolecular decomposition reactions and the mechanisms associated with them continue as investigational topics of high interest. Pritchard, Sowden, and Trotman-Dickenson (67A, 68A) address themselves t o the problem of energy transfer in the decomposition of cyclobutane a t low pressures, compared t o the isomerization of cyclopropane, as the transfer is affected by the presence of some ten inert gases. Stepukhovich and Finlcel (78A, 7QA) interpret the decomposition of ethane in the presence of propylene in terms of the Rice-Herzfeld chain mechanism. Genaux, Kern, and Walters ( 6 8 A ) report on the homogeneous thermal decomposition of cyclopropane from 420 t o 468' C. and initial pressures from 1t o 996 mm. The first-order rate constant decreases below 100 mm. but is essentially constant above this pressure. As in the studies of Pritchard et al. with cyclobutane, the addition of certain inert gases also raises the rate constant. A mass spectrometer was used by Ingold and Lossing ( 4 0 A ) t o determine free radicals formed in thermal decompositions of aromatic compounds. Detailed discussion is given of the many intermediate and final products found. The kinetics of exchange reactions involving diborane and deuterium are studied by Maybury and Koski (58A). A mechanism including the borine radical, deuterium, and the wall is proposed. The decomposition of alkyl bromides is studied by two groups of investigators. Blades and Murphy ( 9 A ) conclude that decompositions of ethyl, isopropyl, and propyl bromides proceed through an intramolecular process. A single step decomposition is assured in the alkyl bromide experiments of Green, Harden, Maccoll, and Thomas (3OA) through the addition of cyclohexene t o inhibit chain mechanism. The C-Br bond strength is the major factor in determining the rate of decomposition. Nitromethane is decomposed thermally by Hillenbrand and Kilpatriclr (%A ) ; the
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rate is partly determined by an intramolecular re-arrangement. The influence of nitric oxide on the thermal decomposition of ethyl nitrate is ascribed by Pollard, ilIarshal1, and Pedler (66A) as due to a direct reaction between these two compounds. Decomposition studies of nitric acid and various oxides of nitrogen form an interesting class of thermal reactions. The decomposition of nitric acid vapor is followed by Johnston, Foering, and Thompson (&A) by optical means recording nitric acid and nitric oxide content against time. A variety of addition agents are tested, and the reaction is considered more complex and the rate faster than previously proposed. A mechanism involving hydroxyl radicals is suggested. Divergences in experimental effects of oxygen on the thermal decomposition of nitric oxide are discussed by Kaufman and Kelso (4QA)and by Wise and Frech (91A). -4general form of the Lindemann theory of unimolecular reactions is analyzed by Johnston (45A)with respect to properties in the high concentration region, and the results are compared with similar deductions found in the low concentration region. The methods are applied to nitrogen pentoxide and nitrous oxide. The same author (44A) also reports on the effect of foreign gases-such as argon, nitrogen, carbon dioxide, and sulfur hexafluoride in low pressure decompositions of nitrogen pentoxide in the presence of nitric oxide. By the Lindemann mechanism for unimolecular reactions, the data are shown to give secondorder rate constants for each reactant and for each foreign gas. Experiments