摘要:

Contents 4259 4269 4277 4287 4295 431 1 4321 4335 Protonation Constant of Caffeine in Aqueous Solution M. Spiro, D. M. Grandoso and W. E. Price Ionic Equilibria in Acetonitrile Solutions of 2-, 3- and 4-Picoline N-oxide Perchlorates, studied by Potentiometry and Conductometry L. Chmurzynski, A. Wawrzyn6w and Z. Pawlak Liquid-phase Adsorption of Binary Ethanol-Water Mixtures on NaZSM-5 Zeolites with Different Silicon/Aluminium Ratios W-D. Einicke, M. Heuchel, M. v.Szombathely, P. Brauer, R. Schollner and 0. Rademacher Influence of Oxidation/Reduction Pretreatment on Hydrogen Adsorption on Rh/TiO, Catalysts. An lH Nuclear Magnetic Resonance Study J. P. Belzunegui, J. M. Rojo and J. Sanz Volumetric Properties of Mixtures of Simple Molecular Fluids A. C. Colin, E. G. Lezcano, A.Compostizo, R. G. Rubio and M. D. Peiia Study of Ultramicroporous Carbons by High-pressure Sorption. Part 4.-Iso- thems and Kinetic Transport in Activated Carbons J. E. Koresh, T. H. Kim, D. R. B. Walker and W. J. Koros Kinetic and Equilibrium Studies associated with the Solubilisation of n- Pentanol in Micellar Surfactants G. Kelly, N. Takisawa, D. M. Bloor, D. G. Hall and E. Wyn-Jones The effect of Carboxylic Acids on the Dissolution of Calcite in Aqueous Solution. Part 1 .-Maleic and Fumaric Acids R. G. Compton, K. L. Pritchard, P. R. Unwin, G. Grigg, P. Silvester, M. Lees and W. A. House 130-2Contents 4259 4269 4277 4287 4295 431 1 4321 4335 Protonation Constant of Caffeine in Aqueous Solution M. Spiro, D. M. Grandoso and W. E. Price Ionic Equilibria in Acetonitrile Solutions of 2-, 3- and 4-Picoline N-oxide Perchlorates, studied by Potentiometry and Conductometry L.Chmurzynski, A. Wawrzyn6w and Z. Pawlak Liquid-phase Adsorption of Binary Ethanol-Water Mixtures on NaZSM-5 Zeolites with Different Silicon/Aluminium Ratios W-D. Einicke, M. Heuchel, M. v.Szombathely, P. Brauer, R. Schollner and 0. Rademacher Influence of Oxidation/Reduction Pretreatment on Hydrogen Adsorption on Rh/TiO, Catalysts. An lH Nuclear Magnetic Resonance Study J. P. Belzunegui, J. M. Rojo and J. Sanz Volumetric Properties of Mixtures of Simple Molecular Fluids A. C. Colin, E. G. Lezcano, A. Compostizo, R. G. Rubio and M. D. Peiia Study of Ultramicroporous Carbons by High-pressure Sorption. Part 4.-Iso- thems and Kinetic Transport in Activated Carbons J. E. Koresh, T. H. Kim, D. R. B. Walker and W. J. Koros Kinetic and Equilibrium Studies associated with the Solubilisation of n- Pentanol in Micellar Surfactants G. Kelly, N. Takisawa, D. M. Bloor, D. G. Hall and E. Wyn-Jones The effect of Carboxylic Acids on the Dissolution of Calcite in Aqueous Solution. Part 1 .-Maleic and Fumaric Acids R. G. Compton, K. L. Pritchard, P. R. Unwin, G. Grigg, P. Silvester, M. Lees and W. A. House 130-2

ISSN:0300-9599    

DOI:10.1039/F198985FX005

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY ASSOCIAZIONE ITALIANA DI CHIMICA FlSlCA DEUTSCHE BUNSEN-GESELLSCHAFT FUR PHYSIKALISCHE CHEMIE KONINKLIJKE NEDERLANDS CHEMISCHE VERElNlGlNG SOCIETE FRANGAISE DE CHIMIE, DIVISION DE CHlMlE PHYSIQUE FARADAY DIVISION GENERAL DISCUSSION No. 90 Colloidal Dispersions University of Bristol, 10-12 September 1990 Orga nising Com mitte e Professor R. H. Ottewill (Chairman) Professor P. Botherol Professor E. Ferroni Or J. W. Goodwin Professor H. Hoff mann Professor A.L. Smith Professor P. Stenius Dr Th. F. Tadros Professor A. Vrij Dr D. A. Young The joint meeting of the Societies will be directed towards examining current understanding of the behaviour of colloidal dispersions. In particular, stability and instability, short range interactions, dynamic effects, non-equilibrium interaction, concentrated dispersions and order-disorder phenomena will form topics for discussion.The preliminary programme is now availablemay be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM No. 26 Molecular Transport in Confined Regions and Membranes Oxford, 17-18 December 1990 Experimental, theoretical and simulation studies which address fundamental aspects of molecular transport will be discussed in the following main areas: a) Transport of atoms and molecules in pores, zeolite networks and other cavities; time-dependent statistical mechanics of small systems in confined geometries b) Molecular transport through synthetic membranes, biological membranes, smectic liquid crystalline phases and Langmuir Blodgett films; the dynamics of the molecules forming the membrane c) Diffusion, reorientation, conformational dynamics, viscosity and conductivity of polymer melts, to include papers dealing with bulk systems since the segments of the polymer will move in the anisotropic environment of the complete chain d) Applications of Brownian dynamics to the study of diffusion in porous media and across membranes including the transport of flexible aggregates such as microemulsions e ) The growth of crystals, colloidal aggregates and droplets on irregular surfaces and in pores Contributions for consideration by the Organising Committee are invited and abstracts of about 300 words should be sent by 31 December 1989 to: Dr D.J. Tildesley, Department of Chemistry, The University, Southampton SO9 SNH. Full papers for publication in the Symposium Volume will be required by August 1990.THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY ASSOCIAZIONE ITALIANA DI CHIMICA FlSlCA DEUTSCHE BUNSEN-GESELLSCHAFT FUR PHYSIKALISCHE CHEMIE KONINKLIJKE NEDERLANDS CHEMISCHE VERElNlGlNG SOCIETE FRANGAISE DE CHIMIE, DIVISION DE CHlMlE PHYSIQUE FARADAY DIVISION GENERAL DISCUSSION No. 90 Colloidal Dispersions University of Bristol, 10-12 September 1990 Orga nising Com mitte e Professor R. H. Ottewill (Chairman) Professor P. Botherol Professor E. Ferroni Or J. W. Goodwin Professor H. Hoff mann Professor A.L. Smith Professor P. Stenius Dr Th.F. Tadros Professor A. Vrij Dr D. A. Young The joint meeting of the Societies will be directed towards examining current understanding of the behaviour of colloidal dispersions. In particular, stability and instability, short range interactions, dynamic effects, non-equilibrium interaction, concentrated dispersions and order-disorder phenomena will form topics for discussion. The preliminary programme is now availablemay be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM No. 26 Molecular Transport in Confined Regions and Membranes Oxford, 17-18 December 1990 Experimental, theoretical and simulation studies which address fundamental aspects of molecular transport will be discussed in the following main areas: a) Transport of atoms and molecules in pores, zeolite networks and other cavities; time-dependent statistical mechanics of small systems in confined geometries b) Molecular transport through synthetic membranes, biological membranes, smectic liquid crystalline phases and Langmuir Blodgett films; the dynamics of the molecules forming the membrane c) Diffusion, reorientation, conformational dynamics, viscosity and conductivity of polymer melts, to include papers dealing with bulk systems since the segments of the polymer will move in the anisotropic environment of the complete chain d) Applications of Brownian dynamics to the study of diffusion in porous media and across membranes including the transport of flexible aggregates such as microemulsions e ) The growth of crystals, colloidal aggregates and droplets on irregular surfaces and in pores Contributions for consideration by the Organising Committee are invited and abstracts of about 300 words should be sent by 31 December 1989 to: Dr D.J. Tildesley, Department of Chemistry, The University, Southampton SO9 SNH. Full papers for publication in the Symposium Volume will be required by August 1990.

ISSN:0300-9599    

DOI:10.1039/F198985BX007

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

ISSN 0300-9599 JCFTAR 85(2) 175-477 (1 989) JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions I Physical Chemistry in Condensed Phases 175 187 199 207 223 237 25 1 269 279 293 305 317 33 1 343 349 363 CONTENTS An Aluminium-27 Nuclear Magnetic Resonance Study of Chemical Exchange between Different Polyatomic Species in Butylpyridinium Chloride-A1C1, Melts K. Ichikawa, T. Jin and T. Matsumoto Solvent Dependence of Kinetics and Equilibria of Thallium( I) Cryptates in relation to the Free Energies of Solvation of Thallium(1) B. G. Cox, J. Stroka, I. Schneider and H. Schneider The Oxidative Coupling of Methane on Lithium Nickelate(1n) M. Hatano and K. Otsuka Thermodynamics for Chemical Equilibria and Kinetics in Solution at Constant Volume Ionic Transport through a Homogeneous Membrane in the Presence of Simultaneous Diffusion, Conduction and Convection V.M. Aguilella, S. Maf6 and J. Pellicer Structure and Reactivity of Zinc-Chromium Mixed Oxides. Part 3.-The Surface Interaction with Carbon Monoxide E. Giamello, B. Fubini, M. Bertoldi, G. Busca and A. Vaccari Characterization Studies of Potassium Phosphotungstate Glasses and a Model of Structural Units Influence of Pretreatment on the Properties of Ag/a-A1,0, Catalysts containing Large (k 1 pm) Pure and Cs-promoted Silver Particles. Part 1 .-- Extent of Oxygen and Hydrogen Sorption and TPD Studies G. R. Meima, L. M. Knijff, R. J. Vis, A. J. van Dillen, F. R. van Buren and J. W. Geus The Interaction of Oxygen with Isolated Silver Particles of ca. 70 nm supported on a-Alumina. Part 1 .--Oxygen Sorption and Temperature-programmed Desorption Measurements G.R. Meima, R. J. Vis, M. G. J. van b u r , A. J. van Dillen, J. W. Geus and F. R. van Buren The Interaction of Oxygen with Isolated Silver Particles of ca. 70 nm supported on a-Alumina. Part 2.-CO Oxidation Measurements G. R. Meima, L. M. Knijff, A. J. van Dillen, J. W. Geus and F. R. van Buren Cationic Lead(I1) Halide Complexes in Molten Alkali-metal Nitrate. Part 1 .-A Thermodynamic Investigation of the Fluoride System L. Bengtsson and B. Holmberg Cationic Lead(r1) Halide Complexes in Molten Alkali-metal Nitrate. Part 2.-A Thermodynamic Investigation of the Chloride, Bromide and Iodide Systems L. Bengtsson and B. Holmberg Statistical Surface Thermodynamics of Quaternary Liquid Systems J.D. Pandey, R. D. Rai and R. K. Shukla Retention of Rod-like Solutes in a Non-ideal Multicomponent Mixed Solvent M. Borowko Photoinduced Electron-transfer Reactions of Micelle-forming Surfactant Ruthenium(I1) Bipyridyl Derivatives F. M. el Torki, R. H. Schmehl and W. F. Reed Cobalt-Manganese Oxide Water-gas Shift Catalysts. A Kinetic and Mechanistic Study G. J. Hutchings, F. Gottschalk, R. Hunter and S. W. Orchard L. M. P. C. Albuquerque and J. C. R. Reis U. Selvaraj, H. G. K. Sundar and K. J. RaoCon tents 373 38 1 389 415 42 1 429 441 455 467 Mixed-metal Hydroxycarboxylic Acid Complexes. Formation Constants of Complexes of Uvl with Fe"', AlIII, In''' and Cu" E. Manzurola, A. Apelblat, G. Markovits and 0. Levy Preferential Solvation. Part 3.-Binary Solvent Mixtures Y. Marcus Interaction of Transition-metal Acetylacetonates with y-Al,O, Surfaces J. A. R. van Veen, G. Jonkers and W. H. Hesselink Tracer Caffeine Diffusion in Aqueous Solutions at 298 K. The Effect of Caffeine Self-association W. E. Price A Room-temperature ENDOR Study of X-Irradiated Pyridoxine Hydro- chloride Single Crystal J. T. Masiakowski and A. Lund Infrared Study of the Adsorption of Ethanoic Acid and Trifluoroethanoic Acid on Barium Sulphate W. Neagle and C. H. Rochester The Hydrogen Exchange Reaction of Surface Deuteroxyl Groups on MgO with H, T. Shido, K. Asakura and Y. Iwasawa Elastic Modulus of Crystal-like Structures of Deionized Colloidal Spheres in Sedimentation Equilibrium as studied by the Reflection-spectrum Method T. Okubo A Mossbauer Investigation of Iron-containing Catalysts prepared at Low Temperatures and Active for Carbon Monoxide Hydrogenation F. J. Berry and M. R. Smith

ISSN:0300-9599    

DOI:10.1039/F198985FP019

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

8/00612A 8/01165F 8/01166D 8/02070A 8/02305K 8/02582G 8/0342D The following papers were accepted for publication in Farartay Transactions I during November 1988. The Influence of Pretreatment on the Properties of Agla-Al203 Catalysts containing Large (k 1 pn) Pure and Cs-Promoted Silver Particles. Part 2.- Co Oxidation Measurements Meima, G. R., Hasselaar, M., van Dillen, A. J,, van Buren, F. R. and Geus, J, W. Tin Oxide Surfaces. Part 19.- Electron Microscopy, X-Ray Diffraction, Auger Electron and Electrical Conductance Studies of Tin@) Oxide Gel Harrison, P. G. and Willett, M. J. Tin Oxide Surfaces. Part 20.- Electrical Properties of T i n ( ~ ) Oxide Gel. Nature of the Surface Species Controlling the Electrical Conductance in Air as a Function of Temperature Harrison, P.G. and Willett, M. J Selective Rareearth-catalysed reactions. Catalytic Properties of Sm and Yb Metal Vapour Deposition Products Imamura, H., Kitajima, K. and Tsuchiya, S. Photocurrent Kinetics in Metal Phthalacyanine Crystals Films and Pellets Bahra, G. S., Chadwick, A. V., Couves, J. W, and Wright, J. D. Chromatic Reaction of Polyaniline Film and its Characterization Jiang, R-2. and Dong, S-J. Hamilton’s Principle of Least Action in Nervous Excitation Dickel, G. Chemical Environments around Active Sites and Reaction Mechanisms in Deuterium-Acmlein Reaction in Normal and SMSI States Yoshitake, H., Asakura, K. and Iwasawa, Y. Channel Elecmde Voltammeby. Waveshape Analysis of the Current-Voltage Curves of EC2 and DISP;! Processes Compton, R. G. and Pilkington, M.B. G.Cumulative Author Index 1989 Aguilella, V. M., 223 Akitt, J. W., 121 Albuquerque, L. M. P. C., 207 Allen, G. C., 55 Apelblat, A., 373 Asakura, K., 441 Bengtsson, L., 305, 317 Berry, F. J., 467 Bertoldi, M., 237 Bond, G. C., 168 Borbwko, M., 343 Boss, R. D., 11 Bowker, M., 165 Brimblecome, P., 157 Busca, G., 137, 237 Chadwick, A. V., 166 Chen, L-f., 33 Clegg, S. L., 157 Conway, S. J., 71, 79 Cox, B. G., 187 Datka, J., 47 De Giglio, A., 23 Dell’Atti, A., 23 Donini, J. C., 91 el Torki, F. M., 349 Falconer, J. W., 71, 79 Finch, J. A., 91 Fletcher, P. D. I., 147 Foo, C. H., 65 Frey, H. M., 167 Fubini, B., 237 Gabriel, C. J., 11 Gabrys, B., 168 Geus, J. W., 269, 279, 293 Giamello, E., 237 Gilbert, P. J., 147 Gottschalk, F., 363 Hasted, J. B., 99 Hatano, M., 199 Hesselink, W.H., 389 Hester, R. E., 171 Higgins, J. S., 170 Higuchi, A., 127 Holmberg, B., 305, 317 Hong, C. T., 65 Howarth, 0. W., 121 Hunter, R., 363 Hutchings, G. J., 363 Ichikawa, K., 175 Ikeda, R., 111 Ishida, H., 11 1 Iwasawa, Y., 441 Jin, T., 175 Jonkers, G., 389 Jutson, J. A., 55 Katoh, T., 127 Keeler, J. H., 163 Kelebek, $., 91 Knijff, L. M., 269, 293 Lawrence, K. G., 23 Levy, O., 373 Loudon, R., 169 Lorenzelli, V., 137 Lund, A., 421 Mafe, S., 223 Manzurola, E., 373 Marcus, Y., 381 Markovits, G., 373 Masiakowski, J. T., 421 Matsuhashi, N., 111 Matsumoto, T., 175 Meima, G. R., 269, 279, 293 Mosier-Boss, P. A., 11 Nakagawa, T., 127 Nakamura, D., ,111 Neagle, W., 429 Nowak, R. J., 11 Okubo, T., 455 Orchard, S. W., 363 Otsuka, K., 199 Pandey, J. D., 331 Pellicer, J., 223 Piwowarska, Z., 47 Price, W.E., 415 Rai, R. D., 331 Ramis, G., 137 Rao, K. J., 251 Reed, W. F., 349 Rees, L. V. C., 33 Reis, J. C. R., 207 Rochester, C. H., 71, 79, 429 Rosen, D., 99 Rowlinson, J. S., 171, 172 Sacco, A., 23 Said, M., 99 Schmehl, R. H., 349 Schneider, H., 187 Schneider, I., 187 Selvaraj, U., 251 Shido, T., 441 Shukla, R. K., 331 Smith, G. W., 91 Smith, J. J., 11 Smith, M. R., 467 Stroka, J., 187 Sundar, H. G. K., 251 Szpak, S., 11 Thamm, H., 1 Vaccari, A., 237 van Buren, F. R., 269, 279, 293 van Dillen, A. J., 269, 279, 293 van Leur, M. G. J., 279 van Veen, J. A. R., 389 Vis, R. J., 269, 279 Wacker, T., 33 Waugh, K. C., 163 Weale, K. E., 165 Yeh, C-t., 65 Young, D. A., 173 (ii)THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No.87 Catalysis by Well Characterised Materials University of Liverpool, 11-13 April 1989 Organising Committee: Professor R. W. Joyner (Chairman) Professor A. K. Cheetham Professor F. S. Stone Dr K. C. Waugh Professor P. B. Wells The understanding of heterogeneous catalysis is an important academic activity, which complements industry’s continuing search for novel and more efficient catalytic processes. The emergence of rele- vant, in particular in siru techniques and new developments of well established experimental approaches to catalyst characterisation are making a very significant impact on our knowledge of catalyst composition, structure, morphology and their inter-relationships. Well characterised cata- lysts, which will be the subject of the Faraday Discussion, include singlecrystal surfaces, whether of metals, oxides or sulphides; crystalline microporous solids, such as zeolites and clays, and ap- propriate industrial catalysts.The elucidation of structure/function relationships and catalytic mechanism will be important aspects of the scientific programme. Contributions describing novel methods for synthesising well characterised catalysts and also reporting important advances in char- acterisation techniques will also be included. The final programme and application form may be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 88 Charge Transfer in Polymeric Systems University of Oxford, 11 -1 3 September 1989 This Discussion aims to bring together physicists and chemists interested in the mechanism of elec- tron and ion transport in polymeric systems. The systems include conducting polymers, redox polymers, ion exchange membranes and modified electrodes.Discussion topics will cover ex- perimental evidence from spectroscopy, electrochemistry and new techniques such as the quartz microbalance. Theoretical models ranging from band theory through polarons to localised chemical structures will be critically evaluated and compared with experiment. The following have agreed to participate in the Discussion: R. Murray W. J. Albery M. B. Armand D. Bloor P. G. Bruce R. Friend A. J. Heeger A. R. Hillman A. G. MacDiarmid M.Ratner S. Roth W. Salaneck G. Tourillon C. Vincent G. Wegner The preliminary programme may be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN. (iii)THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 89 Structure of Surfaces and Interfaces as Studied using Synchroton Radiation University of Manchester, 4-6 April 1990 Organising Committee: Professor J. N. Shewood (Chairman) Professor D. A. King Dr G. King The Discussion will focus on the wealth of novel information which can be obtained on the nature and structure of surfaces using the full spectral range of synchroton radiation. Emphasis will be placed on the scientific results of recent investigations rather than on technical aspects of experimen- tation.Papers will be welcome which shed new light on the structure of the complete range of interfaces: solidkolid, solidgas, solidAiquid, gasAiquid and "dean' surfaces induding both static and dynamic in situ examinations. It is hoped that the discussion will define the utility of synchroton radi- ation examinations in surface science studies at a time of expansion of the availability of such sources and the inauguration of new and more powerful sources. Contributions for consideration by the Organising Committee are invited and abstracts of about 300 words should be sent by 31 May 1989 to: Professor J. N. Shemood, Department of Pure and Applied Chemistry, University of Strath- Clyde, Thomas Graham Building, 295 Cathedral Street, Glasgow G1 1XL Full papers for publication in the Discussion Volume will be required by December 1989.Dr C. Norris Dr R. Oldman Dr G. Thomton THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM No. 25 Large Gas Phase Clusters University of Warwick, 12-1 4 December 1989 Organising Committee: Professor K. R. Jennings (Chairman) Professor P. J. Derrick Professor D. Phillips The Symposium will focus on recent developments in the rapidly expanding field of large gas phase clusters, induding the preparation, structure and reaction of both neutral and ionic dusters. It is hoped that the meeting will bring together scientists working on many different types of duster, e.g. rare gas atoms, metals, inorganic and organic species, and biomolecules, to discuss the chemistry and physics of clusters from diff erent viewpoints.Contributions for consideration by the Organising Committee are invited. Titles and abstracts of about 300 words should be submitted by 15 February 1989 to: Professor K. R. Jennings, Department of Chemistry, University of Wamick, hventry CV4 7AL, England. Full papers for publication in the Symposium volume will be required by 14 August 1989. Dr N. Quirk Dr R. P. H. Rettschnick Dr A. J. Stace~ ~~ ~~ FARADAY DIVISION INFORMAL AND GROUP MEETINGS 7heoretical Chemistry Group Graduate Students' Meetlng To be held at Uniwrsity College, London on 1 March 1989 Further information from Dr P Fowler, Deparbnent of Chemislry, Uniwrsity of Exeter, Exem EX4 4QD ~ ~ ~~~ Neutron Scattering Group Neutron and X-ray Scattering: Complementary Techniques To be held at the Universtty of Kent at Canterbury on 29-30 Mard.11989 Further information from Dr R.J. Newpott, Physics Laboratory, University of Kent, Canterbury CT2 7NR Polar Solids Group Atomic Mechanisms of Mass Transport In Solids To be held at Mansfield College, Oxford, on 2931 March 1989 Further information from Professor R. A. Catlow, Department of Chemistry, University of h i e , Keele, Staffordshire Division join@ with the Colloid and Interface Science Group Annual Congress: Surfactant Interactions in Colloidal Systems To be held at the University of Hull on 4-7 April 1989 Further information from Dr J. F. Gibson, The Royal Society of Chemistry, Burlington House, London W1 V OBN ~ ~~ ~ Molecular Beams Group Surfaces, Ions and Clusters To be held at the Uniwrsity of Liverpod on $1 1 Apnl 1989 Further information from Dr J.M. Hutson, Department of Chemistry, University of Durham, South Road, Durttam DH13LE Electrochemistry Group Spring Informal Meeting To be held at the Uniwrsity of Warwick on 10-1 2 April 1989 Further information from Dr S. P. Tylield, CEGB, Berkeley Nudear Laboratories, Berkeley, Gloucestershire GL13 9PB Electrochemistry Group with the Electroanalytical Group Electroanalysis To be heM at Loughborough University of Technology on 12-14 April 1989 Further information from Dr S. P. Tyfiekl, CEGB, Berkeley Nudear Laboratories, Berkeley, Gloucestershire GL13 9PB Gas Kinetics Group Developments in Gas Kinetics: New Techniques, Results and their Interpretation To be held at the University of York on 3 4 July 1989 Further information from Professor R.J. Donovan, Department of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ Industrial Physjcal Chemistry Group with the Thin Films and Surfaces Group of the IOP Materials for Non-linear and Electro-optlcs To be held at Girton College, Cambndge on 4-7 July 1989 Further information from The Meetings officer, Institute of Physics, 47 Belgrave Square, London SWlX 8QX Polymer Physics Group Biologically Engineered Polymers 89 To be held at ChurdiU College, Camtndge, on 31 July to 2 August 1989 Further information from Dr M. J. Richardson, Division of Materials, National Physical Laborabry, Queens Road, Teddngtm, Middlesex TW11 OLWPolymer Physics Group Biennial Meeting To be held at the University of Reading on 13-1 5 September 1989 Further information from Dr M.J. Richardson, Division of Materials, National Physical bboratory, Queens Road, Teddington, Middlesex W11 OLW ~~ Colloid and Interface Science Group Inorganic Particulates To be held at Chester College on 1921 September 1989 Further information from Dr R. Buscall, ICI plc, Corporate Colloid Science Group, PO Box 11, The Heath, Runcorn, Cheshire WA7 4QE ~~ Division with the Institute of Physics Sensors and their Applications To be held at the University of Kent at Canterbury on 1922 September 1989 Further information from The Meetings Officer, Institute of Physics, 47 Belgrave Square, London SW1X 8QX _ _ _ ~ ~~ ~~~ Division with rhe Deutsche Eunsen Gesellschaft, Division de Chimie Physique of the Societe Francaise de Chimie and Associazione ltaliana di Chimica Fisica Transport Processes in Fluids and Mobile Phases To be held at the Physikalische Institiit, Aachen, West Germany on 2528 September 1989 Further information from Professor G.Luckhurst, Department of Chemistry, University of Southampton, Southampton SO9 5NH Division Autumn Meeting: Chemistry at Interfaces To be held at Loughborough University of Technology on 26-28 September 1989 Further information from Professor F. Wilkinson, Department of Chemistry, Loughborough University of Technology, Loughborough LE11 3TUDEUTSCHE BUNSEN-GESELLSCHAFT FUR PHYSIKALISCHE CHEMIE ASSOCIAZIONE ITALIANA DI CHIMICA FISICA FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SOCIETk FRANCAISE DE CHIMIE, DIVISION DE CHlMlE PHYSIQUE JOINT DISCUSSION MEETING 1989 Transport Processes in Fluids and in Mobile Phases Aachen, 25-27 September 1989 Organised by: H.Versmold (F.R.G.) Al.Weiss (F.R.G.) M. Zeidler (F.R.G.) G. R. Luckhurst (U.K.) The purpose of the meeting is to bring together scientists working on transport and related phenomena in simple and complex fluids, colloidal and micellar systems, and surface phases. Experimental techniques considered include classical methods, optical spectroscopy, light scattering, nuclear magnetic resonance, and neutron scattering. The following persons have accepted invitations to present talks: D. Evans, Canberra; B. U. Felderhof, Aachen; D. Frenkel, Amsterdam; A. Geiger, Dortmund; W. Glaser, Grenoble; H.G. Hertz, Karlsruhe; S. Hess, Berlin; J. Jonas, Urbana; R. Klein, Konstanz; K. Lucas, Duisburg; H.-D. Ludermann, Regensburg; H. Posch, Wen; P. Pusey, Malvern; J. P. Ryckaert, Brussels; W. A. Steele, Penn State; D. J. Tildesley, Southampton; H. Weingartner, Karlsruhe. Further details may be obtained from: Professor H. Versmold, lnstitut fur Physikalische Chemie, RWTH Aachen, Templergraben 59, D-5100 Aachen, Federal Republic of Germany. P. Turq (France) (vii)JOURNAL OF CHEMICAL RESEARCH Papers dealing with physical chemistry or chemical physics which appear currently in J. Chem. Research, The Royal Society of Chemistry’s synopsis + microform journal, include the following: Absolute Rate Data for the Reaction of Atomic Germanium, Ge(43P~), with Halogenated Olefins and Aromatic Compounds by Time-resolved Atomic Resonance Absorption Spectroscopy Subhash C.Basu and David Husain (1988, Issue 10) Benzo-bisdithiazole) Gotthelf Wolmershiiusser, Gerhard Wortmann and Martin Schnauber (1988, Issue 11) Frank Hibbert and Rowena J. Sellens (1 988, Issue 11) Species in Aqueous Perchlorate Solution at Different Temperatures and Ionic Strengths Concetta De Stefano, Carmelo Rigano, Sihrb Sammartano and Rosario Scarcella (1988, Issue 11) Structural and Magnetic Properties of the Radical-cation Sak BBDTA*FeC14- (BBDTA = Electrolyte Effects on the Reactions of Hydroxide Ion in 70% (vh) Dirnethyl Sulphoxide-Water Studies on Sulphate Complexes. Literature Data Analysis of the Stability of HS04- and NaS04- Contribution of an Intramolecular Hydrogen Bond to the Dipole Moment Otto Exner and Jaroslav Pecka (1 988, Issue 12) (viii)NOMENCLATURE AND SYMBOLISM For many years the Society has actively encouraged the use of standard IUPAC nomenclature and symbolism in its publications as an aid to the accurate and unambiguous communication of chemical information between authors and readers.Nomenclature. The following publications provide the IUPAC nomenclature rules and guidance on their use: Nomenclature of Organic Chemistry, Sections A, B, C, D, €, F, and H (Pergamon, Oxford, 1979 edn.) Nomenclature of lnorganic Chemistry (Butterworths, London, 1971, now published by Pergamon). Biochemical Nomenclature and Related Documents (The Biochemical Society, London, 1978). Where there are no IUPAC rules for the naming of particular compounds or authors find difficulty in applying the existing rules, they should seek the advice of the Society’s editorial staff.Units and Symbols. A detailed treatment of units and symbols with specific application to chemistry, based on the Systhme lnternationale d’Unites (SI), is given in Quantities, Units and Symbols in Physical Chemistry, published for IUPAC by Blackwell Scientific Publications, Oxford (1 988 edn.). A comprehensive list of IUPAC publications on nomenclature and symbolism appears in the January issue of J. Chem. Soc., Faraday Transactions.NOMENCLATURE AND SYMBOLISM For many years the Society has actively encouraged the use of standard IUPAC nomenclature and symbolism in its publications as an aid to the accurate and unambiguous communication of chemical information between authors and readers. Nomenclature. The following publications provide the IUPAC nomenclature rules and guidance on their use: Nomenclature of Organic Chemistry, Sections A, B, C, D, €, F, and H (Pergamon, Oxford, 1979 edn.) Nomenclature of lnorganic Chemistry (Butterworths, London, 1971, now published by Pergamon). Biochemical Nomenclature and Related Documents (The Biochemical Society, London, 1978). Where there are no IUPAC rules for the naming of particular compounds or authors find difficulty in applying the existing rules, they should seek the advice of the Society’s editorial staff. Units and Symbols. A detailed treatment of units and symbols with specific application to chemistry, based on the Systhme lnternationale d’Unites (SI), is given in Quantities, Units and Symbols in Physical Chemistry, published for IUPAC by Blackwell Scientific Publications, Oxford (1 988 edn.). A comprehensive list of IUPAC publications on nomenclature and symbolism appears in the January issue of J. Chem. Soc., Faraday Transactions.