and mechanism interpretation for nitrogen pentoxide-nitric oxide (NaOj-NO) also are reported by Cowan, Rotenberg, Downie, Crawford, and Ogg (16d). Ashmore and Chanmugam (S14)explain by a nonbranching reaction scheme the complex reactions between hydrogen and chlorine in the presence of nitric oxide and nitrosyl chloride. Perrine and Johnston ( 6 3 A ) study the kinetics of the fast reaction between nitrogen dioxide and find an empirical second-order rate constant. In two companion papers Spall, Stubbs, and Hinshelwood (77A) and Danby, Spall, Stubbs, and Hinshelwood (18A) study the effect of nitric oxide on the reaction system ethane-ethylenehydrogen. Nitric oxide serves to suppress chain reactions, and the reaction was studied under conditione that allowPd chain formation and also conditions that Ruppressed them. Mechanism for the formation of methane in the system are discussed. I n view of the complex effects of various gases on the chain reaction the activation energies calculated from initial rates of the uninhibited reactions are of little theoretical interest. Oxidation Reactions. In this section are included paperq on slow oxidation reactions: flame and detonation studies are omitted. Cottrell and Graham ( l b A ) and Toyositburo (83A) measured the kinetics of the oxidation of ethylene by nitrogen dioxide. Complex distributions of products are found for the formation of which intermediate mechanisms are postulated. The reactions of olefine, including ethylene, propylene, pentene, hexene, heptene, decene, and octene, with ozone are published by Cadle and Schadt ( 1 2 8 ) . Lleasuiements were over a pressure range of 1 to 4500 microatmospheres and a temperature range of 8" to 50" C. The over-all reactions were found to be complicated; the characteristics of the initial rates were determined. In the slow hydrogen-oxygen reaction, Levy (544) found the interesting result that the effects of water vapor and of methane as additives are directly related to one another. On the basis of these slow reaction results and also because of the effect of these additives on the second explosion limit the author postulates that methane and water vapor influence the kinetics of the hydrogen-oxygen reaction by similar processes. Gray (RQA ) reports the oxidation of ethane a t atmospheric pressure in a flow system with varying reactant compositions, vessel sizes and materials, and flow rates, A narrow region of periodic flames are found and mechanisms to explain the periodicity are suggested. Propylene is oxidized by lLIulcahy and Ridge (61A) and both ethylene and propylene by Burgoyne and Cox (10A) The former authors give an equation for the induction period as a function of the
INDUSTRIAL AND ENGINEERING CHEMISTRY
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FUNDAMENTALS REVIEW concentration of inert gas, of interdiffusion coefficients of an active particle in the propylene and in the inert gas. The latter authors find a negative temperature coefficient in a borosilicate glass tube at and above atmospheric pressure, whereas the negative coefficient does not exist in a steel reaction vessel. The oxidation of butane a t low oxygen concentrations was studied by Appleby, Avery, Meerbott, and Sartor ( I A ) . The variables were composition of reactant mixture, reaction time, vessel material, static, and flow conditions. Under very low oxygen concentrations, the oxygen acts primarily as a dehydrogenating agent. Oxygen also has a large accelerating effect on the thermal cracking of butane. Cyanogen-air mixtures with long induction periods are measured by James and Laffitte (&SA). Special emphasis is placed on a quantitative expression for the time delay. The reaction of mixtures of ammonia and oxygen is studied by Verwimp and van Tiggelen (86A ).