ISSN:0300-9599    

DOI:10.1039/F198985BP021

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I, 1989, 85(2), 175-185 An Aluminium-27 Nuclear Magnetic Resonance Study of Chemical Exchange between Different Polyatomic Species in Butylpyridinium Chloride-AlC1, Me1 t s Kazuhiko Ichikawa," Takashi Jin and Toshiyuki Matsumoto Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, Japan 27A1 n.m.r. measurements have been made for molten n-butylpyridinium chloride-AIC1, mixtures at 61 and 66mol% AlCl, and at various temperatures between 20 and 100 "C. The time evolution of the 27Al longitudinal magnetization recovery (1.m.r.) was obtained from the free- induction decays measured using the inversion recovery method. The observed 27Al 1.m.r. and n.m.r. spectrum consisted of two contributions which were attributed to A1,Cl; (A) and AlCl, (B).The experimental results of the 27Al 1.m.r. and n.m.r. spectrum were reproduced with the aid of the general theory describing the effect of chemical exchange on 1.m.r. and lineshape. Thus the kinetic and equilibrium properties of the chemical exchange process were determined from the temperature dependences of the fractional population, f,, and the lifetime t, (a = A or B), which ranged from 10-3-10-1 s. The rate of the exchange reaction A1 (in B)+AI (in A) is not very fast, since it is small compared with I?:, A (> I?:,.) even at high temperatures for 61 mol% AlC1,. The observed rate of 1.m.r. at high temperatures under the influence of chemical exchange between the different polyatomic species B and A was not equal to the spin-lattice relaxation rates I?;".* and Rr,R.In molten mixtures of AlCl, and 1 -butylpyridinium chloride (BPCl), alkylimidazolium chloride (IMCl) or alkali-metal chloride the predominant equilibria reactions may be expressed as (1) (2) 2 AlCl, g A1,Cl; + C1- 2 AlCl, + Al,CI, e 2 AI,Cl; over the region of a formal AlC1,:MCl mole ratio, x, of 1.0 (i.e. MAlCl, melt or 50 mol YO AlCl,) to 2.0 (i.e. MAl,Cl, melt or 66.7 mol '/O AlCl,). The chloroaluminate melts consist of aluminum tetrachloride and dialuminum heptachloride ions, AlCl, and Al,Cl;, as the major chloroaluminate species, at 1 < x < 2. A Raman spectroscopic study showed that the bands assigned to Al,Cl, or higher polymers (e.g. Al,Cl;,,) did not appear in the observed spectra as far as the available sensitivity permitted us to The potentiometric determination of the equilibrium constant Keq for eqn (1) was carried out using the electrochemical concentration cell and the solvent acid-base properties were also Keq was determined to be ca.at 30 "C and 1 < x < 2 for the BPCl-AlC1, melts because of the very small value of [Cl-] (ca. The aluminium-27 n.m.r. spectrum and 1.m.r. on MCl(M+ = BP+, Im+)-AlCl, melts were measured, and an equilibrium between the principal chloroaluminate species was discussed as far as the available n.m.r. sensitivity permitted us to Proton and carbon chemical shifts at the different sites of IM+ in MeEtIMCl-AlCl, (1 < x < 2) 175 7-2176 Butylpyridinium Chloride-AlC1, Melts melts were obtained from least-squares fits to the observed shift as the average of the unresolved multiplet using the calculated anion mole fractions of B and A under the assumption that [Cl-] << [complex anion] and [All = [B] + 2[A].*, lo The fractional population of B and A was determined by non-linear least-squares fits to the observed 1.m.r.using as a model the effect of rather slow chemical-exchange on its time evolution.1° On the other hand, the spin-lattice relaxation, and the equilibrium and kinetic properties of the dynamic equilibrium reaction associated with the ligand exchange between H,O and SO:- in the inner-sphere shell of aqueous 27A111*,11 were characterized by reproducing the experimental results for the 1.m.r. and n.m.r. spectrum with the aid of the general theory describing the effects of chemical exchange on 1.m.r.12 as well as on lineshape.', The theory showed an exact solution of the coupled expressions for the time evolution of each of the longitudinal magnetizations in two different environments.This paper describes how n.m.r. spectroscopy enables us to characterize an exchange process between different polyatomic species on the basis of experimental and theoretical studies. One can see an exchange process only between B and A in the observed 27Al n.m.r. lineshapes and 1.m.r. at 1 < x < 2, as far as the available sensitivity permitted us to determine. We reproduce their experimental results with the aid of the theory describing the effects of chemical exchange on 1.m.r. and lineshapes. This paper also reports the temperature dependences of the fractional population between B and A, their chemical exchange lifetimes, and the spin-lattice relaxation rates of 27Al in B and A, as well as the equilibrium and kinetic properties for the exchange reaction of B and A.Experimental Materials The preparation of crystalline BPCl and aluminum trichloride has been described previously." The manipulation of all materials was performed under an argon atmosphere in a glove box. The composition of molten BPCl-AlC1, was determined for aluminum by the 8-hydroxyquinoline method with the aid of the absorption spectrum and for chlorine by the precipitation titration method. N.M.R. Measurements We carried out the n.m.r. measurements of molten BPCl-AlCl, at 61 1 and 66f 1 mol% AlCl, between 20 and 100 "C. The melts consist of B and A as the major chloroaluminate species, as mentioned above.The 27Al resonance frequency and the time interval td between the last 90" pulse and the onset of data acquisition were ca. 52.1 MHz and 30 ps or 1 ms on a Varian XL-200, and ca. 130.2 MHz and 400 ps on a JEOL GX-500, respectively. The observed magnetization M,(z) was obtained from the initial intensity of the free-induction decays measured at td = 30 ps, using the inversion recovery (or 18O0-z-9O") method for ca. 10 values of z until M,(z)/M; reached ca. 0.65.l' Thus the experimental points of 1.m.r. were obtained as a function of z. Results The 27Al n.m.r. spectra of molten BPCl-AlCl, at 61 k 1 and 66 k 1 mol % AlCl, between 20 and 100 "C are shown in fig. 1 and 2. The ,'A1 n.m.r. spectra at 61 1 mol O/O AlCl, (ie.x = 1.56, see fig. 1) were partially resolved into two components corresponding to B and A, where the resonance line assigned to the former was located to high field. Previous studies have reported the measurements of the partially resolved lineshapes ofK. Ichikawa, T. Jin and T. Matsumoto 177 100 ~ 52.1401 52.1201 VIMHZ Fig. 1. 27A1 spectra recorded at 52.1 MHz, t, = 30 ps and 61 & 1 mol % AICI, between 30 and 100 "C. The spectra are displayed isometrically on a scale. 27Al in the BPCl or IMCl-AlC1, melts over the region 1 < x < 2 . 7 9 8 9 1 3 * 1 4 Increasing the temperature gives rise to an increase in the concentration of A as well as the motional narrowing of the lineshapes. We can recognize that the chemical exchange rate between B and A in eqn (1) is not larger than the resonance-frequency separation of the two lines Av(= v,-vv,).The effect of chemical exchange on the 1.m.r. is small, but it is still important. The 27Al resonance line was found to depend upon the delay time t, at 66 mol YO AICl, and v,, = 52.1 MHz, as shown in fig. 2(a) and (b). Each of the spectra showed a single peak for t , = 30 ps, because of the BPA12C17 melt (i.e. x = 2), which consisted of the two species BP+ and A; the large signal attributed to 27Al in A masked a much smaller contribution from B. For t, = 1 ms partially resolved peaks were observed [see fig. 2(b)], where a large number of transient accumulations (i.e. 500) were necessary to obtain a good signal-to-noise (SIN) ratio. On the other hand, for v,, = 130.2 MHz and td = 400 ps, clearly resolved peaks were observed at all the temperatures for each of 16 times that the signal was augmented [see fig.2(c)]. The experimental points of the 1.m.r. at 61 and 66 mol YO AlCl, are shown in fig. 3 and 4, respectively. Once we were able to observe the free-induction decays at vAl = 52.1 MHz and t d = 30ps using the inversion recovery method, we were then able to obtain the longitudinal magnetization Mz(z) as a function of time interval z between the 180 and 90" pulses, as mentioned in the Experimental section. At the lower temperatures the non-linear logarithmic longitudinal magnetization originated from the slow exchange rates ; at high temperature single-exponential decays were observed, although the 27Al spectra showed some partially resolved peaks (see fig.1). The 1.m.r. data for the whole signal did not enable us to determine the spin-lattice relaxation rates of 27Al in A (B) R:,, (> without the aid of the theory describing the effects of chemical exchange on the 1.m.r. and n.m.r. spectrum, as mentioned below. Discussion We focus here on the chemical-exchange process between different polyatomic species A and B in BPCI-AICI, melts. We will characterize its equilibrium and kinetic properties178 Bu ty lpy r idin iurn Chloride- Al C1 Melts 100 80 40 21 4 I I I I I 52.1401 V I M H Z 52.12 01 100 - 80 I I I I I I 52.140 52.1201 V I M H Z 90 I I I 1 I 1 130.22 V I M H Z 130.23 Fig. 2. 27A1 spectra at 66k 1 mol YO AlCl, between 20 and 100 "C; (a) for v,, = 52.1 MHz and t, = 30 ,us, (6) for v,, = 52.1 MHz and t , = I ms and (c) for v,, = 130.2 MHz and t, = 400 ,us.K.Ichikawa, T. Jin and T. Matsumoto I79 I I I 1 I 1 - 0 2 4 6 8 10 104 zls Fig. 3. Experimental points of the longitudinal magnetization recovery at 61 f 1 mol YO between 30 and 100 "C. The dashed line is a fit of the data to the theory. v,, = 52.1 td = 30 p ~ . AlCI, M Hz, \ I I I I 1 * - 2 0 2 4 6 0 10 104 zjs Fig. 4. Experimental points of the longitudinal magnetization recovery at 66k 1 mol YO AICl, BPAl,CI, melt between 21 and 100 "C. The dashed line is as for fig. 3. v,, = 52.1 MHz, td = 30 ,us. and obtain the spin-lattice relaxation rates of 27AI in the species by using the theory describing the effects of chemical exchange on 1.m.r. and the n.m.r.spectrum:l2. l3 Calculations of L.M.R. and Lineshape In the case of 27Al n.m.r. experiments the predominant equilibria (1) and (2) can be simplified to (3) 27Al (in B) g 27Al (in A). Here, we assume for simplification that no contributions from AI,CI, or higher polymers appear in the n.m.r. data of the chloroaluminate melts over the region I < x < T7* * * 13, l4 Note that no Raman bands assigned to species such as A12Cl, and A13CI;o were180 Butylpyridiniurn Chloride-AlC1, Melts I I 1 1 1 I I 1 1 I V I M H Z 52.1381 VA VB 52.1221 Fig. 5. Experimental spectra (-) and their simulation (**.*.) at 61 +_ I mol % AlCl, at 50, 70 and 100 "C. (--) and (---) show the individual components of A and B. The parameters used for the simulation are given in fig.8 and 9 (later). Under conditions of chemical exchange between the two sites A and B the time evolution of their longitudinal magnetizations Mz, A(z) and Mz, A(z) and the total magnetization Mz(z) is given by and MZ(') = M Z , A(') + M Z , B(')' (6) Here the coefficients of and the inverse time constant describing the time evolution of the observed M,(z) or MZJz), R,,,(a = A or B) are expressed in terms of the spin-lattice relaxation rate R:, A(R:, B) of A1 in site A (and site B), the lifetime of chemical exchange of site a, z,, and the fractional population of nuclei (e.g. 27Al) between sites A and B (fA = 1 -fB), as shown in eqn (8)-(10) and (13)-(17) in ref. (12). Since there is supposed to be equilibrium in solution between the main A and B species, the relation between f A , and zA, is expressed as 'BfA = ' A f B ' (7)K.Ichikawa, T. Jin and T. Matsumoto 181 J I I I I II I I 130.228 UA U S 130.222 V I M H Z Fig. 6. Experimental spectra (-) as shown in fig. 2(c) and their simulation (-.*.*) at 66f 1 mol YO AlCl, at 50, 70 and 90 "C. (--) and (---) are as for fig. 6. z, used for the simulation is given in fig. 10 (later). 1001 I I I I I I I I 1 1 1.9 Fig. 7. 0 0 0 a I 0 0 I 1 1 1 1 1 1 1 1 1 1 1 7 . 4 0 50 100 T I T Temperature dependences R:,, t, (a) and t, Av (0) at 61 mol % AlCl,. We have been able to investigate the influence of chemical exchange on the 1.m.r. for slow, intermediate or rapid exchange, kBA(ril, k,, = ~i'), for the forward and backward exchange processes. Hence the simulation of the n.m.r.spectrum and the 1.m.r. provides the equilibrium and kinetic parameters of the exchange reaction in eqn (3) as well as the spin-lattice relaxation rate.182 lo-* Y) 1 n W 8 8 n W Butylpyridinium Chloride-AlC1, Melts 1 1 1 1 ~ 1 1 l I - - - - - - 0 Q 0 0 I , , ,j 0 - I 1 1 TIOC i + - 1 % 1 0*- 2.6 2.8 3.0 3.2 3.4 3.6 103 KIT Fig. 8. Temperature dependences of Rl, A (O), R l , , (O), R:, A (@) and R:. , (a) at 61 & 1 rnol % AICI,. We simulated the experimental points of 1.m.r. as shown by the dashed lines in fig. 3 and 4; the observed lineshapes were also simulated, as shown by the dotted lines in fig. 5 and 6, between 21 and 100 "C at 61 and 66 mol O h AlCl,, using equations that appear in ref. (12) and (13). The effect of a delay on the observed free-induction decay was accounted for in the simulation of the recovery curve and the lineshape, since the data were recorded with the delay.', Fig.7 shows the temperature dependence of the product parameters 2, Av and R:,* z, at 61 mol YO AlCl,, where Av = 501 _+ 1 MHz at vAl = 52.1 MHz. The fact that Rf,A z, ranged from 3 to 20 above ca. 40 "C at 61 mol YO AlCl, showsK. Ichikawa, T. Jin and T. Matsumoto 183 I I I 50 60 70 80 90 T I T Fig. 10. Temperature dependences of t, (0) and T~ (0) at 66+ 1 mol % AlCl,. Table 1. Kinetic properties of the exchange reaction of eqn (3) at 61 f 1 mol % AlCl, between 30 and 100 "C forward process backward process AH;,,/kJ mo1-' AS&/J K-I mol-' AHz,/kJ mol-' AS:,/J K-' mol-' 15.5k 1.3 - 149&4 -0.83 & 0.20 - 195+ 1 the effects of the chemical exchange on the 1.m.r.and lineshape to be small but important. Rr,, (a = A or B), z, and f,, which reproduced the data of 1.m.r. and the n.m.r. spectrum as shown in fig. 3-6, are discussed below. The Rate (&,) and Spin-Lattice Relaxation Rate The spin-lattice relaxation mechanism for 27Al is expressed in terms of the interaction of the nuclear electric quadrupolar moment with the fluctuating electric-field gradients (e.f.g.). The local e.f.g. at 27Al in B is much smaller than that in A, because an AlC1; species is characterized by regular symmetry, while the electronic density around 27Al in A1,Cl; with a double tetrahedron sharing one corner is not symmetrica1.2,15*'6 It is reasonable to conclude that R:,, is much larger than R:,, at 61 mol O/O AlC1, (fig.8). The exchange rate between A and B in the BPCl-AlCI, melts is not fast at 61 mol% AlCl, [ie. R;,, z, > 1 (as fig. 7)]. Both R1,* and R l , , become nearly equal to R:,, and R:, , respectively, below ca. 60 "C at 61 mol YO AlC1, (fig. 8), because of the very small effect of the chemical exchange on the 1.m.r. of 27A11*1 Kinetic and Equilibrium Properties of Chemical Exchange between Different Polyatomic Species In our n.m.r. study the lifetimes of A and B, z, and z,, were obtained at 61 and 66 mol YO AlCl, (fig. 9 and 10). z, and z, at 61 mol YO AlC1, range from lo-, to s and cross over; 5, is larger than z, above ca. 50 "C. For all the temperatures at 66 rnol YO AICl, 5, x tA/ 100 because of the fractional population of 27Al in A fA x 0.99.By applying the184 Butylpyridinium Chloride-AlC1, Melts T/OC Fig. 11. Temperature dependences of the anion fractions between A (0) and B (0) at 61 f 1 mol YO AlCl,. theory of rate processes1' we obtained the activation enthalpy and entropy AHiA (AHZB) and ASiA(AS:B) at 61 mol% AlCl, from the temperature dependence of kBA( = ~ i l , kAB = T ; ~ ) , as shown in table 1, for the forward (and backward) path in eqn (3). The large negative value of AS:, for both forward and backward paths in the exchange process between B and A may mean an increase in the coordination number in the activated complex, i.e. an associative mechanism or S , 2 displacement mechanism. l8 MNDO calculations also led us to conclude that in the transition-state geometry one of the four chloride ions in B attacked an A1 in A.19 The temperature dependence of the anion fraction X(a) between A and B at 61 mol O/O AlCl, was obtained fromf, (fig.11); X(A) and X(B) crossed over at ca. 90 "C and X(A) became larger than X(B). For 66 mol% AlCl, X(A) ranged from 0.995 to 0.998. X(a) is not the concentration of the aluminum-containing species present in the melt, since X(a) is obtained from the n.m.r. data which showed the contributions from the major species B and A as far as the experimental sensitivity permitted us to determine. When X(a) was assumed to be equal to the concentration of species present (i.e. [Al'"] = [B] + 2[A] and [Cl] = 4[B] + 7[A])1° we were unable completely to reproduce the formal concentration 61 f 1 mol Yo AlC1, between 30 and 100 "C (i.e.the calculation showed 57 mol YO AlCl, at 30 "C and 61 mol O/O at 100 "C). The equilibrium constant Kn.m.r, for the chemical-exchange reaction of eqn (3) is given by (8) K . m . r . = k A B / k B A = 2X(A)/X(B). The difference AGO( = Gl- G i ) between the Gibbs free energies of the two equilibrium sites in eqn (3) is given by AGO = -RTln Kn.m.r. (9) and the differences in enthalpy and entropy, AH" and AS", can be obtained from the thermodynamical relations between Kn.m.r. and 7'. AH" = 16.0 0.9 kJ mol-1 and AS" = 49.7 f 2.7 J K-' mol-' at 61 mol %. The Gibbs free-energy inter-relations between AGO and AG&, were confirmed at 61 mol YO AlCl,, although the equilibrium and kinetic parameters were obtained independently. The forward reaction in eqn (3) was endothermic.The product A1,Cl; is, however, more stable than the reactant AlCI, at the higher temperatures because of the high entropy contribution.K. Ichikawa, T. Jin and T. Matsumoto 185 Professor T. Ishikawa (Faculty of Engineering) for the loan of the crystalline AlCI,. The n.m.r. measurements were carried out with a Varian XL-200 and a JEOL GX-500 installed in the two n.m.r. Laboratories of the Faculties of Engineering and Science. This work was supported in part by a Grant-in-Aid for Scientific Research no. 61470040 from the Japanese Ministry of Education, Science and Culture. References 1 G. Torsi, G. Mamantov and G. M. Begun, Inorg. Nucl. Chem. Lett., 1970, 6, 553. 2 E. Rytter, H. A. Oye, S. J. Cyvin, B. N. Cyvin and P. Klebol, J. Inorg. Nucl. Chem., 1973, 35, 1185. 3 R. J. Gale, B. Gilbert and R. A. Osteryoung, Inorg. Chem., 1978, 17, 2728. 4 G. Torsi and G. Mamantov, Inorg. Chem., 1971, 10, 1900; 1972, 11, 1439. 5 L. G. Boxall, H. L. Jones and R. A. Osteryoung, J. Electrochem. Soc., 1973, 120, 223. 6 R. J. Gale and R. A. Osteryoung, Inorg. Chem., 1979, 18, 1603. 7 J. L. Gray and G. E. Maciel, J. Am. Chem. Soc., 1981, 103, 7147. 8 J. S. Wilkes, J. S. Frye and F. Reynolds, Inorg. Chem., 1983, 22, 3870. 9 T. Matsumoto and K. Ichikawa, J. Am. Chem. Soc., 1984, 106, 4316. 10 A. F. Fannin Jr, L. .4. King, J. A. Levisky and J. S. Wilkes, J. Phys. Chem., 1984, 88, 2609. 11 T. Jin and K. Ichikawa, J. Chem. Soc., Faraday Trans. I , 1988, 84, 3015. 12 K. Ichikawa, J. Chem. Soc., Faraday Trans. 2, 1986, 82, 1913. 13 See e.g., K. Ichikawa and T. Matsumoto, J. Magn. Reson., 1985, 63, 445. 14 F. Taulelle and A. I. Popon, J. Solution Chem., 1986, 15, 463. 15 S. Takahashi, N. Koura, M. Murase and H. Ohno, J. Chem. Soc., Faraday Trans. 2, 1986, 82, 49. 16 Y. Kameda and K. Ichikawa, J. Chem. SOC., Faraday Trans. I , 1987, 83, 2925. 17 S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 18 M. Eigen, Ber. Bunsenges Phys. Chem., 1963, 67, 753. 19 L. P. Davis, C. J. Dymek Jr, J. J. P. Stewart, H. P. Clark and W. J. Lauderdale, J. Am. Chem. Soc., 1941). 1985, 107, 5041. Paper 712122; Received 30th November, 1987

ISSN:0300-9599    

DOI:10.1039/F19898500175

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chern. Sac., Faraday Trans. I , 1989, 85(2), 187-198 Solvent Dependence of Kinetics and Equilibria of Thallium(1) Cryptates in relation to the Free Energies of Solvation of Thallium(1) Brian G. Cox* Department of Chemistry, University of Stirling, Stirling FK9 4LA, Scotland Jadwiga Stroka University of Warsaw, Institute of Fundamental Problems of Chemistry, Warsaw, Poland Irmgard Schneider and Hermann Schneider Max-Planck-Institut f u r Biophysikalische Chemie, 0-3400 Gottingen, Federal Republic of Germany Stability constants and dissociation rate constants of thallium(1) cryptates have been measured in several solvents at 25 "C. The TI' cryptates are more stable and less sensitive to ligand cavity size than the corresponding complexes of the alkali-metal cations. The stability constants vary strongly with solvent, and the solvent dependence of the complex stabilities appears to reflect mainly changes in the solvation of TI+.It is shown that free energies of transfer of the solvated TI+ among non-aqueous solvents calculated on the assumption that the difference in the free energies of transfer of the T1' cryptates and the corresponding cryptands is zero are in good agreement with literature data. Changes in the stability constants with solvent and ligand are reflected in changes in both dissociation and formation rate constants, but more so in the former. Thus the solvation of the transition state, (Tl+.-Cry):, is rather closer to that of the reactants, and includes additional solvent interactions compared with the stable cryptate complex, TICry'.The solvent dependence of the stability constants of inclusion complexes formed between metal ions and macrobicyclic diazapolyethers, cryptands (Cry), contains potentially important information on the solvation free energies of ions. This follows from eqn (l), which relates stability constants ( K ) (1) - RT In [&.(S)/&(R)] = AGJMCry"') - AGJCry) - AG,,(M"+) for a given cryptate MCry"+ in two solvents S and R ( = reference) to the free energies of transfer from R to S of the species involved in the complexation equilibrium M"+ + Cry S MCry"+ (2) K, = [MCry"+]/[M"+] [Cry]. (3) In a recent study Chantooni and KolthofY concluded that in dipolar aprotic solvents the first two terms on the right-hand side of eqn (1) cancel or nearly so, provided that the ion size is not greater than that of the cavity of the cryptand, i.e.the cations are shielded from direct interaction with the solvent. The relationship (4) AG,,(MCry"+) - AGJCry) = 0 187188 was proposed previou~ly,~? and when introduced into eqn (1) leads to the assumption Solution Studies of Thallium(r) Cryptates RTln [K(X)/K(R)I = AGtr(M"+) ( 5 ) which can be used to estimate the transfer free energies for solvated metal ions from the determination of stability constants. Danil de Namor and coworkers have also confirmed that for some alkali-metal cryptates in a range of aprotic solvents eqn (4) and ( 5 ) may be used to estimate AG,,(M+) with a reliability comparable to that of other commonly used extrathermodynamic assumption^,*-^ and that similar conclusions hold for AHtr(M+) values obtained from heats of cryptate Closer inspection of the results in the treatment of Chantooni and Kolthoffl indicates that for T1+ eqn (4) is rather more general and holds even when the size of T1+ is larger than that of cavity of the ligand.This method then may be very convenient for the study of the properties of TI+ in different media. Results for both the complexation and the transfer free energies of T1+ are of particular interest because of its importance as a probe for the role of alkali-metal cations, especially K+, in biological systems. 'O-" Therefore in this paper we present stability constants and dissociation rate constants for complexes of TI+ with several cryptands (see scheme 1) in water, dipolar aprotic solvents and protic solvents.n (I) (2,1,1)m =o, n = 0 (I1)(2,2,1)m = 1, n = 0 011) (2,2,2)rn = n = 1 The transfer free energies of solvated TI+ calculated using eqn (5) are found to be in good agreement with values from several sources in the literature. Furthermore, the variation of the calculated AG,,(TI+) values with cavity size of the ligand is insignificant and irregular in the different solvents, and covers a range similar to or smaller than that of the literature data. It seems that the higher polarizability of T1+ allows it to adjust to the structures of the different ligand cavities more readily than alkali-metal cations of similar size. The latter ions, for example, show larger differences between log & values for (2,1,1) and (2,2,2) cryptateP than T1+.B.G. Cox, J . Stroka, I . Schneider and H . Schneider 189 Table 1. Stability constants (log 4) of T1' cryptates at 25 "C ~ ~~~~ 3.19" 6.8b 6.64;" 6.4;b 5.5;d 6.3" 5.84" 4.61f MeOH 5.6," EtOH 5.1 2a 1 1 .O," 11 .o,c 8.58" 8.5," PC 6.58h 12.1,h 1 1.78;1 11.9: 10.7," 9.glh DMF 3.1,h 8.6,h 8.06;h 7.7l 6.79" 6.leC 10.7," 10.2,;b 10.1 ;g 10.0: 8.7," 8.30;" 7.9h H*O AN 7.02i 1 1 .92i 12.3,;j 13.4k 10.2,' 10.2,i DMSO 1.4,h 6.gOh 6.3;' 6.2$ 6.1q 4.6,c 4.5,h Abbreviations : MeOH, methanol ; EtOH, ethanol; AN, acetonitrile ; PC, propylene carbonate ; DMF, dimethylformamide ; DMSO, dimethyl sulphoxide. a This work, error in log & & 0.10. P. Gresser, D. W. Boyd, A. M. Albrecht-Gary and J. P. Schwing, J. Am. Chern. SOC., 1980, 102,651. "This work; error in log &&0.05.dG. Anderegg, Helu. Chim. Actu, 1985, 58, 1218. J-M. Lehn and J. P. Sauvage, J. Am. Chern. SOC., 1975, 97, 6700. M. K. Chantooni Jr and I. M. Kolthoff, Proc. Nutl Acad. Sci. USA, 198 1, 78, 7245. E. Lee, J. Tabib and M. J. Weaver, J. Electronanal. Chem., 1979, 96, 241. hM. K. Chantooni Jr and I. M. Kolthoff, J. Soh Chem., 1985, 14, 1. iB. G. Cox, J. Stroka and H. Schneider, to be published. I. M. Kolthoff and M. K. Chantooni Jr, Proc. Nutl Acad. Sci. USA, 1980,77, 5040. ' M. Lejaille, M. Livertoux, C. Guidon and J. Bessiere, Bull. SOC. Chim. Fr. 1978, 1-373. 'J. Gutknecht, H. Schneider and J. Stroka, Inorg. Chem., 1978, 17, 3326. The rate constants for cryptate dissociation (k,) and formation (kf), on the other hand, show a more complex dependence upon size and solvent than the equilibrium quantities.Both kd and kf values for the TI+ cryptates depend upon the ligand cavity size, but the former more so than the latter. The transition states for complex formation all lie closer to the reactants than to the product complexes, but the difference between the transfer free energies of the transition state and the reactants show a correlation with the solvent donor numbers . Experimental and Results Materials The cryptands (2,1, l), (2,2, l), (2,2,2), (2,,2,2) and (2,,2,,2) were commercial samples (Merck) and were used without further purification. The purities of the cryptands used were determined from the equivalent points in pAg potentiometric titrations of silver with the respective cryptands, in conjunction with the determination of stability constants. In all cases the purity was found to be better than or equal to that of the manufacturer's specification.Solvents were purified by fractional distillation under vacuum15 or, when sufficiently pure, used as supplied. AgClO, was dried under vacuum at 80 "C for at least 12 h. TlC10, was prepared from T1,C03 and HClO, by metathesis in water, recrystallized twice from water and dried under vacuum. l6 Tetraethyl- ammonium perchlorate (TEAP) was purified as described previously. Stability Constants The stability constants of T1' cryptates were determined by a disproportionative reaction of TI+ cryptates with Ag' and calculated using the stability constant of the respective Ag' ~ r y p t a t e . ~ . l ~ Total metal concentrations were (1-5) x mol dm-3 and total cryptand concentrations 5 x lO-,-2 x mol dm-3.Where not available the stability constants of Ag+ cryptates were determined additionally (total Ag+ con- centration = 5 x x mol dm-3, total cryptand concentration = 5 x 2 x mol dm-3). No activity coefficient corrections were necessary in the calculation of stability constants from potentiometric data because the ionic strength was constant190 Solution Studies of Thallium(1) Cryptates Table 2. Stability constants (log 4) of Ag' cryptates at 25 "C used in this work for the determination of stability constants of T1+ cryptates (table 1) solvent (2,1,l) (2,2,1) (2,2,2) (2,,2,2) (2,,2,,2) H,O 8.5" - 9.6" 9.25b - MeOH 10.6," 14.6,' 12.2," 11.4,b 11.8; EtOH 9.70" 13.8," 11.5," 10.2,b 10.85b PC - - - - 15.5,;"' 15.4," DMSO - - - - 6.8,b DMF - - - - 9.3 ;b 9.4; "B.G. Cox, J. Garcia-Rosas and H. Schneider, J. Am. Chem. Suc., 1981, 103, 1384. bThis work, error in log &,+0.05. clog 4 + O . 1. B. G. Cox, D. Knop and H. Schneider, J. Phys. Chem., 1980, 84, 320; B. G. Cox, P. Firman, I. Schneider and H. Schneider, Inurg. Chim. Acta, 1981, 49, 153. "B. G. Cox, Ng van Truong and H. Schneider, J . Am. Chem. Suc., 1984, 106, 1273. f B . G. Cox, J. Garcia-Rosas and H. Schneider, Ber Bunsenges. Phys. Chem., 1982, 86, 293. ( I < 0.10 mol dm+)). Where the liquid junction potential was sufficiently stable over 1 h and the potential reading during a titration remained undisturbed, no TEAP was added to maintain constant ionic strength. In order to avoid the necessity of activity coefficient corrections in these cases, equal volume increments of a metal cryptate solution and an equilmolar metal ion solution were added simultaneously to the two half-cells, which contained equal amounts of a silver-ion solution.Otherwise the ionic strength was maintained constant at 0.05 or 0.10 mol dm-3 in the two half-cells and the salt bridge. The variation of log & with I was found to be smaller than the experimental error. In table 1 the stability constants of T1' cryptates determined in this study, as well as values obtained from the literature, are collected. In the course of this work several previously unreported stability constants of Ag+ complexes were also determined, and these are listed in table 2.Kinetic Measurements The dissociation reactions of Tl+ cryptates were followed conductimetrically in stopped- flow experiments using an all-glass apparatus. The variations in conductance, which followed from protonation of the uncomplexed cryptands [resulting in loss of highly mobile H+ (protic solvents) or increased dissociation of weak acids (aprotic solvents)], were monitored with a Wheatstone bridge operating at 40 kHz. An equilibrium mixture of Tl+ cryptate, with a concentration ratio of T1+ to cryptand always > 1, was mixed with an excess of acid.18 The pseudo-first-order rate constant k, was found to be linearly dependent on the acid concentration. In protic solvents strong acids (HClO,, CF,SO,H) were used as scavengers, and k, depends on the H+ concentration in the following way : l8 The mean molar activity coefficients, y + , - were calculated by using the Davies equation." In dipolar aprotic solvents a weak acid (dichloroacetic acid or trifluoroacetic acid) was used as scavenger and the dependence of k, on the acid concentration is given by20-21 k e = kci + k , [H+l/~2,* (6) k, = k, +k,,[HA].(7)B. G. Cox, J. Stroka, I. Schneider and H. Schneider 191 Table 3. Rates of dissociation (kJs-l) of TI+ cryptates at 25 "C 1.1ox 10 5.99 8.06 x 10 1.6 x lo2 2.58 x 5.21 x 1.24 4.32 MeOH EtOH < 4.10-3 5.99 x 1.34 x 0.28 0.99 AN 4.28 x 1.16 x 2.63 x 5.32 x lop2' PC 15.9 6.22 x 1.34 x 1.88 x 2.51 x lop2 DMF 1.41 x lo-' 1 . 8 2 ~ lo-' 4.07 2.10 x 10 DMSO 2.03 1.87 8.6 ca. 0.3 H2O a B. G. Cox, 3. Stroka and H.Schneider, to be published. The r,ate constants kd of the uncatalysed dissociation were determined by extrapolation of k , to zero acid concentration and are listed in table 3. These values may be combined with the stability constants in table 1 to determine k , values for cryptate formation Discussion Thallium(1) is a d" s2 ion, and has an ionic radius of 1.44 A, which is only slightly smaller than that of rubidium(I), 1.48 A.22 It is strongly poisonous for man because T1+ may substitute for K+ in cells. With respect to Pearson's hard-acid - soft-base clas~ification,~~ the behaviour of T1' corresponds to that of a soft acid, although not strongly so, and it has properties which are characteristic of both the hard acid potassium(1) and the soft acid silver(^).^^ Because of the ease with which T1' can be monitored by spectr~scopic,~~~ 26 fluores~ence,~' n.m.r.28.29 and polo rag rap hi^^'*^^ methods, in sharp contrast to the alkali-metal cations, this ion is very appropriate for a variety of experimental investigations, and it has been used as a probe for the role of K+ in biological system~.~'-~~ In fact, TI' is found to activate a number of K+-activated enzymes.32 Complexes of T1' with macrocyclic ligands which are able to wrap around the ion and to shield it partly or completely from the solvent have been studied frequently alongside those of the alkali-metal cations.The data available for 15-crown-5, 18-crown-6 and their benzo-derivatives show that log & values for the three ions K', T1' and Ag+ are of similar magnitude, and larger than those of both Na' and Rb+.33 The introduction of nitrogen donor atoms to form the diaza-18-crown4 ligand (2,2), however, leads to a strong differentiation in the behaviour of the ions.The stabilities of complexes of (2,2) decrease strongly in the series Ag+ & T1' 9 alkali-metal ions.34 A strong and specific interaction of Ag+ with the two nitrogen atoms of (2,2) results in the extraordinary large stability of the Ag' complexes, and this is also observed in silver complexes with the bicyclic cryptands. The decrease in stability of the alkali-metal complexes of (2,2) compared with T1' seems to result mainly from a strong preference of these cations for oxygen donor atoms [KS(l8c6) %- &(2,2)] rather than from any particularly strong interaction of TI+ with the nitrogen donor atoms, as found for Ag+ complexes.Considering now the results for the cryptate complexes, there are again some noticeable differences between the behaviour of the complexes of T1+ and those of the alkali-metal cations. The relative stability constants of the alkali-metal cryptates are strongly determined by the ligand cavity size, apart from a general shift towards higher stabilities for complexes of the smaller cations in poorly solvating media. Thus the most stable complexes of (2,1,1) and (2,2,1) are formed with Li' and Na+, respectively, in all solvents, and of (2,2,2) with K' in all except nitr~methane.~ The T1+ cryptate stabilities, however, are less strictly determined by the ligand's cavity size, as shown by the (& = k f / k d ) '192 Soh t ion Studies of Thallium( I) Cryp ta tes / / \ / 'x K' Li' \ \ \x Rb' \ \ \ \ \ 'x CS' /'\ I \ \\ x TI' Na+/ ' 8 K' I I \ I / / I '; Rb' I \ / \ x' Li + \ \ \ \ \ k CS' 0.6 1.0 1.1 1.6 0.1 0.6 0.8 1.0 1.2 rM*/r2,2,1 rM*/r2.2.2 Fig.1. Stability constants of (2,2,1) and (2,2,2) cryptates with alkali-metal ions and with TI+ in propylene carbonate at 25 "C. sequences of log 4 values for complexes of T1+ and the larger alkali-metal cations in different solvents :33 (2,1,1) N ~ + , ~ 1 + > K+ > Rb+ ( > cs+) (2,2,1): Tl+,Na+ > K+ > Rb+ > Cs+ (2,2,2): T1+ > K+ > Rb+ > Na+ > Cs+. A further comparison is provided in fig. 1, which shows stability constants of (2,2,1) and (2,2,2) cryptates ofTl+, alkali-metal cations and Ag' in propylene carbonate.The results, which are plotted against the ratio of cation size to cavity size, clearly show the ordering of the alkali-metal cations according to the criterion of optimal matching of ion and cavity size, and the different behaviour of T1+ and especially Ag'. For T1+, log & is similar to that of Na+ for (2,2,1) and to that of K' for (2,2,2), despite having an ionic size close to that of Rb+. Taken together, these stability constant comparisons show that (i) there is an extra stability of up to five orders of magnitude, depending upon the solvent, for cryptates of T1+ compared to those of Rb+, the alkali-metal cation of closest size, and (ii) T1+ seems to be able to adjust its ionic shape and surface charge distribution to the structures of the cavities of the cryptands much more readily than the alkali-metal cations.However, there is no clear evidence for T1+ of the remarkably specific and (probably) covalent interactions with the ligand donor atoms shown by Ag+ (e.g. fig. 1). Across the range of solvents studied the stability constants of T1+ cryptates vary by over 12 orders of magnitude (table I), but the selectivity pattern among the various ligands is remarkably independent of solvent. This is illustrated in fig. 2, which shows that in the different solvents the log &. values change in a clearly parallel manner, with the sequence for different ligands (2,2,1) 2 (2,2,2) > (2,,2,2) > (2,,2,,2) > (2,1,1). The free energies of the cryptate formation reaction [eqn (2)] may be calcuated from the stability constants in table 1 and used to discuss the free energies of transfer [eqn (l)] among the various solvents.For this propylene carbonate has been chosen as reference solvent because of its high dielectric constant, aprotic nature and lack of specific interactions with The results { - RTln [&.(S)/&. (PC)]) are listed in table 4, together with the free energies of transfer of solvated T1+, AG,,(Tl+), taken from the literature, and are shown in fig. 3. The transfer free energies of cryptate formation are strikingly independent of crypt-B. G . Cox, J . Stroka, I. Schneider and H. Schneider 193 0 (2,1,1) (2,2,1) (2,2,2) (2&2,2)(28,2&2) cryptate Fig. 2. Stability constants of TI' cryptates at 25 "C: 0, PC; Cl, MeOH, +, DMF; x , DMSO.Table 4. Transfer free energies of complex formation and of T1' solvation in kJ mol-' at 25 "C 19.4 30.4 29.3 27.9 29.7 - -8.37;b - 1 1 ' MeOH 5.3 7.8 8.6 11.5 8.6 8.4k2.2 -4.2ib -6.0id -6.9' EtOH 8.3 6.4 4.2 12.3 7.0 7.6k3.0 -9.7;" -4.0' DMF 19.6 20.1 21.2 22.5 21.0 20.9+ 1 . 1 -20.1;b -26.1 le -21.4;d DMSO 29.3 30.4 31.3 34.6 29.9 31.1 k2.1 -33.5;b ---32.9;" -30.5id H2O AN -2.5 1.20 -3.0 2.8 -2.4 -0.8k2.6 0.84;b -3.9;" -0.86;d -3.0' -22.5' - 32.4' a In the calculations always the first log & value from several ones in table 1 has been taken. Ref. (29) (B. G. Cox, TATB assumption). "ef. (33) (Y. Marcus, average values). "ef. (1) (M. K. Chantooni Jr and I. M. Kolthoff, TATB assumption). "Ref. (32) (G. Gritzner, bisbiphenyl- chromium assumption).and structure [apart from (2,1,1) in water] and show no systematic trends when considered over the range of solvents. Furthermore, a comparison with AG,,(Tl+) shown on the right-hand scale of fig. 3 demonstrates clearly the agreement between Bressiere's assumption [eqn (4)12 for TI+ cryptates and other well accepted extrathermodynamic assumptions in these dipolar aprotic and protic, non-aqueous solvents. Except for water, the AG,,(Tl+) values determined from cryptate stabilities via eqn (5) show a scatter within a given solvent which is not larger than that of the various AGtr(Tl+) data from the literature. Even (2,1, l), the smallest of the cryptands studied, with a cavity size much194 Solution Studies of Thalliurn(1) Cryptates 30- - E +e 2 20- 5 +E E g 10- W u s k 4: I 0- -10- / / I / I x G, DMF I -10 - H20 EtOH H20 MeOH A N .M . M, " K. ' 8 c. " EtOH Fig. 3. Free energies of transfer of T1' in kJ mol-' at 25 "C. [C, Cox, ref. (37); G, Gritzner, ref. (40); K, Kolthoff, ref. (1); M, Marcus, ref. (41).] smaller than the size of Tl+, does not provide an exception to this behaviour. Therefore the free energy of transfer of T1+ estimated from the stability constants of Tl+ cryptates may be used as an additional or alternative source of single-ion transfer free energies among non-aqueous solvents. The advantage of this method in comparison to other extrathermodynamic assumptions [tetraphenylarsoni~m/tetraphenylborate,~~*~~ ferro- cene/ferrocinium bisbiphenylchromium (0/ 1)39940 or others4'. 42] lies in the various and relatively simple possibilities available for the determination of the stability constants of T1+ cryptates.In water there is a significant difference, amounting to ca. 20 kJ mol-', between AG,,(Tl+) obtained from the T1+ cryptate stability constants and the literature data. Depending upon the reliability of assumptions such as PhAs+/BPh;, this indicates that AG,, [Tl(Cry+)] for transfer from propylene carbonate to water is ca. 20 kJ mol-' more positive than that of the corresponding free ligand. This probably results from a stronger hydration of the nitrogen and oxygen atoms in the latter, which are not involved in ion binding. The smallness of the water molecules may also allow them to interact with the enclosed thallium (I) ion through the space between the arms of the cryptands, and this would also influence the observed complexation behaviour.Some evidence for this comes from n.m.r. studies of T1+ cryptates, which show that spin-spin splitting between T1+ and the protons in the (2,2,2) complex is observed in CHC1343 but not in water. Also the 205Tl n.m.r. chemical shifts of TI+ cryptates in solution are independent of solvent for a given cryptand molecule, except when water is the This, however, does not seem to be a major factor in determining the transfer free energies of the Tl+ complex stabilities, as it would tend to produce a deviation in the opposite direction to that observed in fig. 3.B. G. Cox, J. Stroka, I. Schneider and H . Schneider 195 -5' 211 221 222 2822 28282 cryptate Fig.4. Stability constants (log 4; X) and rate constants for formation (log k,; 0) and dissociation (log k,; +) of T1' cryptates in propylene carbonate at 25 "C. Table 5. Rates of formation (k,/dm3 mol-' s-l) of T1' cryptates at 25 "C - 6.9 107 2.4 x 107 5.5, x 107 6.5 x 106 1.4, x lo9 9.9, x lo8 2.1, x 10' 8.6, x lo8 H2O AN - 3.5, 108 2.1, x 109 4.5, x 107 9.0, x 108 PC 6.o5X107 8.3,x 1 0 9 8 . 0 , ~ 1 0 9 1 . 0 , ~ 109 1.6,x 108 DMF - 5.7, 107 2.1 x 107 2.5, x 107 2.9, x lo7 DMSO - 1.2, x 107 3.7, x 106 4.0, x 105 ca 1 x 104 MeOH - EtOH < 5.3 x 10' 6.1, x lo8 1.3, x 10" 2.5, x lo7 3.8, x lo8 Complexation Kinetics The dissociation rate constants, k,, of the T1' cryptates (table 3) vary over about six orders of magnitude, compared with a range of about nine orders of magnitude for the corresponding stability constants (table 1).There is an evident correspondence in the variations of log k, and -log & (e.8. fig. 4), although in general this is less strict than that observed for the alkali-metal cryptates." For all of the cryptates k, is highest in water, and it is also noticeable that in water k, is a minimum for T1(2,2,2)+, whereas in all other solvents T1(2,2,1)+ dissociate most slowly. Both of these factors are probably related to the ability of water to form hydrogen bonds with the ligand donor atoms and to interact with T1+ even in the complex, as discussed above. The formation rate constants vary over a smaller range than k, values, and lie in the range 106-109 dm3 mol-1 s-', except for the benzo-substituted cryptates in DMSO (table 5).In water, DMF and DMSO they are considerably below the diffusion-controlled196 Solution Studies of Thallium(r) Cryptates Fig. 5. Variation of free energies of transfer of TI’ cryptate transition states referred to the corresponding cryptand, AGtt(T1+..Cry) - AGJCry), with solvent donor number, ND. [AGJTI’) from ref. (1) and for EtOH from ref. (39).] limit, but in the poorer cation solvents they approach the maximum values observed for multistep substitution complexations reaction^.^' It is of interest to consider the variations in the free energies of the transition states for the various complexation reactions in a similar manner to that discussed above for the stable cryptate complexes. The stronger contribution of the dissociation rate constants to the observed variations in stability constants indicates that the transition state for complex formation lies closer to the reactants than to the products, and this might also be expected to show up in its solvation behaviour.The free energy of transfer of the transition state, AGti(Tl+ ..Cry), referred to propylene carbonate as reference solvent (R) is related to the formation rate constants and the free energies of transfer of the reactants in solvent (S) by - RT In [k,(S)/k,(R)J = AGL(Tl+.--Cry) - AGJCry) - AGt,(T1+). (8) A comparable assumption to that in eqn (4) but involving the transition state rather than the stable complex, would result in a correlation between the left-hand side of eqn (8) and AG,,(Tl+). In fact, no such correlation is observed, and indeed it would require k, to be independent of solvent, i.e.the free energy of transfer of the transition state is equal to that of the stable cryptate: AGti(Tl+-..Cry) = AG,,(TlCry+) - RTln [k,(S)/k,(R)]. (9) Thus in terms of solvation there is in the transition state an additional interaction between the solvent and T1+ and the ligand binding groups over that of the stable cryptate. This is consistent with the T1+ being at least partly outside of the ligand’s cavity in the transition state. The specific solvent dependence of this interaction is illustrated in fig. 5, in which AGi,(Tl+-..Cry)-AG,,(Cry) (calculated using eqn (8) and the data in tables 4 and 5) is plotted against the donor number of the The linearity observed is independent of which of the extrathermodynamic assumptions are used to estimate AG,,(Tl+), and undoubtedly reflects mainly the (residual) interaction between T1+ in the transition state and the solvent.This is confirmed by a parallel behaviour with solvent of AG,,(Tl+) and AGi,(Tl+---Cry) except for a change in the sequence of AN, MeOH and EtOH. This latter effect is indicative of the solvation of the transition state also involving the binding groups of the cryptands.B. G. Cox, J . Stroka, I. Schneider and H. Schneider 197 Conclusion (i) Thallium(1) forms stable complexes with a range of cryptand ligands in water and non-aqueous solvents. The stability constants are very sensitive to solvent (variations over 12 orders of magnitude in the stability constants were observed in the different solvents).(ii) The T1+ complexes are more stable and less strongly dependent upon ligand cavity size than those of alkali-metal cations of similar ionic radii (K+, Rb+). The effects, however, are less marked than those of the corresponding Ag+ complexes. (iii) The solvent dependence of the complex stabilities are governed mainly by changes in the solvation of TI+. In a range of dipolar aprotic and polar, protic solvents the assumption that changes in the free energies of the cryptate complexes and the free ligands are equal leads to values for AGtr(Tl+) among solvents which are in good agreement with literature values based on other commonly used extrathermodynamic assumptions. (iv) The formation rate constants normally lie in the range 106-109 dm3 mol-' s-', depending upon the solvent and ligand.The dissociation rate constants vary over a wider range, and correlate more closely with the complex stabilities. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 M. K. Chantooni Jr and I. M. Kolthoff, J. Soln Chem., 1985, 14, 1. M. E. Lejaille, M. H. Livertoux, G. Guidon and J. Bessiere, Bull. SOC. Chim. Fr. 1978,I-373 ; J. Bessiere and M. F. Lejaille, Anal. Lett., 1979, 12, 753. J. Gutknecht, H. Schneider and J. Stroka, horg. Chem. 1978, 17, 3326. A. F. Danil de Namor, L. Ghosaini and W. H. Lee, J. Chem. SOC., Faraday Trans. I , 1985, 81, 2495. A. E. Danil de Namor, H. Berroa de Ponce and E. C. Viguria, J. Chern. SOC., Faraday Trans. I , 1986, 82, 281 1.A. F. Danil de Namor and H. Berroa de Ponce, J. Chem. SOC., Faraday Trans. I , 1987, 83, 1569. A. F. Danil de Namor and L. Ghosaini, J. Chem. SOC., Faraday Trans. I , 1985, 81, 781. A. F. Danil de Namor, L. Ghosaini and T. Hill, J. Chem. SOC., Faraday Trans. I , 1986, 82, 349. A. F. Danil de Namor and L. Ghosaini, J. Chem. SOC., Faraday Trans. I , 1986, 82, 3275. R. J. P. Williams, Q. Rev. Chem. SOC., 1970, 24, 331. J. P. Manners, K. G. Morallee and R. J. P. Williams, J . Chem. SOC. D, 1970, 965. S. Krasne and G. Eisenman, in Membranes, a Series of Advances, ed. G. Eisenman (Marcel Dekker, New York, 1973), vol. 2, pp. 277-328. A. G. Lee, J. Chem. SOC. A, 1971, 880; 2007. C. H. Sueltor, in Melal Ions in Biological Systems, ed. H. Sigel (Marcel Dekker, New York, 1974), B. G.Cox, J. Garcia-Rosas and H. Schneider, J. Am. Chem. SOC., 1981, 103, 1384. I. M. Kolthoff and M. K. Chantooni Jr, J. Phys. Chern., 1972, 76, 2024. B. G. Cox, H. Schneider and J. Stroka, J. Am. Chem. SOC., 1978, 100, 4746. B. G. Cox, J. Garcia-Rosas and H. Schneider, J. Am. Chem. Soc., 1981, 103, 1054. C. W. Davies, lon Association (Butterworths, London, 1962). B. G. Cox, J. Garcia-Rosas and H. Schneider, J. Am. Chem. SOC., 1982, 104, 2434. B. G. Cox, W. Jedral, P. Firman and H. Schneider, J. Chem. Soc., Perkin Trans. 2, 1981, 1486. L. Pauling, The Nature of the Chemical Bond (Cornell University Press, New York, 3rd edn, 1960). R. G. Pearson, J. Am. Chem. SOC., 1963, 85, 3533; Science, 1966, 151, 172. E. C. Taylor and A. McKillop, Acc. Chem. Res., 1970, 3, 338. R. Gresser, D. W. Boyd, A. M. Albrecht-Gary and J. P. Schwing, J. Am. Chem. Soc., 1980, 102, 651. B. G. Cox, J. Stroka and H. Schneider, unpublished work. G. Cornelius, W. Gartner and D. H. Haynes, Biochemistry, 1974, 13, 3053. D. Gudlin and H. Schneider, Inorg. Chirn. Acta, 1979, 33, 205. J. F. Hinton and K. R. Metz, in NMR ofNewly Accessible Nuclei, ed. P. Laszlo (Academic Press, New York, 1983), vol. 2, p. 367 H. Schneider and H. Strehlow, J. Electroanal. Chem., 1966, 12, 530. E. L. Yee, J. Tabib and M. J. Weaver, J. Electroanal. Chem., 1979, 96, 241. J. J. Dechter, Progr. Knorg. Chem., 1982, 29, 285. R. M. Izatt, J . S. Bradshaw, S. A. Nielsen, J. D. Lamb, and J. J. Christensen, Chem. Rev., 1985, 85, 271. vol. 111, p. 201.198 Solution Studies of Thalliurn(1) Cryptates 34 B. G. Cox, P. Firman, H. Horst and H. Schneider, Polyhedron, 1983, 2, 343. 35 H. L. Friedman and C. V. Krishnan, in Water, A Comprehensive Treatise, ed. F. Franks (Plenum Press, 36 R. Alexander and A. J. Parker, J. Am. Chem. SOC., 1967, 89, 5549. 37 B. G. Cox, Annu. Rep. Progr. Chem., Sect. A , 1973, 70, 249. 38 H. M. Koepp, H. Wendt and H. Strehlow, Z. Elektrochem., 1960, 64,483. 39 G. Gritzner, V. Gutmann and R. Schmid, Electrochim. Acta, 1968, 13, 919. 40 G. Gritzner, Inorg. Chim. Acta, 1977, 24, 5 . 41 Y. Marcus, Rev. Anal. Chem., 1980, 5, 53. 42 0. Popovych, Crit. Rev. Anal. Chem., 1970, 1, 73. 43 J-M. Lehn, J. P. Sauvage and B. Dietrich, J. Am. Chem. SOC. 1970, 92, 2916; E. Grell, personal 44 R. Winkler, Dissertation, (Gottingen University 1969). 45 V. Gutmann and E. Eychera, Inorg. Nucl. Chem. Lett., 1966, 2, 257; V. Gutmann, Coordination New York, 1973), vol. 3, pp. 1-118. communication. Chemistry in Non-aqueous Solutions (Springer, Wien, 1968). Paper 711779; Received 5th October, 1987