References R a t e Theory and Homogeneous Reactions
Appleby, W.G., Avery, W.H., Meerbott, W. K., and Sartor, A. F., J . Am. Chem. Soc., 75, 1809-14 (1953). Ashmore, P. G., and Chanmugam, J., Trans. Faraday Soc., 49, 254-65 (1953). Avramenko, L. I., and Lorentso, R. V., Zhur. Fiz. Khim., 26, 1084-9 (1952). Bauer, E., and Wu, Ta-You, J . Chem. Phys., 21,72633 (1953). Benson, S. W., Ibid., 20, 1605-12 (1952). Benson, S. W., and Axworthy, A. E., Jr., J . Chem. Phys., 21, 428-33 (1953). Ibid., 20, 1064 (1952). Bigeleisen, J., and Wolfsberg, M., Ibid., 21, 1972 (1953). Blades, A. T., and Murphy, G. W., J . Am. Chem. Soc., 74, 6219-21 (1952). Burgoyne, H., and Cox, R. A, J . Chem. Soc., 1953, 876-83. Busnel. R. G., and Picard, D., J . chim.p h y s . , 50, 102-6 (1953). Cadle, R. D., Schadt, C., J . Am. Chem. Soc., 74, 6002-4 (1952). Carrington, T., and Daxidson, N., J . Phys. Chem., 57, 418-27 (1953). Chem. Eng. Progr. Symposium Ser. No. 4 (1952). Cottrell, T. L., and Graham, T. E., J. Chem. Soc., 1953, 55663. Cowan, G. R , Rotenberg, D., Downie, A., Crawford, B. L., Jr., and Ogg, R. A., Jr., J . Chem. Phys., 21, 1397-8 (1953). Damkohler, G., 2. Elektrochem., 48, 62, 116 (1942). Danby, C. J., Spall, B. C., Stubbs, F. J., and Hinshelwood, C. N., Proc. Roy. Soc. (London),A218,450-64 (1953). Danckwerts, P. V., Chem. Eng. Sei., 2, 1-13 (1953), Dognon, A., and Simonot, Y., J . chim.phys., 5 0 , 9 4 4 (1953). Farkas, L., Memorial Volume, Research Council of Israel, Jerusalem, Special Publication No. 1, 1952. “Fourth Symposium on Combustion and Detonation Waves,” Baltimore, Williams and Wdkins Co., 1953. Franck, E. U., 2, physik. Chem., 201, 16-31 (1952). Frank-Kamenestski, D. A,, Zhur. fiz. Khim., 14,30 (1940). Freedman, E., J. Chem. Phys., 21,1784 (1953). Friess, S. L., and Weissberger, A., eds., Investigation and Rates and Mechanisms of Reactions, Technique of Organic Chemistry,” Vol. 8, New York, Interscience Publishers, 1953. Gaydon, A. G., “Flames: Their Structure, Radiation, and Temperature,” London, Chapman-Hall, 1953. Genaux, C. T., Kern, F., and Walters, W. D., J . Am. Chem. Soc., 75, 6196 (1953). Gray, J. A., J . Chem. Soc., 1953, 741-50. Green, J. H. S., Harden, G. D., Maccoll, A., and Thomas, P. J., J . Chem. Phys., 21, 178 (1953). Halla, F., J. Phys. Chem., 57, 599-600 (1953). Hearon, J. Z., Bull. Math. Biophys., 15, 121 (1953). Hentz, R. R., J . Am. Chem. See., 75,5810 (1953). Higgins, H. G., and Williams, E. J., Australian J . Chem., 6, 195-206 (1953). Higgins, H. G., and Williams, E. J., Australian J . Sci. Research, 5A, 572-6 (1952). Hillenbrand, L. J., Jr., and Kilpatrick, Mary L., J. Chem. Phys., 21, 525-36 (1953). Hoare, D. E., Trans. Faraday Soc., 49, 1292 (1953). Huhn, P., Magyar Kdm. Folydirat, 58, 380-4 (1952).
May 1954