ISSN:0300-9599    

DOI:10.1039/F19898500187

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1989, 85(2), 199-206 The Oxidative Coupling of Methane on Lithium Nickelate( 111) Masaharu Hatano and Kiyoshi Otsuka* Department of Chemical Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152, Japan Kinetic studies and isotopic exchange measurements (CH,-CD, and 1602-1802) of the oxidative coupling of methane over stoichiometric LiNiO, indicate a redox mechanism involving lattice oxygen atoms. The formation of C, products is second-order in methane, both in the presence and absence of gaseous oxygen. Methane is dissociatively adsorbed on Ni3+-02- sites, and the rate-determining step is the coupling of adsorbed CH,. Reduction of the catalyst by methane forms NiO, over which deep oxidation occurs. Adsorbed oxygen or gaseous oxygen is responsible for the deep oxidation.The oxidative coupling of methane is a potentially attractive method for the production of ethylene from natural gas. Since Keller and Bhasinl reported the synthesis of C, compounds (C,H, + C,H,) by partial oxidation of methane over metal oxides, many groups have published preliminary results on catalytic activity and C, selectivity for this reaction., We have shown that Li-doped NiO gives fairly good yield of C, compounds and C, ~electivity.~ The reaction was suggested to proceed via the redox of surface lattice oxygen atoms of the o x i d e ~ . ~ , ~ However, the fundamental studies carried out so far are not sufficient to clarify the mechanism of methane activation on solid surfaces. We now report kinetic studies on the oxidative coupling of methane over a stoichiometric solid solution of lithium and nickel oxide, LiNiO,.The picture of methane activation and the detailed reaction mechanism will be discussed. Experimental The LiNiO, used was prepared by means of the impregnation method using powder NiO and aqueous solution of LiNO, (Ni : Li = 1 : 1). The Li-impregnated NiO was calcined in air at 673 K for 2 h and subsequently at 1073 K for 20 h. X.r.d. analysis for this sample showed the transformation to the homogeneous solid solution of Li and NiO, which is wetten by the formuia Li,(Ni2+),-2,(Ni3+),0.4 Lattice parameters of this sample, a = 2.900 A and c = 14.25 A, assuming rhombohedra1 structure, suggested the for- mation of LiNiO (1 : 1) solid solution Li+Ni3+0,.5,6 The surface area of the sample was 0.33 m2 g-'.Kinetic studies were carried out using a fixed-bed reactor with a conventional gas-flow system at atmospheric pressure using helium as a carrier gas. The amount of catalyst used in the reactor was between 0.01 and 1 .OO g. The volume of the reactor was 15.3 cm3. The range of reactant flow rate was 20-150 cm3 (s.t.p.) min-l. The gas-solid reaction of methane with the catalyst and the CH,-CD, exchange and oxygen tracer experiments were carried out using a closed gas-circulation apparatus of ca. 360 cm3 dead volume. A small quantity of the gas in the system was sampled during the reaction and the relative quantities of the isotope-exchanged products were measured using a quadrupole mass spectrometer. The total amounts of isotopic methanes (CH, + CH3D + 199200 Oxidative Couplings of Methane on Lithium Nickelate(m) ( w / F ) / l ( ~ ~ g h dm3 Fig.1. Yields of products as functions of W/F. A, CO,; 0, C, total; 0, C,H,; A, C,H,. T = 973 K, CH, pressure = 40.5 kPa, 0, pressure = 20.3 kPa. CH4 pressure/kPa Fig. 2. Formation rates of C, and CO, as functions of CH, pressure. 0, CO, (973 K); 0, C , (973 K); A, CO, (953 K); A, C, (953 K). 0, pressure = 5.01 kPa, W/F = 1.67 x g h dm-3. CH,D2 + CHD, + CD,) and oxygens (l80l8O + 1s0180 + l60l6O) were measured by gas chromatography. Thus the absolute amounts of each product were evaluated. The conversion of methane, the rates of formation of the products, the selectivities and the yields of the products were calculated on the basis of the carbon number of the reacted methane.Results and Discussion Kinetic Studies on Oxidative Coupling of CH, over LiNiO, The oxidation of methane over LiNiO, in temperature range 873-1023 K produced C2H,, C2H,, CO, and H20. Kinetic studies on this reaction were carried out using a fixed-bed reactor with the gas flow apparatus under the conditions where the conversion of 0, was < 5 YO. Fig. 1 shows a plot of the yields of C, compounds and CO, as functions of W/F (= weight of catalysts/flow rate of reactants). The formation of ethylene was detected only at the W/F > 3 x g h dm-3. It is clear from the curves for C,H, and C,H, formation that C2H, is formed successfully from C,H, (2CH, -+ C,H, --+ C,H,). The straight lines from the origin for the yields of CO, and C, suggest that the formation of CO, is not ascribed to the oxidation of C, compounds, but to the oxidation of methane itself.M.Hatano and K. Otsuka 20 1 '0 10 20 Q pressure/kPa Fig. 3. Formation rates of C, and CO, as functions of 0, pressure. 0, CO, (973 K); 0, C, (973 K); A, CO, (953 K); A, C, (953 K). CH, pressure = 40.5 kPa, W/F = 1.67 x g h dm-3. CH4 pressure/kPa Fig. 4. Initial rate of formation of C , as a function of CH, pressure (gas-solid reaction at 973 K). W = 1 .OO g. Fig. 2 shows the rates of C, and CO, formation as functions of CH, pressure. The experiments were carried out at 953 and 973 K and at a constant pressure of oxygen (5.0 kPa). The results in fig. 2 show that the rate of formation of C , compounds depends roughly on the square of the CH, pressure.However, the rate of CO, formation does not change appreciably at pressures > 10 kPa. Thus the selectivity to C , hydrocarbons increases sharply with increasing methane pressure. Fig. 3 shows the effect of oxygen pressure on the rates of formation of C , and CO,. The rate of C, formation decreases gradually on increasing the oxygen pressure, but the rate of CO, formation increases with pressure. The decrease in the rate of formation of C, cannot be ascribed to the deep oxidation of C, because the latter reaction was not appreciable under the experimental conditions applied in this work (fig. 1). Rather, it may be ascribed to competitive adsorption of methane and oxygen on the active sites for C, formation. It was shown previously3 that the reaction of methane with the lattice oxygen atoms of LiNiO, produced C , compounds selectively.Therefore, the effect of methane pressure on the rate of the gas-solid reaction has been examined at 973 K in the absence of202 Oxidative Couplings of Methane on Lithium Nickelate(1rr) -1.2 -1.5 n * 'M k 2 -1.8 2 41 - v M -2 1 -2.4 06 Id KIT Fig. 5. Temperature effects on the formation rates of C, and CO,. 0, C,; A, CO,. CH, pressure = 40.5 kPa, 0, pressure = 20.3 kPa, W/F = 1.67 x lop3 g h dm-3. gaseous oxygen. The C , compounds were produced very selectively (> 95 O h ) in the early stages of the reaction (< 5 min). The initial rate of C, formation is plotted as a function of methane pressure in fig. 4; the results show that the rate depends on the square of methane pressure, similar to the results shown in fig.2. Moreover, note that the rates of C, formation in the presence (fig. 2) and absence (fig. 4) of gaseous oxygen are approximately the same at the same methane pressure. These observations strongly suggest that the oxidative coupling of methane over LiNiO, proceeds via the reaction of CH, with surface lattice oxygen atoms. Temperature effects on the rates of CO, and C, formation are shown in fig. 5. The straight line for the formation of C , compounds give an apparent activation energy of 250 10 kJ mol-'. The results in fig. 5 show that the C, selectivity increases sharply with a rise in temperature. CH4-CD, Exchange Hydrogen exchange between CH, and CD, (1 : 1) on LiNiO, has been examined at 973 K.The kinetic curves for the distribution of deuterated methane are shown in fig. 6. The progress of the exchange reaction as indicated in fig. 6 suggests that methane is dissociatively adsorbed on the catalyst. Moreover, the kinetic curves suggest that the exchange occurs stepwise, because CHD, and CH,D predominate over CH,D, : CH,D, CD,H. (1) CH, s CH, + H CD, CD, + D The isotope effect by which CD,H is formed in preference to CH,D is not easily explained. The observation might be ascribed either to a higher surface concentration of CD, than CH, or to a higher concentration of H than D. Moreover, the formation of H,O, HDO and D,O may further complicate the situation.M. Hatano and K. Otsuka 203 reaction time/min Fig. 6. CH,-CD, exchange at 973 K. Initial pressure CH, = CD, = 2.7 kPa.0, CH,; a, CD,; 0, CH,D; 0, CH,D,; A, CD,H. reaction time/min Fig. 7. Oxygen tracer experiments at 973 K. Initial reactants : CH, (5.3 kPa), 180180 (0.53 kPa), LiNiO, (1.00 8). Upper plot: Changes in the amount of gaseous oxygen isotopes. V, lsO180; a, 1601sO; A, 160160. Lower plot: Changes in the amount of CO, isotopes. 0, C160160; A, C160180; 0, C180180. Dotted curve: amount of C, formed. Oxygen Tracer Experiments The distribution of l80 in the oxygen-containing products, i.e. CO, and H,O, has been followed during the oxidative coupling of methane (5.3 kPa) with I8O2 (0.53 kPa) as the initial gas mixture at 973 K using a closed gas-circulation apparatus. The ratio of the amount of gaseous oxygen to that in the catalyst at the starting point was roughly 6 x The kinetic curves of the C160160, Cl60l8O and C180180 formed are shown in fig.7. Since a considerable amount of CO, was captured in the catalyst,* the amounts204 Oxidative Couplings of Methane on Lithium Nickelate(r1r) 100 @ $ 5 0 Fig. 8. Changes in the mole fractions of H2"0 and H,lBO formed during oxidation in fig. 7. 0, H2160; A, H2lB0. of CO, isotopes shown in fig. 7 include both CO, on the catalyst and that in the gas phase, assuming the same isotopic compositions of CO, in both phases. Changes in the amounts of the gaseous oxygen isotopes are shown in the upper part of fig. 7. The dotted curve in fig. 7 shows the kinetic curve of the C, compounds produced. C2H6 was the main C, product in the early stages of the reaction.The results in the upper part of fig. 7 show that oxygen exchange between gaseous 0, and LiNiO, occurs rapidly. All the oxygen in the gas phase was consumed in the oxidation of methane within 15 min. However, the rate of total CO, in the gas phase still increased after 15 min owing to the reaction of CH, with lattice oxygen atoms of the catalyst. Fig. 8 shows the changes in the mole fractions of H,lsO and H,180 in the gas phase measured at the same time during the oxidation of CH, in fig. 7. We confine our attention to the early stages of the reaction, at which point the products and the reduction of the catalyst do not seriously complicate the situation. Note that the l80- containing CO, (C180180 and C'80160) are the main products in the early stages of the reaction (fig. 7).This observation clearly shows that the adsorbed or gaseous oxygen is responsible for the deep oxidation of methane to CO,. On the other hand, the results in fig. 8 show the preferential contribution of lattice oxygen atoms to the formation of H,O in comparison with the contribution of adsorbed oxygen (or gaseous oxygen). Reaction Mechanism As suggested earlier with regard to the results in fig. 1, C, compounds and CO, are produced concurrently from methane. The quite different pressure effects on the rates of formation of C, and CO, observed in fig. 2 and 3 strongly suggest that both reactions proceed via different reaction intermediates or on different active sites. The observation that the rate of formation of C, products is second-order in methane pressure has not been reported previously.2 This observation implies that the coupling of methyl groups adsorbed is the rate-determining step in the oxidative coupling of methane.On the basis of the kinetic results described earlier, we propose the following reaction mechanism. The CH,-CD, exchange experiments have suggested the dissociative adsorption ofM. Hatano and K. Otsuka 205 methane on LiNiO, (fig. 6). Therefore, let us hypothesize that this adsorption occurs readily on a pair of sites comprising Ni3+-02- on LiNiO, as follows: It is generally suggested that the vacant d-orbital of a transition-metal cation should make electrophilic attachment on the oCH orbital of methane, resulting in the breaking of the C-H bond. This C-H activation on LiNiO, must be promoted by the resulting formation of OH with the partner lattice oxygen anion of Ni3+.The initial rates of adsorption and desorption of CH, [eqn (2)] can be roughly estimated from the initial slopes of the kinetic curves in fig. 6, neglecting the isotopic effect of H and D. Assuming a steady-state concentration of methyl groups in the early stages of the reaction, the rates of adsorption and desorption were estimated to be 2.6 x mol g-' h-', respectively. The initial rate of C,H6 formation [eqn (3)] was 9.1 x lop4 mol g-l h-l from the dotted curve in fig. 7. Note that the rates of the forward and reverse steps in eqn (2) are faster than the rate of C,H, formation. When the migrations of CH, and H on the surface are slower than the adsorption and desorption rates in eqn (2), the true values of the latter two cannot be estimated by CH,-CD, exchange experiments because the observable exchange rate cannot exceed the rates of migration of CH, (or CD,) and H (or D).The adsorption and desorption rates estimated above are the lower limits for the rates of the both steps. Therefore, it seems reasonable to assume that reaction (2) is in equilibrium and the coupling reaction (3) is the rate-determining step. This assumption explains the observation that the rate of formation of C, compounds depends on the square of the methane pressure (fig. 2 and 3). The large activation energy for the formation of C , compounds (fig. 5) implies that the bond dissociation energy of CH3-Ni2+ is fairly large, and so the surface migration of CH, groups must be restricted.and 1.7 x Oxygen Species Responsible for the Formation of C,H, and CO, On the basis of the results of the oxygen-isotope experiments (fig. 7 and 8) we can comment further on the oxygen species responsible for the reaction. As described earlier, the selective formation of C2H6 occurs through reactions (2) and (3). Here, the lattice oxygen atoms of LiNiO, play an important role in the activation of methane on eqn (2). The formation of OH in eqn (2) would facilitate the forward reaction by lowering the activation energy. The OH formed in eqn (2) must be desorbed as water as follows: (4) where O* is a lattice oxygen atom or oxygen originating from the lattice oxygen atoms. This is one reason why the mole fraction of H2160 observed was greater than that of H,"O in fig.8. However, the amount of H,O accompanied by deep oxidation of CH, was at least twice as large as the amount of H,O from which hydrogen atoms had arisen through the initial abstraction from CH, in reaction (2). The abundance of H,160 observed in fig. 8 can be explained by the assumption that the lattice oxygen atoms also oxidize the methane hydrogen during deep oxidation. However, we will not discuss this further, since the situation may be complicated by the possible occurrence of hydrogen migration on the surface. 20*H + H,O* + O* 8 FAR I206 Oxidative Couplings of Methane on Lithium Nickelate(m) The results in fig. 7 clearly indicate that CO, is generated via the reaction with adsorbed or gaseous oxygen. Thus C, compounds are produced with 100% selectivity in the absence of gaseous oxygen in the early stages of the rea~tion.~ The reduction of LiNiO, by CH, inevitably generates NiO according to the following stoichiometric reaction :, 2LiNi0, + 2CH, + Li,O + 2Ni0 + C,H, + H20.Li20 + 2Ni0 + 9, + 2LiNi0,. ( 5 ) (6) We believe that the deep oxidation of methane occurs on a different active site, i.e. on NiO present on the surface under steady-state reaction conditions. In fact, NiO catalysed only the deep oxidation of methane under the experimental conditions applied in this work. The presence of gaseous oxygen is indispensable for regenerating LiNiO, :, References 1 G. E. Keller and M. M. Bhasin, J. Catal., 1982, 73, 9. 2 W. Hinsen, W. Bytyn and M. Beams, Proc. 8th Int. Congr. Catal., (1984), vol. 3, p. 58; T. Ito, Ji-Xiang Wang, Chiu-Hsun Lin and J. H. Lunsford, J. Am. Chem. SOC., 1985, 107, 5062; K. Otsuka, K. Jinno and A. Morikawa, Chem. Lett., 1985,499; K. Otsuka, K. Jinno and A. Morikawa, J. Catal., 1986,100, 353; K. Otsuka and T. Komatsu, Chem. Lett., 1987,483; T. Moriyama, N. Takasaki, E. Iwamatsu and K. Aika, Chem. Lett., 1986, 1165; I. Matsuura, Y. Utsumi, M. Nakai and T. Doi, Chem. Lutt., 1986, 1981; H. Imai and T. Tagawa, J. Chem. SOC., Chem. Commun., 1986, 52; K. Asami, S. Hashimoto, T. Shikada, K. Fujimoto and H. Tominaga, Chem. Lett., 1986, 1233; I. T. A. Emesh and Y. Amenomiya, J. Phys. Chem., 1986,90,4785; N. Yamagata, K. Tanaka, S. Sasaki and S . Okazaki, Chem. Lett., 1987, 81; C. A. Jones, J. J. Leonard and J. A. Sofranko, J. Catal., 1987, 103, 31 1. 3 K. Otsuka, Qin Liu, M. Hatano and A. Morikawa, Chem. Lett., 1986, 903; K. Otsuka, Qin Liu and A. Morikawa, Inorg. Chim. Acta, 1986, 118, L23. 4 M. Hatano and K. Otsuka, Inorg. Chim. Acta, 1988, 146, 243. 5 L. D. Dyer, B. S. Borie, Jr and G. P. Smith, J. Am. Chem. SOC., 1954, 76, 1499. 6 N. Perakis and F. Kern, C.R. Acad. Sci. Paris, Ser. B, 1969, 269, 281. Paper 712247 ; Received 23rd December, 1987

ISSN:0300-9599    

DOI:10.1039/F19898500199

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1989, 85(2), 207-222 Thermodynamics for Chemical Equilibria and Kinetics in Solution at Constant Volume Lidia M. P. C. Albuquerque and Joiio Carlos R. Reis Departamento de Quimica, FacuIdade de Cismias, Centro de Electroquimica e Cine‘tica da Universidade de Lisboa, 1294 Lisboa Codex, Portugal The relation between isobaric and isochoric equilibrium parameters has been examined from a new viewpoint based on specifically designed partial molar properties at constant temperature and solvent concentration. These are defined by and solutes in the corresponding ideal solution conform to x R ( T , ‘A) = (ax/anR>’f’,,A,,’ @( T, cA) = PR( T, c,) + RTln (rR/ri) where A is the Helmholtz energy and rR = nR/nA. On this basis, standard equilibrium constants are introduced for reactions at constant T and c , not involving the solvent stoichiometrically.These equilibrium constants are related to an ideal process consisting of mixing standard solutions containing the reactants, complete transformation of reactants into products and separation to standard solutions containing the products. This ideal process at constant T and c, is rendered isochoric (in the sense of constant total volume) by an appropriate selection of standard solution compositions. A whole set of standard molar quantities of reaction Ar Xo( T, c,) is defined in terms of xi( T, c,). Exact equations linking Ar Xo( T, c,) where X = A , U, S and C,, with the more usual A, Xo( T,p) quantities where X = G, H, S and C,, respectively, are derived.Particular attention has been paid to the thermodynamics of the quasi-equilibrium of activation at constant ( T , p ) and at constant (T,cA), and to their interrelationship. The results are compared with those of previous approaches and shown to be generally equivalent in the limit of infinitely dilute solutions. This approach is unique in its interpretative capabilities and in giving a rationale of the ‘pressure of activation’. The quantities x,(T, c , ) and X’,(T, cA) are suitable for studying mineralogically and metallurgically important interstitial solid solutions. 1. Introduction Half a century has elapsed since Evans and Polanyi’ advanced the original proposal that a better insight into rate processes in solution could arise from measuring their dependence on temperature at constant volume.The phrase ‘constant volume principle ’ (CVP) was coined by Brummer and Hills2 to express such an interest in isochoric activation parameters because, in Hills’ ‘most theoretical descriptions of condensed phases are based on statistical-mechanical principles which lead to the Helmholtz free energy and thus to AUv.’ However, Blandamer and c o - ~ o r k e r s ~ - ~ have recently raised some doubts on the usefulness of the CVP on the grounds that the thermodynamic meaning of conventional isochoric activation parameters is not clear. More specifically, Blandamer et al.5 have asked ‘what volume is held constant?’ and ‘what reference states are used in the definition of isochoric activation parameters?’ Although these questions were then partly and further clarified by 207208 Constant-volume Solution Thermodynamics Wright,’ the arguments advanced by these authors4v7 were not accepted by Whalley.8 The aim of the present paper is thus contributing ‘to find the point of view from which the subject appears in its greatest simplicity.’ 2.Thermodynamics of Chemical Equilibria in Solution 2.1. Isothermal-Isochoric Conditions Let us consider the general reaction in a solvent A -ZR V , R e x p V , P (1) where vi is the stoichiometric coefficient of chemical species i = R, P, which are assumed to be present at chemical equilibrium. Under these conditions it follows from (2) thermodynamics that where pi is the chemical potential of species i. Eqn (2) expresses a general condition without reference to how equilibrium was attained.However, in order to use theoretical methods of solution chemical thermodynamics (partial molar properties, ideal solution, solute standard state), it is convenient to assume further that the reacting solution reaches equilibrium while holding constant two independent intensive thermodynamic variables. The most commonly made is that of isothermal-isobaric equilibrium assumption which allows the use of partial molar properties of substance B at constant temperature T and pressure p . These are defined by where X stands for any extensive property of the reacting solution and n’ indicates that the amounts of substance of all components apart from B are held constant. From the identity pB = GB(T,p), where G is the Gibbs energy, results the equivalent form of condition (2) : Ci vip;q = 0 x13(T, P ) = p , n’ Z i v i F ( T , p ) = 0.(3) Now the CVP requires derivatives to be taken at constant total volume I/ of the equilibrium reacting solution ; however, as noted b e f ~ r e , ~ f xB(T, = V , n‘ (4) is a pseudo-partial molar property because the independent variable I/ is extensive. This difficulty can be circumvented by defining partial molar properties at constant temperature and solvent concentration, xB(T7 ‘A) = cA, n‘ ( 5 ) where c, = n,/V, and whose formalism is developed in Appendix 1. Since the solvent was assumed to be a non-reacting species, then for B # A constraints ( T , V,n’) and (T, c,, n’) become identical and, from eqn (4) and (5), + Xi( T, c,) = xt( T, V ) ; i = R, P. It follows from eqn (A 1.5) that pi = xi(T, c,), where A is the Helmholtz energy.Hence equilibrium condition (2) can be written as Ci vi @( T, c,) = 0. (6) Just as the usual isothermal-isobaric treatment of chemical equilibria is based on eqn (3), so too is provided an equally fundamental basis for the thermodynamic analysis of isothermal-isochoric processes in solution by eqn (6). In fact, a true isochoric process (in the sense of constant total volume) is observed in a closed system where a chemical reaction is progressing towards equilibrium under conditions of ‘ iso-solvent-con- centration ’, provided the solvent is not involved stoichiometrically.L. M. P. C. Albuquerque and J . C. R. Reis 209 2.2. Isothermal-Isochoric Equilibrium Constant In order to express the composition dependence of a solute chemical potential at constant Tand c,, we write where R is the gas constant, ri = ni/nA is the solute mole ratio and yi is an activity coefficient.This is a dimensionless quantity designed to measure the difference between the chemical potential of a species in a real solution and in an ideal reference solution of that solute in the same solvent and at the same T, c, and Ti. By convention, lim yi = 1. Therefore X:(T,c,) is the partial molar Helmholtz energy of species i in the ideal solution at arbitrary solute mole ratio r:. The definition and properties of the ideal solution for constant (T, c,) are given in Appendix 2. all f i + O Combining eqn (6) and (7) yields Ei vi x( T, c,) = - RTln [ n , ( y ~ q r : q / r ~ ) Y i ] .(8) This equation suggests defining a standard equilibrium constant for conditions of constant (T, cA) as Equilibrium constants so defined are related not only to the properties of the actual equilibrium mixture but also to those of ideal reference solutions. In general, given a pair ( y , z ) of independent intensive variables and the corresponding ideal reference solutions, the change in (molar) standard property X due to a chemical reaction at specified values of y and z is defined as (10) (1 1) We now enquire about the conditions under which KO( T, c,) can be regarded as a true isothermal-isochoric equilibrium constant. We begin by noting that eqn (1 1) relates K O ( T, c,) for reaction (1) at chemical equilibrium with Ar A"( T, c,) referred to an ideal thermodynamic process at constant (T, c,), as depicted in table 1.The initial and final states of this process are constituted by, respectively, the R and the P disjoint ideal solutions described in table 1. Next let the arbitrary r; be so chosen that the ideal process involves no change of total solvent amount. From table 1, this condition reads Ar Xo( y , z ) = Ci vi Xp( y , z). A, A"( T, c,) = - RTln KO( T, c,). Hence, by using definitions (9) and (lo), eqn (8) takes the simple form: Furthermore, if the rp comply with eqn (12), it follows from the values in table 1 for volumes of standard solutions that the total ideal volume, Vid = -CR(v, mol/rg)/c, = Cp(vp mol/ri)/c, (13) is kept constant. We have therefore identified a general isochoric process carried out at constant temperature, solvent concentration and total volume, and comprising the following steps: (i) mixing the standard solutions containing the reactants; (ii) one mole of chemical transformations" according to eqn (1); and (iii) separating into standard solutions containing the products. In conclusion, K"(T, c,) given by eqn (9) becomes an isothermal-isochoric equilibrium constant whenever the ideal isochoric condition [eqn (1 2)] is fulfilled.210 Constant-volume Solution Thermodynamics Table 1.Ideal thermodynamic process at constant T and c, ideal process : - C, v, R(id sln : T, c,, r i ) -, Xp vp P(id sln : T, c,, rOp) specification of each ideal standard solution n, = - v, mol nA = - vR mol/ri V = - v, mollc, r: n p = v,mol nA = vpmol/r~ V = v, mollc, r; real system : closed ; fixed T, c, ; chemical equilibrium : - C, vR R(reacting sln : T, c,, r?) e C, v, P(reacting sln : T, c,, r;q) For later use, we record here the well known relationships A,.G"(T,p) = -RTln Ko(T,p) KO( T, p ) = ni(ffqxfq//xP)"~ and where xi are mole fractions andh are activity coefficients.2.3. Relating A,. Xo( T, c,) with Ar Xo( T,p) Let us relate iso-solvent-concentration to isobaric quantities for the pairs: Ar Xo( T, cA), where X = A , S, U and C,, and, respectively, A,. Xo(T,p), where X = G, S, H and C,. Here S is entropy, U is internal energy, H is enthalpy, C , is isochoric thermal capacity and C , is isobaric thermal capacity. By systematic use of eqn (lo), this problem is transIated into an exercise in relating partial molar properties of different kinds.However, this method requires a common thermodynamic state being fixed so that equations from Appendix I can be used. The state at infinite dilution is the most convenient and practical choice. Such a state is characterized by COA = l/C(T,PO) (16) where V z is the molar volume of pure solvent. The following general procedure will be used in obtaining the various relationships. (i) From eqn (lo), we write (1 7) and (1 8) (ii) Xy(T,ci) and X:(T,po) in the above equations are expressed in terms of, respectively, Xid(T, ci) and XY(T,po) at a common arbitrary composition by using formulae in Appendix 2 for the former. (iii) Equations so obtained, one for constant (T, c i ) and the other for (T,po), are subtracted from each other and the infinite-dilution limit of the resulting equation is taken.In this limit, Ar Xo( T, c:) = Zi vi a;( T, c i ) Ar Xo( T, po) = X i vi Sp( T, po). q"( T, C i ) = X?( T, C i ) and X y y T , p o ) = S?(T,po). Since now RF(T, c i ) and X,"(T,p,) are properties of the same solution, equations from Appendix 1 are used to connect them. (iv) Lastly, standard changes are obtained by summation as indicated in eqn (1 7) and The aforementioned relationships are readily derived in the following sequences of (18)- operations by referring to steps (ii)-(iv) above.L. M. P. C. Albuquerque and J. C. R. Reis 21 1 The Relationship between AT A"(T, c:) and AT Go(T, po) (ii) A;(T, ci)-RTln r: = Ay(T, c i , ri) - RTln ri cp( T,p,) - RTln xP = @'( T,po, xi) - RT In xi where xi and r; are chosen so that xi = xari.(iii) $IT, c",-GP(T,p0)--RTln(rP/xp) = Af.d( T, c i , ri) - e( T,p,, xi) + RTln x i = A;"( T, c i ) - G?( T,p,) = o because the left-hand side is a constant and x i = 1 at infinite dilution, and the last equality is a consequence of eqn (A 1.5). The Relationship between A,. So(T, c:) and Ar So((T, po) (iv) A,Ao(T, c:) = A,Go(T,po)+RTlnni(r~/x~)'~. (19) (ii) sp( T, ci) + R In rp = Sid( T, c i , ri) + R In r; s:( T, po) + R In xp = sid( T, p,, xi) + R In xi. sP( T, c i ) - sp( T, po) + R In (rP/xP) (iii) = sid( T, c i , ri) - sid( T, po, xl) - R In x i = S?( T, c:) - S?( T,p,) = -<a,*/.,*) ~P(T,PO) by eqn (A 1.13), and where a: and K,* are, respectively, the isobaric thermal expansivity and the isothermal compressibility of the pure solvent at temperature T and pressure Po.(iv) Since v?( T, po) = c( T, p,), A, So( T, c:) = A, So( T,po) - (a,*/rc,*) Ar Vo( T,po) - R In rI,(rp/xP)'f. (20) The Relationship between A, U"(T, c:) and A, Ho(T, p,) (ii) oP( T, c i ) = o:d( T, c i , ri) H:( T, p,) = Hid( T, po, xi). (iii) Up( T, c:) - HP( T,po) = U p ( T, c:) - H p ( T,po)212 by eqn (A 1.15). Cons tan t- vo lume Soh t ion Thermodynamics Other Relationships Since q( T, c l ) is identically zero for every solute, it is obvious that Ar V,(T, c:) = 0. Finally, we consider the change of pressure upon complete transformation of reactants into products under conditions of constant total volume. Because pressure is an intensive property, the meaning of the analogue of eqn (17) is not obvious.However, there is a definite change of pressure associated with step (ii) of the ideal isochoric process drawn in section 2.2. For its computation, we resort to the mean solute technique described by Friedman.". l2 Defining the total mole ratio of reactant species as the mean reactant partial molar volume at constant (T,p) is given by (23) K(T,P) = %(rR/rR) %(T,P). (24) rR = C , r , Here rR/rR = n R / x C , n , is the solute fraction of species R. The application of eqn (A 2.10) to an ideal solution containing the mean reactant yields (25) Since we are concerned with the ideal solution obtained by mixing standard reactant solutions, it can be seen from table 1 that pid( T, C:, R) = PO -I- C i r R V,"( T,po)/K,*- r R = vR/%(vR/G)- (26) (27) By a similar procedure, we find that an ideal solution containing stoichiometric amounts of the products is at a pressure (28) Subtracting eqn (27) from eqn (28) and calling into play the ideal isochoric condition [eqn (12)] yields the isochoric change of ideal pressure (29) Inserting eqn (23) and (24) into eqn (25) and using eqn (26) gives p i d ( T , ci, R, = PO + c:[CR vR v,"(T,pO)]/K,* zR,(vR/rg)- Pid(T, c:, P) = Po + c:[Cp v p v w , PO)I/K2 L O p / r ; ) .ArpF(T, c:) = C: A r V o ( T , p 0 > / ~ ~ Ep(vp/rOp). 3. Thermodyngmics for Chemical Kinetics in Solution 3.1. The Equilibrium Assumption in Transition-state Theory Transition-state theory (TST) assumes that reactants are in ' quasi-equilibrium ' with activated complexes which are transformed into products by a first-order kinetic process.Therefore TST treats phenomenological single-step rate constants, k , as if they were referred to a chemical equilibrium characterized by K * , followed by a first-order consecutive reaction with rate constant k*. Hence, within the usual approximations, we may write k = K'kfL. M . P. C. Albuquerque and J. C. R. Reis 213 with the theory giving k' = rCkB Tlh where ic is the transmission coefficient, which is unity if every activated complex gives rise to products, k, is Boltzmann's constant and h is Planck's constant. Eqn (30) applies to the general chemical reaction path where we made v+ = 1. The bridge between kinetics, as interpreted by TST, and thermodynamics is provided by K * , which, however, has the status of a pheno- menological equilibrium constant.The units in which K * and k are expressed should be consistent with eqn (30), as recently emphasized by Hamann and le N0b1e.l~ By noting that the formalism developed in section 2 implies definite choices of composition units, and that TST is as valid for rate processes in solution at constant ( T , p ) as for processes at constant (T, cA), we can write in self-evident notation: Then, with reference to eqn (3 l), the standard quasi-equilibrium constants of activation become K*"(T,p) = and Here, and hereafter, i = R, $. . 3.2. Isobaric and Iso-solvent-concentration Quantities of Activation We define the phenomenological parameters of activation Gibbs energy at constant ( T , p ) and Helmholtz energy at constant (T, c,) by A*G,(T,p) = -RTln[k,(T,p)/k*] (34) and A*A,(T,cA) = -RTln[k,(T,c,)/k*) (35) respectively. Insertion of eqn (32) and (33), respectively, into eqn (14) and (1 1) together with definitions (34) and (35) lead, after rearrangement, to A*Go(T,p)-RTlnlli(x~)"~ = A*G,(T,p)-RTlnlI,(f:q)"l (36) and to A*AO(T,c,)-RTln llj(rp)"t = A*Ay(T,cA)-RTln Ili(y:q)"i.(37) We observe that neither A*G,(T,p) nor A*A,(T, c,) are quantities independent of the actual reacting mixture composition. However, by choosing values for the independent intensive variables in accordance with eqn (16) and by taking the infinite-dilution limit of the right-hand side of eqn (36) and (37), we obtain214 Constant-volume Solution Thermodynamics and, in view of eqn (19), A*A,"(T, c;) = A*G,"(T,p,). (40) Therefore, k,( T,p) and k,( T, c,), and thus A* G,( T,p) and A*Ar( T, cA), both referred to the same actual system, may be different from each other, unless they refer to first-order reactions or to reactions at the infinite-dilution limit. Furthermore, eqn (38) at various T and p, and eqn (39) at various T and c, express numerical equalities between physically distinct quantities.The left-hand sides of both equations refer to ideal thermodynamic processes, whereas on the right-hand sides are infinite-dilution limits of experimental quantities. Let us differentiate eqn (38) with respect to pressure at constant temperature. Because of the relation we may specify that the partial derivative of the left-hand side of eqn (38) is also at constant xp. However, this restriction is meaningless while differentiating the right-hand side of eqn (38).Here, what is of interest is the pressure dependence of the indicated experimental quantity at constant temperature only. The result is the usual relation [aA*Go(T,P&/aPIT,zp = x i vi[aGp(T,pO)/aPIT,xp, A* V"(T,po) = A* V,"(T,p,). (41) Alternatively, if we were using eqn (36) instead of eqn (38), the pressure effect on the activity coefficients should be taken into account, as pointed out by Hamann.14 Entropies of activation are obtained from the derivatives with respect to temperature of eqn (38) and (39). By partial differentiation of the left-hand side of eqn (38) at constant p and xp, and of the right-hand side at constant p only, it is found that Similarly, since [aA*A"(T, c ; ) / ~ T ] c,,rP = Xi V, [i3$(T, c;)/aT] c,,rP it is the partial derivative of the left-hand side of eqn (39) with respect to Tat constant c , and r: that equals the derivative of the right-hand side with respect to Tat constant A*S"(T,p,)+Rln IIi(xp)"i = A*SZ(T,po).