(39A) Ingles, T. A., and Melville, H. W., Proc. Roy. SOC. (London), A218, 175-89 (195.3). (40A) Ingold, K. U., and Lossing, F. P., Can. J . Chem., 31, 30-41 (1953). (41A) Ingold, K. U., and LoBsing, F. P., J. Chem. Phys., 21, 368 (1953). (42A) Ivin, K. J., et al., J . Phys. Chem., 56, 967-72 (1952). (43A) James, H., and Laffitte, P., Compt. rend., 236, 1038-41 (1953). (44A) Johnston, H. S., J . Am. Chem. Soc., 75, 1567-70 (1953). (45A) Johnston, H. S., J . Chem. Phys., 20, 1103-7 (1952). (468) Johnston, H. S., Foering, Louise, and Thompson, R. J., J . Phys. Chem., 57,390-5 (1953). (478) Karsulin, Mircslav, Bull. soc. chim. Belgrade, No. Jubilaire 1897-1947, 113-35 (Pub. 1951) (English summary). (48A) Kassel, L. S., J . Chem. Phys., 21,1093-7 (1953). (498) Kaufman, F., and Kelso, J. R., Ibid., 21,751 (1953). (508) Kirkwood, J. G., and Crawford, B., Jr., J . Phys. Chem., 56, 1048-51 (1952). (51A) Kistiakowsky, G. B., and Sternberg, J. C., J . Chem. Phys., 21, 2218 (1953). (52A) Kodama, S., Fukui, K., and Mazume, A,, ~ N D .ENG.CHEM., 45, 1644-8 (1953). (53A) Lautout, Marguerite, Wyllie, G., and Magat, M., J . chim. phys., 50,199-208 (1953). (54.4) Levy, A,, J . Chem. Phys., 21,2132 (1953). (55A) Lindstrom, O., and Lamm, O., J . Phys. & Colloid Chem.. 55, 1139-46 (1951). (56A) Lotka, A. J., J . Am. Chem. Soc., 42, 1595 (1920). (578) Martin, H., and Meyer, H. J., 2. Elektrochem., 56, 740-2 (1952). (58A) Maybury, P. C., and Koski. W.S., J . Chem. Phys., 21, 742-7 (1953). (59A) bleixner, J., 2. Naturforsch.,7a, 553-9 (1952). (60A) Miyagawa, I., Koshino, M., and Inoue, K., Research Repls. Fac. Engr. Nagoya Univ., 3 , 3 1 4 (1950). (61A) Mulcahy, M. F., and Ridge, M. J., Trans. Faraday SFC.,49, 1297 (1953). (628) Panchenkov, G. M., Zhur. Fiz. Khim., 26,454-60 (1952). (638) Perrine. R. L., and Johnston, H. S., Univ. iMicrofiZms, Univ. Michigan, Ann Arbor, Pub. No. 5811 (1953). (648) Perry, R. H., and Pigford, R. L., IND. ENG.CHEM.,45, 1247-53 (1953). ( 6 5 4 Pollard, F. H., Marshall, H. S. B., and Pedler, A. E., hTature, 1’71, 1154-5 (1953). ( 6 6 4 Porter, G. B., and Benson, S. W., J. Am. Chem. Soc., 75, 2773 (1953). (67A) Pritchard, H. O., Sowden, R. G., and Trotman-Dickenson, A. F., Proc. Roy. Soc. (London),A217,563-71 (1953). ( 6 8 4 Ibici., A218, 41621 (1953). (69.4) Prudhomme, R. O., Picard, D., and Busnel, R. G., J . chim. phys., 56, 107 (1953). (70A) Rust, H. H., Angew. Chem., 65,249-52 (1953). (71A) Serruys, M., Compt. rend., 236, 1341-3 (1953). (72A) Shtandel, A. E., Zhur. Fiz. Khim., 26, 933-41 (1952). (73A) Slater, N. B., Proc. Roy. SOC.(London),A218, 224-44 (1953). (74A) Slater, N. E.,Trans. Roy. Soc. (London),A246, 57-80 (1953). (75A) Smith, R. P., and Eyring, H., J . Am. Chem. Soc., 75, 5183 (1953). (76A) Smith, R. P., Ree, T., Magee, J. L., and Eyring, H., Ibid., 73, 2263 (1951). (77.4) Spall, B. C., Stubbs, Ii’. J., and Hinshelwood, C. N., Proc, Roy. Sac. (London),A218, 439-49 (1953). (78ii) Stepukhovich, A. D., and Finkel, A. G., Zhur. Fiz. Khim., 26, 1413-18 (1952). (79A) Ibid., pp. 1419-24. (80-4) Szabo, Z. G., Acta Chim. Acad. Sei. Hung., 3, 139-66 (1953) (in English). (81A) Szabo, Z. G., Huhn, P., and Bergh, A., Magyar K6m. Folydirat, 58, 370-9 (1952). (82-4) Takeuchi, T., Sholcubai No. 7, 47-51 (1951). (83A) Toyosaburo, T., Ibid., No. 7, 47-51 (1951). (84.4) Trick, G. S., and Winkler, C. A., Can. J . Chem., 30, 915-21 (1952). (854) Trotman-Diokenson, -4.F., Quart. Reus. (London), 7, 198 (1953). (86A) Verwimp, J., and Tiggelen, A. van, Bull. soc. chim. Belgas, 62, 205-22 (1953). (87A) Virtanen, A. I., and Ellfolk, N., Acta Chem. Scand., 6, 660-6 (1952). (88A) Weber, A. P., Chem. Eng. Progr., 49,26-34 (1953). (89A) Whittle, E., and Steacie, E. W. R., J. Chem. Phys., 21, 993-9 (1953). (90A) Wilhelm, R. H., et al., IND.ENG.CHEM.,45, 894-911 (1953). (91A) Wise, H., and Frech, M. F., J . Chem. Phys., 21, 752 (1953). (92A) Yagi, S., and Miyauchi, T., Chem. Eng. (Japan), 17, 382-6 (1953).
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