(42) C, only. Hence A * S "( T, c;) + R In IIi( rp)"i = A * S,"( T, c;). (43) Combining eqn (41), (42) and (43) with eqn (20) yields Further application of the above procedure leads to the following results :L. M . P . C. Albuquerque and J . C. R. Reis 21 5 Additionally, it is clear that analogues of eqn (45) and (46), or else of eqn (21) and (23), can be written in terms of the corresponding standard quantities of activation. Granted a set of data reporting k, over a range of T , p and composition, the conversion to k, as a function of T, c, and composition would generally yield a collection of points not suitable for obtaining k,"( T, c,) by extrapolation.Therefore, with the exception of specifically designed experiments, the quantities A *Xm( T, c:) are most accurately obtained from the relevant A*X"(T,po) quantities by using p , V, T data for the pure solvent. The ideal isochoric condition for the thermodynamic process of activation follows from eqn (12) by recalling that V + = 1 : The total ideal volume associated with this isochoric process is, by specializing eqn (48) (131, Lastly, in view of eqn (29) and (41), the expression for the ideal pressure of activation Vid = -ZR(vRmoI/ri)/cl = mol/r: cl. is A*pF(T, c:) = C: r: A* V,"(T, p o ) / ~ z . (49) 3.3. Isochoric Standard Quantities of Activation for First- and Second-order Reactions The conventional formalism relating isochoric to isobaric activation quantities makes use of phenomenological activation parameters.However, some of these may differ from the corresponding standard activation quantities, a situation evidenced by eqn (38), (39), (42) and (43). Thus it seems desirable to know which standard-state compositions lead to a formalism close to the conventional one while complying with the ideal isochoric condition [eqn (47)]. Choices meeting these requirements are obtained for kinetics of elemental reactions in the following, where a subscript V means that eqn (47) is observed. Since vR = - 1 for reactions with first-order kinetics, the choices x: = x i and r: = r i yield, respectively, from eqn (38), (39), (42) and (43), A*G0(T,po) = A*G,"(T,PO) A*A",T, c:) = A*A,"(T, c l ) A+S0(T, Po) = A*S,"(T, Po) and A*S",T,c;) = A*S,"(T,cl).Consequently, besides the analogues of eqn (45) and (46) for standard activation quantities, we find that the above standard quantities are linked by relationships entirely similar to eqn (40) and (44). All of these simple results can also be obtained for reactions with second-order kinetics. If vR = -2, the formalism is simplified by making x: = (xi)2 and r: = (ri)2. Since, in addition, the ideal isochoric condition requires that r: = 2r:, we are led to the single choice r: = and r: = i. If V, = v,, = - 1, it is then required that x i = x ~ x ~ , and that r: = rkr;, with r i + r ; . = 1. A sensible choice is, of course, r; = r l , = f and r: = a.4. Comparison with Other Approaches The traditional approach to relate isochoric and isobaric quantities was initiated by Evans and Polanyi' while defining Arrhenius- type energies of activation at constant volume by applying the operational equation216 Constant-volume Solution Thermodynamics to the logarithm of rate constants. Subsequently Brummer and Hills2 were the first to interpret the derivatives thus obtained in terms of isochoric changes in standard quantities of activation. This line of thought attained its full development with Whalley,15 who extended the formalism to higher-order derivatives. As recently reiterated,8 the isobaric thermal expansivity a and the isothermal compressibility K appearing in eqn (50) should be referred to the actual sample undergoing reaction.Although this identification is mathematically unquestionable, interpreting thermo- dynamically the resulting constant-volume parameters is by no means self-evident. Let us elaborate this point. Application of eqn (SO) to the logarithm of an equilibrium constant defined in terms of activities such as Ko(T,p) in eqn (lS), yields a In KO( T, p ) or, in terms of standard quantities with precise meaning, Furthermore, since eqn (51) is readily transformed to ArG"(T,p) = ArA"(T,p)+pA, V"(T,P) The mere observation that the left-hand sides of both eqn (51) and (52) have the same dimensions as A, So( T,p) cannot lead by itself to an unambiguous identification of these quantities with any standard entropy of reaction at constant volume.The same can be said of all the other traditional isochoric parameters. This weakness has given rise to interesting controversies. Thus Williams's proposal" relating conventional constant-volume quantities of activation for a process in the bulk with a specific isochoric hypothetical standard transformation was disc~ssedl'-~~ at large in the sixties. In the midst of the discussion Hills and c o l l a b o r a t o r ~ ~ ~ - ~ ~ turned attention to rate processes in solution. These authors, by drawing on a possible connection between the macroscopic coefficients a and K for one, and their 'local values' in the vicinity to the activated complex for another, stirred up further contro~ersy.*~-~~ During this debate Caldin27 remarked that ' the interpretation (of activation parameters) would probably be simplest if A V* were kept constant, and this is nearly achieved in constant- pressure experiments at 1 atm.' However, Hills and Viana2O' 21 calculated derivatives at constant volume of activation for two solvolytic reactions and found the parameters thus defined to be quite distinct quantities from either isobaric or conventional isochoric activation parameters. In spite of these contributions, the precise significance of constant-volume quantities remained unclear when the debate was resumed.Thus Blandamer and co-~orkers~-~* 28 contend that isochoric quantities can be defined without ambiguity by eqn (SO) only if M: and K are equated to those properties of the pure solvent at experimental temperature and pressure.This procedure then yields pseudo-isochoric parameters in that they refer to constant molar volume of pure solvent, which is an isochoric condition extrinsic to the actual system. Haak et aL6 conclude that 'isochoric activation parameters are extremely difficult to interpret.' Wright's analysis' of this problem revealed further that two senses of 'isochoric' are involved: on the one hand, the extensive, total volume of actual samples while collecting experimental data to calculate infinite-dilution quantities and, on the other hand, the intensive, molar volume of pure solvent while connecting isochoric with isobaric parameters by eqn (50). Since this subtle difference vanishes at infinite dilution, Wright7 concludes that, in this limit, the resulting isochoric quantity is indeed 'a certain type of AX,'L.M . P . C. Albuquerque and J . C. R. Reis 217 Our viewpoint departs fundamentally from those above. For we begin by identifying a suitable intensive, volume-related, thermodynamic property of actual systems to take the place of pressure as an independent variable in a chemical-thermodynamics formalism. The differences between the various approaches are perhaps best evidenced by examining the so-called pressure of activation, A * p . Whalley15 introduced this parameter aiming to measure ‘the change of pressure when a fixed amount of the transition state is formed at constant volume.’ It was defined15 by relations amounting to [a In (k,/k*)/a V ] , = A*p/RT or equivalently A*p = A* Y,(T,p)/ VK.(53) Although this definition has been reproduced in the 22, 29-31 we are unaware of any experimental value being reported for A*p. This lack of interest in activation pressures may be explained by Weale’s remark3’ that ‘AP* is less obviously useful than AV* for the purpose of relating kinetic behaviour to reaction mechanism,’ but also, no doubt, because the question of what volume should be used in eqn (53) is now overwhelming. If for V we were to take ‘ the volume of the actual reaction mixture’, then A*p, besides becoming a ‘molar pressure’, could not be calculated from eqn (53) unless that volume was reported. If, however, Vmeans ‘molar volume of the pure solvent ’, and if eqn (53) is rewritten as then no precise meaning could generally be attached to this dimensionally correct pressure of activation.Nonetheless reinterpreting eqn (53) and (54) is rendered possible by drawing on their striking similarity to eqn (49). Replacing in the latter c i by its value according to eqn (16) yields A*p = A’ V,“(T,p)/ V: IC: (54) A*pF( T , c i ) = r t A* V;( T, p 0 ) / V: IC:. On the other hand, from substituting r: c i given by eqn (48) into eqn (49), A*p;( T, ci)/mol = A* V,“( T,po)/ Vid~:. ( 5 5 ) Eqn (55) reduces to eqn (54) for r t = 1. However, this choice of standard-state composition is permissible for first-order reactions only, as discussed in section 3.3. Therefore eqn (54) cannot yield an unambiguous pressure of activation for second-order reactions. In its turn, eqn (53) in the limit of infinite dilution becomes almost identical to eqn (56) but for the dimensions of A*p and the value of V.We stress that our approach allows the interpretation of V in these equations as the volume of an ideal solution for constant ( T , c,) containing stoichiometric amounts of the reactants ; and A*pF( T, c,) as the change of pressure when one mole of activated complexes is formed in the ideal solution above at constant temperature and volume. 5. Conclusion This study shows that developing a system of formal thermodynamics appropriated for isothermal-isochoric solution chemistry is possible. Now we answer concisely the timely questions posed by Blandamer et aZ.495 It is simpler to begin by the second question, namely, ‘what reference states are used in the definition of isochoric activation parameter^?'^ By defining partial molar properties specified for studies in solution at constant temperature and solvent concentration (Appendix 1) and by introducing the concept and properties of the corresponding ideal solution (Appendix 2), we have been able to design isothermal-isochoric standard equilibrium constants for chemical equilibria in solution (section 2.2) and thus for the quasi-equilibrium of activation (section 3.1).Their associated standard states provide the desired answer. It seems to us that the first question of Blandamer et ~ l . , ~ . ~ ‘what volume is held con~tant?,’~ should218 Constant-volume Solution Thermodynamics be restated as follows : .‘what volume, or volume-related quantity, of the actual reacting mixture and of the associated ideal process is held constant?’ Our analysis shows that the solvent concentration, which is a volume-related intensive property, is held constant in the actual system as well as in the standard solutions during the course of the ideal process (section 2.2).Additionally, by noting that we are dealing with closed, non- stoichiometric, solvent-participating reaction mixtures, conditions of iso-solvent- concentration also imply that actual volumes are kept constant, whatever volumes are being handled. Of course this latter sense of ‘isochoric’ corresponds to Whalley’s8 and to one of Wright’s7 senses. However, these volumes have not entered into our thermodynamic treatment, but in determining the value of solvent concentration. Lastly, we could identify a total, or extensive, well defined volume which can indeed be made constant through every step of the ideal iso-solvent-concentration model process.This volume is given by eqn (1 3) for chemical equilibria and by eqn (48) for activation quasi-equilibria. Therefore, by ideal isochoric condition we mean holding constant the total volume of the standard solutions containing the reactants throughout mixing, complete transformation into products and respective separation. Our approach in relating isochoric to isobaric quantities at the same temperature differs significantly from the conventional onel. 2 y l5 and its modification^,^-^^ 28 For we have not relied upon applying operational eqn (50) to any given sort of equilibrium constant. In fact, such a procedure has been traditionally used on the supposition that the isochoric parameters thus derived could be interpreted as precisely defined changes in standard quantities, until first questioned by Blandamer et al.4 Despite the fact that pure solvent properties appear in our formulae as they do in the treatments of Blandamer et al.49 and of Wright,’ the conclusions are not restricted to infinite-dilution conditions because, provided that pertinent activity coefficients are given, the equations derived here link isobaric quantities for a concentrated reaction mixture at equilibrium with isochoric quantities pertaining to the same mixture but at a different pressure. Moreover our formulae could readily be adjusted to the conventional formal appearance because they use standard-state compositions disengaged from the definitions of ideal solutions.This is exemplified in section 3.3 for the activation step in first- and second-order reactions. In spite of all approaches yielding identical equations in the limit of infinite dilution, their interpretative capabilities are quite distinct, as evidenced in section 4 in the discussion of the pressure of activation. The present results can easily be extended to activated rate processes in solution other than chemical reactions. However, they do not apply to processes in the bulk or to equilibria involving the solvent stoichiometrically . Finally, the quantities X,( T, c,) and F:(T, c,) studied in the appendices may be useful in the thermodynamic description of interstitial 33 We thank Prof. Graham J.Hills and Prof. Cksar A. N. Viana who first aroused our interest in isochoric quantities. We are grateful to the University of Lisbon for granting sabbatical leave and to the Instituto Nacional de InvestigaGiio Cientifica for financial support (grants QL4-LA3/LA5). We thank Mrs Leonor Rodrigues for typing the manuscript. Appendix 1. Partial Molar Properties at Constant Temperature and Solvent Concentration Considering a homogeneous solution of solutes B, C, . . . , W, in a solvent A in the absence of external fields, the partial molar property at constant temperature and solvent concentration of the Bth component corresponding to the system extensive property X (A 1.1)L. M. P. C. Albuquerque and J. C. R. Reis 219 In common with other properly defined partial molar proper tie^,^ these quantities possess the ' summability feature '34 the running index varying from A to W.Another summation rule is:' X = EB nB x B ( T, 'B nB[axB(T, cA)/an,]T, cA, n' = O- (A 1.2) The general link between xB( T, c,) and xu( T,p) is derived using known relations among partial derivative^^^ as follows : 'BCT9 'A) = cA, n' = ~ B ( T , P ) - [ v , ( T , P ) - - 6 A B / c A l (ax/av>T,nB (A 1.3) Kronecker delta function, whose value is 1 for the solvent and zero otherwise. In the above derivatives, ' at constant nB ' means constant composition. since ( a c A / a n B ) T , p , n' = 6 A B / V-CA vB( T,p)/ v, where 6 , ~ = ( i ? n A / i h B ) , , p . ,,, is the Since V,(T, c,) = 1 / c A and VB(T, c,) = O for the solutes, we can write 'B( T, cA) = BAB/CA.(A 1.4) As a result, if a derivative is taken at constant C, and composition, then it is also at constant VB( T, cA). For X = A, eqn (A 1.3) gives the important relation 'A) = 'B(T,P) +P[vB(T,p)-sAB/cA] = G B ( T , P ) - P - ~ , B / c A = p B - P 6 A B / c A . (A 1.5) For X = SZ = -pV, where R is the Grand potential, nB(T, = -p VB(T, p) - [ vB(T, P) - BAB/CAI (K-l -PI = - vB( T, p ) / K + 6 A B ( K - ' -P)/CA. (A 1.6) On the other hand, from defining eqn (A 1.1) and by using eqn (A 1.4) nB(T, 'A) = - P 6 A B I C A - V(aP/anB)T,c,, n" Combining eqn (A 1.6) and (A 1.7) leads, for B # A, to (A 1.7) It is convenient for formalistic purposes to define a ' partial ' pressure pB( T, cA) by (A 1.9)220 Constant-volume Solution Thermodynamics s B ( T, CA) = gB(T7 p)- vB( T7 p)- 6AB/CA] (A 1.13) and cV,B(T, 'A) = cV,B(T,P)- T[vB(T,p)-GAB/cAl (a2P/aT2)V,nB* (A 1.14) By noting that ( a 2 p / a T 2 ) V , nB = [a(a/~)/aTIp, nB + a ~ - ' [ a ( a / ~ ) / a p I , , nB and by using the relationg eqn (A 1.14) is transformed to Finally, it can be shown that the relations among xB(T, cA) when X = A , U, G, H, R, S, V and Cv, and T and pB(T,cA) are entirely analogous to those holding for the corresponding molar properties of pure substances together with T and p, However, this similarity fails in other instances.For example 'A) = -[axB(T, vB(T, cA), nB and cV.B(T7 cA) = [auB(T, vB(T, cA), nB whilst c ~ , B ( ~ 7 'A) # [aRB(T, ' A ) l a U p B ( T , cA), nB' Appendix 2. Ideal Solutions at Constant Temperature and Solvent Concentration The concept of ideality plays a central role in solution chemical thermodynamics.Ben- Naim36,37 discusses various kinds of ideal mixtures and solutions in terms of the Kirkood-Buff theory of solutions. We believe that dilute ideal solutions can be meaningfully defined on the basis of chemical thermodynamics by using some statistical- mechanical properties of ideal-gas mixtures. For simplicity, the following development is restricted to a single solute B in a solvent A. To this end let us introduce the general concept of an ideal solution with respect to a pair ( y , z ) of independent intensive thermodynamic variables by (a,#/anB)y, z , nA = the same as for an ideal-gas mixture. (A 2.1) This definition allows the use of generalized partial molar properties to describe the corresponding ideal solution.However, the complete characterization of a dilute ideal solution requires that some sort of normalizing conditions are fixed. We thus make the following reasonable assumptions : lim X z ( y , z ) = X;"(y,z) = X ; ( y , z ) nB+O and (A 2.2) where Xg( y , z ) is referred to the real solution and X ; ( y , z ) is a molar property of the pure solvent, both at the fixed values y and z .L. M. P . C. Albuquerque and J . C. R. Reis 22 1 It follows from eqn (A 2.1) that an ideal solution at constant (T, c,) can be defined by (a&/anB)T,cA, nA = RT/nB which is readily transformed to (ap:/arB)7', cA = RT/rB and, in view of eqn (A lS), to [azz(TT, cA)/arB]T,cA = RT/rB* (A 2.3) At constant (T, c,), integration of eqn (A 2.3) with respect to the composition variable (A 2.4) rB gives By applying eqn (A 1.2) to X = A we find that eqn (A 2.2) and (A 2.3) imply that At( T, c,) = &( T, c,) + RTln (rB/r",.Zf( T, CA) = A :( T, CA) - R Tr, which, by referring to eqn (16), is the same as z,d(T,ci) = A:(T,po)-RTrB. (A 2.5) Eqn (A 1.10) written for the solvent at c i is ci) = p + [ci vA(T,p)- l]/K. (A 2.6) By substituting p,d(T, c i ) given by eqn (A 2.5) into eqn (A 1.1 1) and by recalling eqn (A 1.4), one obtains P W , 4) = Po. (A 2.7) Now the summability feature implies that c i v A ( T, p) + c i rB VB( T, p) = 1 . Thus combining eqn (A 2.6), (A 2.7) and (A 2.8) yields (A 2.8) Pid = PQ + c i rB vB( T,p)/K. Partial differentiation of this equation gives (dpid/arg)T.cA = ci vB(T,P)/K+ ci rB{a[vB(T,p)/Kl/arB3*,,A' (A 2.9) Comparison of this equation with eqn (A 1.8) shows that {a[ vB(T,P)/Kl/arB)T.cA = for the ideal solution, thereby eqn (A 2.9) can be reduced to (aPid/arB)T.c, = ci vg(T,pO)/K: whose integral form at constant (T, c,) is Pid = Po C i rB V g ( T, pQ)/K:. (A 2.10) Expressions for other X f ( T , c,) originate in eqn (A 2.4) by bearing in mind eqn (A 1.1) and the mathematical identity and222 Constant-volume Solution Thermodynamics References 1 M. G. Evans and M. Polanyi, Trans. Faraday SOC., 1935, 31, 875. 2 S. B. Brummer and G. J. Hills, Trans. Faraday SOC., 1961, 57, 1816. 3 G. J. Hills, in Second Australian Conference on Electrochemistry, ed. R. W. Cattrall, K. G. Neill, 4 M. J. Blandamer, J. Burgess, B. Clark and J.M. W. Scott, J. Chem. SOC., Faraday Trans. I , 1984, 80, 5 M. J. Blandamer, J. Burgess, B. Clark, R. E. Robertson and J. M. W. Scott, J. Chem. SOC., Faraday 6 J. A. Haak, J. B. F. N. Engberts and M. J. Blandamer, J. Am. Chem. SOC., 1985, 107, 6031. 7 P. G. Wright, J. Chem. SOC., Faraday Trans. I , 1986, 82, 2557. 8 E. Whalley, J. Chem. SOC., Faraday Trans. I, 1987, 83, 2901. 9 J. C. R. Reis, J. Chem. SOC., Faraday Trans. 2, 1982, 78, 1595. J. E. A. Walkley and J. Tregellas-Williams (Butterworths, Sydney, 1968), p. 39. 3359. Trans. I, 1985, 81, 11. 10 T. CvitaS and N. Kallay, Educ. Chem., 1980, 17, 166. 1 1 H. L. Friedman, J. Chem. Phys., 1960, 32, 135 1. 12 H. L. Friedman, J. Solution Chem., 1972, 1, 387. 13 S. D. Hamann and W. J. le Noble, J. Chem. Educ., 1984, 61, 658. 14 S. D. Hamann, High Temp. High Pressures, 1983, 15, 511. 15 E. Whalley, A h . Phys. Org. Chem., 1964, 2, 93. 16 G. Williams, Trans. Faraday SOC., 1964, 60, 1548. 17 G. J. Hills, P. J. Ovenden and D. R. Whitehouse, Discuss. Faraday SOC., 1965,39, 207. 18 G. J. Hills, in Chemical Physics oflonic Solutions, ed. B. E. Conway and R. G. Barradas (Wiley, New 19 F. Barreira and G. J. Hills, Trans. Faraday SOC., 1968, 64, 1359. 20 G. J. Hills and C. A. Viana, in Hydrogen-bonded Solvent Systems, ed. A. K . Covington and P. Jones (Taylor and Francis, London, 1968), p. 261. 21 C. A. N. Viana, Rev. Fac. Cien., Univ. Lisboa, 2a Ser., 1967-1968, 8 11, 5. 22 E. Whalley, in Advances in High Pressure Research, ed. R. S. Bradley (Academic Press, London, 1966), vol. 1, p. 143. 23 E. Whalley, Ber. Bunsenges. Phys. Chem., 1966, 70, 958. 24 E. Whalley, Annu. Rev. Phys. Chem., 1967, 18, 205. 25 J. B. Hyne, in ref. (20), p. 271. 26 D. A. Lown, in ref. (20), p. 271. 27 E. F. Caldin, Discuss. Faraday SOC., 1965, 39, 62. 28 M. J. Blandamer, J. Burgess and J. B. F. N. Engberts, Chem. SOC. Rev., 1985, 14, 237. 29 B. T. Baliga, R. J. Withey, D. Poulton and E. Whalley, Trans. Faraday SOC., 1965, 61, 517. 30 K. E. Weale, Chemical Reactions at High Pressures (Spon, London, 1967), pp. 170, 171. 31 H. Kelm and D. A. Palmer, in High Pressure Chemistry, ed. H. Kelm (D. Reidel, Dordrecht, 1978), p. 32 C. H. P. Lupis, Acta Metallurg., 1977, 25, 751. 33 C. H. P. Lupis, Acta Metallurg., 1978, 26, 211. 34 M. M. Abbott and K. K. Nass, in Equations of State. Theories and Applications, ACS Symp. Ser. 300, 35 W. E. Acree Jr, Thermodynamic Properties of Nonelectrolyte Solutions (Academic Press, Orlando, FL, 36 A. Ben-Naim, Water and Aqueous Solutions (Plenum Press, New York, 1974), chap. 4. 37 A. Ben-Naim, in Solutions and Solubilities, ed. M. R. J. Dack (Wiley, New York, 1975), part I, chap. York, 1966). p. 521. 281. ed. K. C. Chao and R. L. Robinson Jr (American Chemical Society, Washington D.C., 1986), p. 2. 1984), chap. 1. 2. Paper 8/00330K; Received 26th January, 1988

ISSN:0300-9599    

DOI:10.1039/F19898500207

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1989, 85(2), 223-235 Ionic Transport through a Homogeneous Membrane in the Presence of Simultaneous Diffusion, Conduction and Convection Vicente M. Aguilella, Salvador Mafit and Julio Pellicer” Department of Thermodynamics, Faculty of Physics, University of Valencia, 46100 Burjassot, Valencia, Spain The problem of ionic transport through a homogeneous membrane when diffusion, conduction and convection are involved simultaneously has been considered. We have discussed the effect that the convective flow exerts on the whole flow and on the so-called ‘lag time’. Thus, expressions have been derived showing to what extent convection increases the matter flow and reduces the time required for ions to cross the membrane. The assumption of infinite collecting volume has been analysed and conditions making it applicable have been given.The case of a charged membrane is also discussed. The problem of ionic transport across a homogeneous membrane when diffusion, conduction and convection occur simultaneously is interesting, both from a theoretical and from a practical point of view. Classical analyses on this matter are due to Schlogl, who integrated the steady-state transport equations. Schlogl also introduced the ‘constant field’ assumption as a first approximation to the problem.’ Meares’ contribution must be mentioned, especially in the case of charged membranes. A good example is the study by Meares and Page2 of the transport through nuclepore membranes. More recent studies have been carried out by Kontturi and c o - ~ o r k e r s ~ * ~ and they are focussed on a practical problem of separation of ions by using electric current and convection simultaneously (‘ countercurrent electrolysis ’).The resulting equations are solved in the steady state, either analytically or numerically. If the volume of the porous membrane is very small compared to the volume of bulk solutions, the fluxes across the membrane are nearly stationary. However, this is not always convenient if we want to avoid ohmic losses, to obtain effective stirring when using forced-flow convection or to increase the separation efficiency. Thus, Kontturi and Kontturi have recently proposed a non-stationary solution to the problem of ‘countercurrent electrolysis’ in a porous membrane, by using a different procedure (a Laplace transformation) from that employed here.Nevertheless, the above authors have focussed their analysis on a qualitative study of the time needed to reach the stationary state, and so other results derived from the solution (fluxes, amount of matter transported in the steady state etc.) have not been r e p ~ r t e d . ~ From a different viewpoint we have considered here a non-stationary convective diffusion problem. We discuss the effects that the convective flux exerts on those parameters of the system of practical interest : the flux enhacement and the effective lag time. The assumption of infinite volume for the bulk solutions will be analysed in detail. The case of a charged membrane is also discussed. t Present address : Department of Applied Physics, University of Castilla-La Mancha, Albacete, Spain.223224 Membrane Transport Fig. 1. Schematic representation of the transport problem. We consider I + d. The membrane is envisaged as a region between x = 0 and x = d through which convective diffusion is supposed to take place. The dashed line indicates the concentration profile for t = 0. Formulation of the Problem : Approximations The membrane is regarded as an unstirred layer of constant thickness, placed between two homogeneous solutions of the same electrolyte at different concentration. These solutions are considered as infinite source and sink, respectively ; i.e. the characteristic length 1 of the two bulk solution reservoirs is large enough so that I >> d (this is a first approximation that will be revised later).This amounts to assuming that concentration gradients are confined inside the membrane, and so the concentrations at the boundary points x = 0 and x = d are equal to those of each bulk solution, respectively. Any particular detail due to the channel and pore structure of the membrane is omitted, and the transport is considered to take place only in the x-direction. An outline of the experimental situation considered is shown in fig. 1. The transport equations are assumed to be approximately represented by the Nernst-Planck flux equations : j . = - D . t[2 -+ ( [ T ) z i c i $ ] + c i v ; - i = 1,2 where j , , D,, zi and ci are, respectively, the flux, the diffusion coefficient, the charge number and the local molar concentration of ion i, x denotes the position inside the membrane, q5 the local electric potential and v the convection (‘bulk velocity’ of the fluid).Constants F, R, T, have their usual meaning. It is well known that eqn (1) is only a first approximation6-8 to the problem. This equation is only justified in the case of dilute solutions, where cross-terms and activity coefficients can be omitted. Likewise it includes implicitly Einstein’s relation between ionic mobilities and diffusion coefficients. To assume the latter constant through the membrane requires small concentration gradients. The convection v is an experimental parameter fixed externally, as is the current density i to be introduced next. Its value can be determined from the balance equation for the linear momentum of the liquid (Navier-Stokes equation).Since the membrane has no fixed charges, and macroscopic volumes of solution can be regarded as electroneutral, v is only due, at a first approximation, to the pressure gradient. We will assume that this gradient can be fixed externally in times much smaller than those characteristic of the convective diffusion. Thus, for each fixed value of the pressure gradient, the time dependence of v vanishes rapidly. In addition, if the density of the solution is assumed to be nearly constant with time and space, it readily follows from the mass-balance equation that v does not depend on the position x in the membrane. This approximation fits well to dilute solutions.8 The current density crossing the membrane is defined as: 2 i = F C z i j i i = 1V.M . Aguilella, S. Mafe' and J . Pellicer 225 The current density i can be assumed to be constant provided that we analyse the system for times much greater than that of the electric relaxation. We will comment on this aspect later. Eqn (1) and (2) obey the conservation laws for mass and charge, respectively. The former is the so-called continuity equation. where t denotes the time variable. The latter follows immediately from eqn (3) using the definition in eqn (2). The ionic formalism employed here requires an equation for the electric charge in the region over which transport occurs (membrane). A general equation which relates the electric potential # with the charge density p is Poisson's equation, but his solution involves a serious problem, and one has often to resort to numerical technique^.^.lo However, if our analysis is concerned with times that are ' large ' compared to those associated with the electric relaxation, t,, Poisson's equation can be replaced by its approximation of 'electroneutrality ' : 1 1 , l2 2 c ziti = 0. (4) i = l The electric relaxation times are of the order of s."*'* The physical magnitudes studied here involve times much greater. Therefore, we will regard eqn (4) as an excellent approximation. Furthermore, let us note that eqn (4) is a less restrictive hypothesis than that of 'constant field', particularly in the presence of convective flux.13 Solution of Transport Equations We consider a binary electrolyte that dissociates into two ions of charge numbers z1 = - z 2 = 1.Consider eqn (1)-(4). If we solve for the electric potential #, then a differential equation involving ci(x, t ) is obtained. Taking into account that c, = c, = c [eqn (4)] it readily follows that Eqn ( 5 ) is the so-called 'equation for convective diffusion'. Note that under the conditions of zero convection, constant electric field and only one ionic species present, an equation formally analogous to eqn ( 5 ) is obtained. The only difference being that 2- is replaced by - (D/d)(FV/RT), where V is the potential difference applied externally. This problem has been studied recently by Keister and Kasting,'-' and their solution technique is literally applicable here. Thus, we will go straight to the final solution. [The reader interested in the mathematical details may see ref.(14)]. The resulting general solution is (c, - c,) exp ( r x l d ) + cL exp ( r ) - c, exp ( r ) - 1 4(c, - c,) sinh ( r / 2 ) exp ( r ) - 1 c(x, t ) = + Note that eqn (6) does not agree, formally, with eqn (4) of ref. (14) because of the different boundary conditions imposed here. Eqn ( 5 ) and its solution, eqn (6), exhibit an explicit dependence on the diffusion (0, d ) and convection ( t i ) parameters, but no dependence on the electric current density (although the latter is implicit in the boundary conditions for the flux). The parameter r is the so-called Peclet number,6 which can be regarded as a measure of the ratio between convective and diffusive flux.226 Membrane Transport Results Eqn (6) enables us to calculate the amount of electrolyte transported between the bulk solutions, as well as the resulting flux enhacement and effective lag time.Ionic Transport From eqn (2), we solve for @+/ax) and substitute it in eqn (1) (for i = 1). We then find that j , = - D(ac/ax) + f, i/F+ CU (7) where is the transport number for ion i in the Nernst-Planck formalism. Note that z1 = - 2 , = 1 and c, = c2 = c lead to tl = Dl/(Dl + D2). By using eqn (7), the total amount of matter transported m(t) from solution R to solution L during time t can be evaluated from j l ( x = 0, t ) (we assume here that c, > c,). If we consider an effective membrane area A , = [ dzjl(x = 0, Z) = - D dz[(&/i3x)]x,o + [ f , ( i / F ) + C, U ] t. s, (9) From eqn (6) it follows that r(cR - cL)/d 4(c, - c,) sinh (r/2)/d O0 (nn)2( - 1)" exp ( - [ ( r m 2 + m21 t ) (g)x=o = exp(r)- 1 + d 2 / D c 1z - 1 (r/2I2 + m2 exp ( r ) - 1 (10) Hence, by integrating over z and rearranging terms, eqn (9) becomes m(t) - tli D r -- -t + - [c, exp ( r ) - c,] A F d exp ( r ) - 1 2d2 c,-c, sinh(r/2) 1: (nn)2( - 1)" c c, exp ( r ) - cR r/2 [(r/2)2 + (nn)2]2 [ (- d 2 / D (1 1) Eqn (1 1) shows that the current density contributes to m(t) through an additive term.Diffusion and convection are coupled through a function of r, thus giving the second term on the right-hand side of eqn (11). Note also that the transient behaviour represented by the exponential function appears only in the diffusion-convection term (i.e. no electric transient term is found). This result is in agreement with our initial hypothesis [eqn (4)] which implicitly assumes analysis of the system at times much greater than that of the electric relaxation.Although in our case the relaxation may be more complicated than that occurring in a non-homogeneous solution in the absence of electric current,15 it is clear that the times involved in that relaxation are much smaller than those of the diffusion+onvection relaxation. Indeed, the transient part of eqn (1 1) gives a typical relaxation time of the order of d2/D. On the other hand, the electroneutrality assumption [eqn (4)] is valid for times t %- z, = L2,/D, where L , is the Debye length.15 Since most membranes have d % L,, then d2/D 9 Z, is assumed. Note that the inequality d %- L , is not only a characteristic of most artificial membranes, but also a requirement for the continuum macroscopic model underlying the transport equation^.^V.M. Aguilella, S. Mafe‘ and J . Pellicer 227 Note also that if c, = c, = c,, the second term in eqn (1 1) is (covt), and then no lag time appears owing to the assumption made of instantaneous attainment of the extermal pressure gradient. It is interesting to consider now the steady state in our problem, since it is of practical interest. One obtains ms(t) - tli D r - -t + - [c, exp (r) - c,] A F d exp (r) - 1 d2 cR-cL sinh(r/2) (-1)n(nz)2 6 0 c, exp ( r ) - c , r/2 [(r/2)2 + ( n ~ ) ~ ] ~ Before studying the implications of eqn (12), the consistency of the analysis can be checked by taking the limits i, r + 0, i.e. the conditions of pure diffusion.Applying L’H6pital rule yields r sinh (r/2) lim = 1; lim = 1. r-0 exp (r) - 1 7-0 r/2 Eqn (14) is the same as that for passive diffusion, which is obtained from integration of Fick’s second law under the boundary conditions used here [ref. (16), p. 511. The negative sign of m,(t) arises from the definition of eqn (9) (the boundary conditions of fig. 1 imply j , < 0). Now, it is convenient to evaluate the infinite sum of eqn (12), which will be useful in later calculations. A standard technique, based on complex-variable theory can be used [see ref. (14) for details]. The final result is1* (15) Thus, eqn (1 2) becomes : m,(t) - f , i D r - -t +- [c,exp ( r ) - c,] ( t - z,) = mf(t - 5;) + mL(t - ZL) A F d exp (r) - 1 = TI, C, - cL 6 [r coth (r/2) - 21 r2 z;, = 0, tf;, = - where z , ~ is the effective lag time (the conduction term exhibits Z: = 0 for the reasons mentioned above).Flux Enhacement and Effective Lag Time Let us define the flux enhacement, yJ, and the effective lag time, y,, as yJ = (mf+mL)/mf; y, E ~,./t;. (17) where rn; and z:, were defined in eqn (14). Tt is convenient to analyse the two limits separately.228 Membrane Transport (a) r + 0 Now, YJ = + ((‘1 i / F ) / [ - (‘R - CL)/dl) ( 1 8 4 Y, = 1 (1W yJ shows the linear superposition of the electric term and the diffusion term. The resulting steady state is well known. (b) i + 0 We have now in the steady state that: In order to study the behaviour predicted by eqn (19), we write c, = ac,(O < a < 1). It is convenient to study (1) a = 0. In this case the two cases separately: a = 0 and a # 0 r exp(r)- 1 YJ = 6 r2 y, = - [r coth (r/2) - 21.Functions (20) are plotted in fig. 2 [by applying L’Hbpital rule twice to the function y,(r), one can easily prove that lim y, = 1 when r + 01. Fig. 2(a) shows that yJ(r) becomes rapidly linear in r, its slope being unity, for negative convection v (in the same direction as the concentration gradient). For positive values of v , yJ tends to zero asymptotically. y, is plotted in fig. 2(6). A remarkable feature is its symmetry with respect to r [y,(r) = y,( - r)]. This symmetry disappears as we (2) a # 0. Take, for instance, a = i: will see next, when a f 0. - (21 a ) These two functions are plotted in fig. 3. Fig. 3(a) shows that yJ becomes rapidly linear (slope = 2) for u < 0, but now yJ is strictly zero for a certain ro [yJ(ro = ln2) = 01.y, is plotted in fig. 3(b). y, is no longer symmetric with respect to r in this case. It exhibits a pole at the same point where yJ = 0; i.4. the effective lag time becomes infinite when the connective flux and the diffusive flux have the same magnitude but opposite direction (and then gives zero net flux). Fig. 2 and 3 show that significant decreases in the effective lag time require convections at least u > D / d ; i.e. Peclet numbers I r I > 1. Thus, y, = needs I r I x 10 in fig. 2(b). Likewise the way y, approaches zero when r ---* - 00 is: I y, cc -6/r for a = 0 y, K - 3 / r for a =V . M. Aguilella, S. Mafe‘ and J . Pellicer L 7 -1 0 0 10 229 . - -1 00 -10 10 100 - Fig.2. Plot of functions y,(r) (a) and y,(r) (6) given by eqn (20). yJ is never zero because it has been calculated from the flux at the interface x = 0. At this interface there is only a diffusive flux [c(O, t ) = 01 and it decreases with r because an increase of the positive values of convection causes a decrease in the concentration gradient through the interface (the gradient never vanishes completely). As shown in fig. 2 and 3, convection not only increases the matter flux, but also decreases the time needed for matter to cross the membrane. Fig. 2(6) and 3(b) show two apparently surprising facts: y, is symmetric with respect to r (i.e. the effective lag time z, remains unchanged when v changes its sign) in the case a = 0 [2(b)]; on the other hand, y, < 0 for r > In 2 for the case a #O [3(b)].Let us study these questions. It is evident that eqn (1 6) is only valid for t & z,. Eqn (1 6 ) shows that for t ‘large ’ the amount of matter that has crossed the x = 0 interface is not proportional to t , but to (t-t,), z, being the characteristic time for the establishment of the stationary concentration gradient over the diffusion zone 0 < x < d. It is therefore worthwhile studying the evolution of the concentration gradient for ‘small’ times ( t + z,) in the surroundings of the contact plane between the two solutions (x < d ) . To accomplish it, consider again the two cases. (1) a = 0. The dependence of the concentration gradient on the direction of convection in the surroundings of x = d can be studied with the help of eqn (6).Thus, one obtains :230 Membrane Transport 10 + -1 0 / - -1 00 I 1 f 0 - 100 Fig. 3. Plot of functions yJ(r) (b) and y,(r) (6) given by eqn (21). Note that for r = In 2, yJ = 0 and y, = 00. The case r > In 2 leads to values yJ,, < 0 and is discussed in the text. Unlike the case in fig. 2, now c(0, t ) # 0, so that at the interface x = 0 there coexist convective and diffusive fluxes which may couple with each other to give zero total flux. since C(r) is an even function, the sign of v affects only the first term in eqn (23). We distinguish two cases: (i) v > 0 ( r > 0): then (ac/tIx), decreases if r increases; (ii) v < 0 (r < 0) : then (&/ax), (i) If v > 0, a very small convective flux [since c(x -c d, t zz 0) x 01 exerts two opposite effects upon the total flux: first, it makes the total flux smaller, since it occurs against diffusion ; secondly, it increases that total flux, by increasing the concentration gradient around x = d (when compared to that corresponding to r = 0), which increases the diffusion flux [fig.4 ( a ) ] . (ii) If v < 0, two opposite effects appear again on the total flux: now the small convective flux has the same direction as the diffusion flux, but the former decreases the value of the latter, through a decrease in the concentration gradient around x = d. In both cases, a balance of the effects that v causes on the initial total matter flux is possible. This would explain the behaviour of y,(r) shown in fig. 2(b). Note that the expression ‘total flux’ refers here to that produced initially ( t 6 rL) around x = d. The effect of r on the flux for t % T,, once the concentration gradient is established, is shown in fig.2(a). decreases if I r ]increases. Hence: (2) a # 0. It follows immediately that no balance can exist in this case. Although a convection opposite to diffusion may enhance the total flux via an increase of the concentration gradient, such a convection acts against diffusion and has a high value in this case [c(x < d, t x 0 ) # 0; fig. 4(b)], i.e. convection for v < 0 is comparable withV. M. Aguilella, S. Mafe‘ and J . Pellicer 23 1 I I 0 d Fig. 4. Schematic representation of concentration profiles around x = d for t 2 0 in the cases a = 0 (a) and a # 0 (b). ( c ) shows the case of r > In 2 with a # 0.In the latter situation, I Ddc/dx I < I u cl , and the total flux is negative (y,, < 0), so that the T,, obtained from the interface x = 0 is also ‘negative’ (y, < 0). diffusion, but has the opposite sign. This would explain the behaviour observed for 0 < r < In 2 [fig. 3(b)]. Now, let us attempt to explain the behaviour y, (r > In 2) < 0 for the case a # 0. The fact is that rid becomes negative because the amount of matter m(t) is transported from x = 0 to x = d [fig. 4(c)] when r > In 2. However, we have evaluated m,(r) and 5, from the interface x = 0. Indeed, from this problem, in the experimental situation outlined in fig. 1 (matter flowing from x = d to x = 0), it readily follows that whether m,(t) be calculated fromj,(x = 0, t ) or fromj,(x = d, t ) , respectively.Eqn (24h) gives ‘z, = -d2/4D’. Despite this, the physical meaning of both equations is clear: eqn. (24a) shows that for calculating the amount of matter that has crossed the interface x = 0 after a time t B d 2 / D has elapsed, it must be borne in mind that the stationary concentration gradient (c, - c,)/d requires a time t x d 2 / D to become established. Therefore, less matter has passed through x = 0 than it would have passed for an ‘instantaneous’ gradient over 0 < x < d (the perturbation involved in the initial concentration gradient has to reach x = 0 from x = d ) . On the other hand, eqn (246) shows that a greater amount of matter has crossed the interface .K = d than that resulting from an ‘instantaneous’ gradient ( c , - c J / d [the gradient for t > 0 is (c,-cL)/Ax, where Ax + d ] .232 Membrane Transport However, it should be mentioned that the difference between the matter ‘lost’ (reservoir R) and ‘gained’ (reservoir L), when computed from eqn (24), will not be strictly equal to the amount of matter over 0 < x < d i n the steady state.This is due to the fact that eqn (24) have been derived for ‘large’ times, neglecting the exponential functions of the diffusion relaxation. Strictly speaking, this approximation is only valid for infinite t , while the results derived [eqn (24)] contain ‘finite’ t. Revision of the Assumption of ‘Infinite Collecting Volume’ for Bulk Solution L We have to bear in mind the crude assumptions made in the transport proposed here.Still, some of them can be relaxed, and it is useful analysing what happens then. Consider the hypothesis of ‘infinite collecting volume’ for bulk solution L. This assumption seems to be reasonable, but note that in the problem studied here, the change in the concentration of the solution L is more easily measured when the size of the recipient L is sma1117 (the volume of recipient R can be assumed to be large enough for the concentration c , = co be taken as constant). From eqn (1 1) (take the case i = 0) we obtain for the change in concentration of solution L where V is the volume of compartment L. Eqn (25) is valid for any time t. The symbol ‘ - ’ has been introduced because m(t) has been derived under the initial boundary condition c,(t = 0) = 0 (‘ infinite collecting volume’ ; we will consider here the case a = 0).The assumption of ‘infinite collecting volume’ holds for times t such that : CO where 9tt is defined from eqn (25). Consider eqn (26) in the steady state, which gives Vd exp ( r ) - 1 Ad r coth(r/2) - 2 +- t < - ( AD r V r2 Then the perturbation introduced in compartment L for t several times zIA is (28) Adrcoth(r/2)-2 CO V r[exp(r)- 13 a In the case of pure diffusion (r + 0), eqn (27) and (28) require, respectively, that: Ad - 4 1 V for the assumption of ‘infinite collecting volume’ to be valid. The problem of finite volume L has been discussed previously by Paterson and Doran17 for pure diffusion. They show that the analyses corresponding to ‘infinite’ and ‘finite’ collecting volume are indistinguishable if some conditions [see eqn ( 5 ) and (6) in their paper] are met.Taking into account that our analysis is restricted to distribution coefficients (at the membraneV. M. Aguilella, S. Mafe‘ and J . Pellicer 233 interfaces) equal to unity, the mentioned conditions in that paper coincide with the limiting cases accounted for in our eqn (30) and (29), respectively. From eqn (28) and taking into account that in the worst case, CL(f - z,) z c,(Ad/V)F(r) c, Z c, F(r) being defined by comparison between eqn (28) and (31), one obtains: I -(Ad/ V ) F(r) exp (r) r = I -(Ad/ V ) F(r) exp ( r ) - 1 (32b) The expressions (32) generalize those obtained before [eqn (20)] when V cannot be considered as ‘infinite’. They hold for t x z,, and, as expected, coincide with eqn (20) for V 9 Ad.As in the cases studied before, it must be verified that yJ, -+ 1 when r -+ 0. This can be readily accomplished by’taking the quotient of the limits and later the product of them (L’H6pital rule has to be applied for each limit). Summarizing, eqn (28) shows that the perturbation introduced in the concentration of compartment L, for typical steady-state times, depends on two quotients: one, ‘geometric ’, relating the liquid volume in the membrane termed ‘diffusive-convective ’, relating convection (its sign included) and diffusion. Note that in the above development we have confined ourselves to analysing the perturbation introduced in the compartment L. Relating this phenomenon to the estimation of the error involved in the experimental determination of the ‘lag time’ is a hard task.18 Actually, an important systematic error observed in this kind of experiment arises from the incomplete attainment of the steady state at the beginning of the measurements and not from the finite volume of compartment L.” 1 -(Ad/V)F(r) 6[rcoth(r/2)-2] = 1 -(Ad/ V ) F(r) exp ( r ) r2 Discussion The non-stationary ionic transport through a homogeneous membrane in the case of simultaneous diffusion, convection and electric conduction has been considered. The effect convection exerts on some experimental parameters of interest has been studied.Likewise, conditions have been given under which the assumption of ‘infinite collecting volume’ is valid. Some approximations have been made, both in the membrane model and in the transport equations.We have dealt with a one-dimensional problem. Although one- dimensional models are useful,’, 4 * a cylindrical pore model accounting for the electric double layer on the pore walls seems more realistic, especially in membranes where the pore size is much greater than the Debye length.2 Despite this, the model considered has two advantages: it contains the essential trends of the transport problem and it makes possible an analytical solution, rather general and simple, by using standard techniques. l4 This work is part of the CAICYT project no. PB 85-0202, Ministry of Education and Science of Spain. CAICYT’s support is gratefully acknowledged. Appendix : An Homogeneous, Charged Membrane Charged membranes are currently used, so it seems necessary to study the changes to be made in the equations of the problem to account for the fixed charge X(assumed to be234 Membrane Transport constant with time and position).Consider, for this purpose, the Nernst-Planck equation [eqn (l)] and the equation for the current density [eqn (2)]. Both of these are constrained by the electroneutrality approximation, now written in the form 2 ~ z i c i + w x = o - - , c l = c , + x i - 1 where it has been considered, without loss of generality that w = - 1 (cation-exchange membrane). We denote c, = c. From eqn ( l ) , (2) and (A 1) and solving for the potential gradient, one obtains F3! RTax = [ F ax [(D,+D,)C+D,X] By substituting eqn (A 2) into eqn (1) and applying the continuity equation (3), an equation for c(x, t ) containing its derivatives with respect to x and t is readily obtained.For instance, in the case of i = 2 we obtain G(c) = (Dl + D,) c + D,x. Eqn (A 3) generalizes the previous result for the case X # 0. Unlike eqn (9, the former depends explicitly on the current density i. Unfortunately, eqn (A 3) is a non-linear differential equation with variable coefficients, suggesting the necessity of further approximations. In view of the characteristics of the theoretical model proposed, it seems evident that one of the conditions that should be met is that X < c, at most, because we have neglected any specific interaction between ions and the membrane structure (ideal ionic behaviour). Having in mind this, X < low5 cm2 s-’ (a weekly charged membrane) and D,, D, M lop5 cm2 s-’.If we accept as typical values v M cm s-’, co z lop5 mol cmP3, i M 10 mA cm-, and d M lo-, cm, the four terms in eqn (A 3) are of the same order of magnitude. This fact makes it difficult to introduce further simplifications. However, if the concentration gradient imposed is small c(0)-c(d) = dc, 4 c,, c, being the scaling concentration of the problem], the last term in eqn (A 3) is nearly an order of magnitude smaller than the remaining three terms. Indeed, if dc, M mol ~ m - ~ , the first three terms in eqn (A 3) take values around lo-’ mol s-l, while that of is around lo-’ mol cm-3 s-l. Moreover, we can approximate in this case G(c) M (D, +D,)c,+D,X = constant. Thus, the condition dc,/c, 6 1 (‘very small’ gradient) involves linearizing the equations, thus neglecting as a first approximation the term in (i3c/i3x)2.The condition also permits taking the coefficients as constants. Then, eqn (A 3) would lead to mol cm-3 and c, M Eqn (A 4) is formally analogous to eqn (9, so that the solution discussed before might be valid by changing u + u’ and D -+ D’. However, two new features appear in the case X # 0. First, v depends now on both the pressure gradient and the electric potential gradient across the membrane (electro-osmotic term). Secondly, this case calls for a specific model for the interfaces (a Donnan relationship, for instance).V. M. Aguilella, S. Mafe' and J. Pellicer References 235 1 R. Schlogl, Ber. Bunsenges. Phys. Chem., 1966,70, 400. 2 P. Meares and K. Page, Philos. Trans. R. Soc. London, B 1972, 272, 1. 3 A. Ekman, P. Forssell, K. Kontturi and G. Sundholm, J. Membrane Sci., 1982, 11, 65. 4 K. Kontturi, P. Forssell and A. Sipila, J. Chem. Soc., Faraday Trans. I , 1982, 78, 3613. 5 K. Kontturi and A-K. Kontturi, Acia Chem. Scand., Part A , 1986, 40, 555. 6 V. G. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, N.J., 1962). 7 R. P. Buck, J. Membrane Sci., 1984, 17, 1. 8 J. Newman, Electrochemical Systems (Prentice Hall, Englewood Cliffs, N.J., 1973). 9 T. R. Brumleve and R. P. Buck, J. Electroanal. Chem., 1978, 90, I . 10 J. Garrido, S. Mafk and J. Pellicer, J. Membrane Sci., 1985, 24, 7. 1 I J. L. Jackson, J. Phys. Chem., 1974, 78, 2060. 12 S. Mafk, V . M. Aguilella and J. Pellicer, J. Phys. Chem., 1986, 90, 6045. 13 S. Mafk, J. Pellicer and V. M. Aguilella, Ber. Bunsenges. Phys. Chem., 1986, 90, 476. 14 J. C. Keister and G. B. Kasting, J. Membrane Sci., 1986, 29, 155. 15 S. Mafk, J. A. Manzanares and J. Pellicer, J. Electroanal. Chem., 1988, 241, 57. 16 J. Crank, The Mathematics of Diflwion (Oxford University Press, Oxford, 1975). 17 R. Paterson and P. Doran, J. Membrane Sci., 1986, 26, 289. 18 J. H. Petropoulos and C. Myrat, J. Membrane Sci., 1977, 2, 3. 19 J. H. Petropoulos, J. Membrane Sci., 1987, 31, 103. Paper 8/oO33 1 I ; Received 22nd January, 1988

ISSN:0300-9599    

DOI:10.1039/F19898500223

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1989, 85(2), 237-249 Structure and Reactivity of Zinc-Chromium Mixed Oxides Part 3.-The Surface Interaction with Carbon Monoxide Elio Giamello,* Bice Fubini and Massimo Bertoldi Dipartimento di Chimica Inorganica, Chimica Fisica e Chimica dei Materiali, Universita di Torino, Via P. Giuria 9, 10125 Torino, Italy Guido Busca Istituto di Chimica, Facolta di Ingegneria, Universita di Genova, Fiera del Mare, 16129 Genova, Italy Angelo Vaccari Dipartimento di Chimica Industriale e dei Materiali, Universita di Bologna, Viale del Risorgimento 4, 40136 Bologna, Italy The reactivity towards carbon monoxide of a series of Zn-Cr non- stoichiometric spinels (NSS) with an excess of zinc, active in the synthesis of methanol and higher alcohols, has been investigated by infrared spectro- scopy and adsorption microcalorimetry.A fraction of the total CO taken up is irreversibly oxidized to surface carbonates by the chromate groups pres- ent. A second fraction is strongly but reversibly coordinated in the form of a 'carbon-down' CO complex, the heat of adsorption being between 80 and 50 kJ mol-' and the C-0 stretching frequency in the range 2192-2205 cm-'. The strongest active sites for CO coordination are surface Cr3+ ions acting as a-acceptors, but also capable of d-n backdonation. The number of active sites for CO coordination is very low in the stoichiometric spinel ZnCr,O, (inactive in methanol synthesis), whereas it grows in the zinc-excess non- stoichiometric spinels owing to modifications of the ' collective ' properties of the solid introduced by the presence of the excess zinc into the spinel lattice.Zn-Cr mixed-oxide systems have been widely employed in the past in the catalytic synthesis of methanol from carbon monoxide and hydrogen,' and have recently found a new interest owing to the possibility of syngas conversion to mixtures of methanol and higher alcohols.2 In spite of the extensive utilization of this catalyst, information concerning the nature of its surface and the mechanisms of CO and H, activation and of the catalytic reaction is still lacking, owing to a lack of detailed surface characterization. We have recently carried out a systematic characterization of a family of well defined zinc-chromium mixed oxides having different Zn/Cr ratios. All the members of this series of compounds are monophasic in the composition range 33 : 67 < Zn : Cr < 50 : 50, and can be regarded as zinc-excess non-stoichiometric spinels (NSS) with an excess of Zn2+ ions located at B-type sites of the AB,O, spinel lattice (with octahedral Above the 50: 50 ratio the systems are biphasic, with a separate ZnO phase in addition to the ' spinel-like' one.Differences in surface properties and methanol decomposition between stoichiometric and non-stoichiometric spinels have been reported in previous paper^.^,^ The present one is devoted to a detailed investigation of the surface activity towards carbon monoxide by adsorption microcalorimetry and Fourier- transform infrared spectroscopy. As the CO molecule is directly involved in syngas catalytic reactions, the investigation of its interaction with the catalyst surface can afford useful information on the nature and number of active sites : 9 237 FAR 1238 Reactivity of Zn-Cr Mixed Oxides Table 1.Bulk and surface composition of some C-Zn-Cr samples Zn : Cr (bulk) Zn : Cr (surface) C r * / [ C r I + C r I 'I] 33 : 67 38:62 44: 56 50:50 22: 78 24: 76 41 : 59 47: 53 0.33 0.33 0.28 0.32 this approach has been adopted previously in the characterization of other systems active in methanol ~ynthesis.~-~ Experimental The Zn-Cr catalysts were prepared by coprecipitation from solutions containing Zn and Cr nitrates followed by successive calcination. The preparation procedure, sample composition and characterization have previously been described in detail.,, The samples investigated, hereafter denoted by their Zn/Cr ratio, are Zn : Cr = 33 : 67 (stoichiometric spinel, ZnCr,O,), Zn : Cr = 38 : 62, Zn : Cr = 44: 56 and Zn :Cr = 50 : 50 (all monophasic), and Zn : Cr = 75 : 25 (biphasic : ZnO + NSS phase). A sample of pure chromia was also employed.The catalysts were studied in their calcined and reduced states. The calcined catalysts (labelled C) were outgassed at 573 K for 1 h in order to eliminate surface poisoning due to atmospheric agents. The reduced catalysts (denoted R) were treated with 100 Torr CO (1 Torr z 133.3 Pa) for 20 h at 373 K and then outgassed at 573 K. Reduction with CO eliminated the surface chromates always present at the surface after calcination. X.P.S. experiments to measure the surface composition were performed in a Perkin Elmer PHI 5400 ESCA system at a pressure < 1 x Pa.All samples were measured with the same instrumental settings, and the sensitivity factors were previously determined with the same instrument on samples of single elements. The values employed were Zn(2p3/,) = 4.80 and Cr(2p) = 2.30 [relative to the F( 1 s) = 1 .OO]. In the case of Cr the area under both signals, 2p,/, and 2p,,, was considered taking into account the non-complete separation between the two signals. The infrared spectra were recorded at room temperature and 173 K using a Nicolet MXI Fourier-transform spectrometer. The samples were pressed in self-supporting discs and placed in a cell with KBr windows connected to a greaseless vacuum line. The heats of adsorption of CO were measured by means of a Tian-Calvet microcalorimeter connected to a volumetric apparatus, adsorbing small successive doses of the gas.Each adsorption run was followed by stepwise desorption.1° For each dose the amount adsorbed (or desorbed) and the related heat were measured, except in the case of the last dose of desorption for which, being obtained by direct evacuation, only the heat of adsorption is measurable. Results Surface Composition In table 1 the compositions in atomic percentage of both the bulk and the surface are reported for some Zn-Cr samples, as obtained by photoelectron spectroscopy. In no case was zinc enrichment of the surface observed : it is therefore possible to exclude the presence at the surface of amorphous or highly divided ZnO phases not detectable by X-ray diffraction.This hypothesis was advanced (inter alia) in a previous paper5 to explain the differences in surface behaviour between the stoichiometric and the zinc- excess, non-stoichiometric spinels.E. Giamello et al. 239 0 20 40 60 90 0.40 0.60 O. *O n, l-1 m-2 0 Fig. 1. CO adsorption onto a C-Zn : Cr = 75 : 25 sample. (a) Calorimetric isotherms (Qint us. p ) for three successive runs. Open symbols: adsorption; full symbols: desorption; 0 @, run I ; a#, run 11; H W , run 111. (b) Partial molar heat of adsorption us. amount adsorbed for the three runs reported in (a). We have also performed a rough determination of the Crv'/[Crvl + CrIII] surface ratio (on the basis of the areas of the 576.6 and 579.6 eV signals) by means of a peak-fitting program.For all samples we found values near 0.3 (table 1,3rd column) similar to those obtained by chemical analysis and previously reported in ref. (3). The Interaction of CO with C Samples In fig. 1 are reported the calorimetric isotherms (evolved heat, Qint, us. pressure,p) and the corresponding partial molar heats of adsorption (evolved heat per amount adsorbed for each dose, AQint/An, vs. amount adsorbed, n,) for three adsorption- desorption runs for CO onto the sample with C-Zn:Cr = 75:25. Run I1 was performed immediately after 9-2240 Reactivity of Zn-Cr Mixed Oxides 1800 1600 1400 1200 1000 800 vim-' Fig. 2. Infrared spectra of CO interaction onto C-Zn: Cr = 50: 50. Full line: background; dashed line: 100 Torr CO 2 min after immission.Dotted line: 100 Torr CO 30 min after immission. Dotkdash line: effect of heating 30 min at 473 K under 100 Torr CO. run I, while run I11 was obtained after a period of 20 days, during which the sample was kept under a pressure of 200 Torr CO at room temperature. The samples with different Zn : Cr ratios behave in a similar way, except for the values of the total amount adsorbed, which are different in each case. The three isotherms in fig. 1 (a) are not coincident, and a noticeable decrease in the heat evolved is observed on passing from run I to run 111; moreover, in the case of runs I and I1 a consistent fraction of the heat evolved is not recovered upon direct evacuation, indicating that a fraction of the adsorbate is irreversibly held at the surface.In the case of run 111, where adsorption and desorption are coincident, no irreversible fraction is observed. The partial molar heat curves [fig. 1 (b)] show that the heat of adsorption decreases with coverage in all cases, and the initial values in the three runs decreases from 230 kJ mol-' in run I to 70 kJ mol-' in run 111. The shape of the calorimetric peaks indicates the presence of slow adsorptive phenomena in the case of runs I and 11, whereas in the case of run I11 the adsorption is practically instantaneous. The experiment described above clearly indicates that the centres able to cause irreversible adsorption are progressively eliminated by prolonged contact with CO : after saturation in CO for 20 days the residual adsorption (fast, reversible, with a differential heat < 80 kJ mol-l) is exclusively related to the mere coordination of CO onto surface- unsaturated cations.The high value of the heat of interaction, as well as the slow kinetics in the irreversible process, indicate that a surface reaction occurs which is probably the oxidation of CO to surface carbonates. This is confirmed by infrared spectroscopy: fig. 2 reports the i.r. spectra recorded on a C-Zn:Cr = 50:50 sample in the region between 800 and 1800 cm-' recorded, respectively, after outgassing at 573 K (full line,E. Giamello et al. 0.004 24 1 I I I 0 0 .016 .012 .008 background), under 100 Torr CO 2 min after immission (dashed line), 30 min after immission (dotted line), after heating at 473 K in CO for 30 min (dotteddashed line). The narrow band at 1OOOcm-' and the wider one at 950cm-', already assigned to chromate~,~ are slightly eroded by CO at room temperature, with a parallel increase of absorption in the region between 1200 and 1600 cm-', indicating the formation of various types of surface carbonates.When the temperature of the system is raised to 473 K the decrease in the chromate bands and the increase in the carbonate bands become dramatic. The admission of CO also causes the appearance of a sharp band in the region typical of vco of metal carbonyl whose features will be discussed in the following section. The Interaction of CO with R Samples In fig. 3 are reported, as calorimetric isotherms, three adsorption-desorption cycles of CO successively performed on the surface of an R-Zn:Cr = 75:25 sample.The differences between the three isotherms [note that the ordinate scale in fig. 3 is expanded by comparison with fig. 1 (a)] are very small by comparison with those on the C sample [fig. 1 (a)], and a minor fraction of irreversibly adsorbed CO is observed in the first and second cycle only, due to residual CO oxidation. The third adsorption isotherm in fig. 3 (111) is completely reversible and almost coincides with the third one in fig. l(a), where prolonged contact with CO ensures the complete exhaustion of the oxidation process: the two treatments are therefore equivalent, and the reduction by CO at 373 K can thus be adopted as the standard method for eliminating the superimposition of surface oxidation on reversible adsorption of CO.This latter process on the whole series of R samples is, in all cases, fast and non-activated. The partial molar heat, corresponding to isotherm I11 in fig. 3, is reported in fig. 4, The heat of adsorption decreases with coverage from an initial value at ca. 80 kJ mol-' to ca. 45 kJ mol-'. The heat of desorption, in the more limited range of coverage in which it can be measured,242 80 - i 2- 40- 2 I 1 I I - c. I C J C . I I I 1 I 0 0.1 0.2 0.3 0 . 4 0.5 0.6 'E 3 =t 2 0.4 0.2 0 20 40 pmorr 60 Fig. 5. Volumetric isotherms (n, us. p ) for CO adsorption onto the whole series of stoichiometric and non-stoichiometric R-samples. ., Cr,O,; 0, ZnCr,O,; 0, Zn:Cr = 38:62; A, Zn:Cr = 44:56; 0, Zn:Cr = 50:50; V, Zn:Cr = 75:25.E. Giamello et al. 243 I I 1 I I 0 0.2 0.4 0.6 0.8 n, /pmol m-' 0 Fig.6. Partial molar heat of adsorption for CO onto the whole series of samples. Symbols as in fig. 5 . fits the trend shown by the heat of adsorption, indicating that the evacuation of surface sites exactly follows the inverse order of filling. The adsorption-desorption cycles described above have been performed for all the R samples of the series, and for a sample of pure chromia. Significant differences in adsorption capacity are found for the various samples. Fig. 5 reports the volumetric isotherms for the whole series of samples considered in the present paper. The corresponding heats of adsorption are reported in fig. 6 as a function of coverage, and exhibit a similar trend to that shown in fig. 4. The variations in adsorptive capacity (fig.5 and 6) do not involve different kinds of adsorption sites., but rather a different site energy distribution : in particular, inspection of fig. 6 indicates that the main differences among the various samples is determined by the different numbers of sites having heats of adsorption > 60 kJ mol-'. The six samples reported in fig. 6 can be easily divided into three groups: the stoichiometric oxides (Cr,O, and ZnCr,O,) which adsorb ca. 0.1 pmol CO m-,, the monophasic non-stoichiometric spinels on which the total adsorption is much higher, ranging between 0.6 and 0.8 pmol rn-, and the biphasic one, with an intermediate value. The non-stoichiometry of the solid is therefore related to a considerable improvement in the chemisorptive capacity. The amount of CO adsorbed by the various non-stoichiometric samples decreases with an increase in the zinc excess present in the solid : maximum adsorption is observed for the sample at the beginning of its departure from stoichiometry (Zn: Cr = 38 : 62).5 The total chemisorptive capacities of the various samples examined (taken at 60 Torr equilibrium pressure), as a function of composition, are reported in fig.7 (upper curve). The value reported for ZnO is from ref. (7). The lower curve in fig. 7 reports the amounts of CO adsorbed with heats of adsorption > 60 kJ mol-', as deduced from fig. 6. As the lower curve follows a trend nearly parallel to the upper one it can be confirmed that the pronounced differences in the CO adsorption capacity between the various samples must be ascribed to differences in high-energy sites, which are completely absent in the pure Zn0.7 When a prereduced sample (R) is put in contact with CO the only modification observed in the i.r.spectrum is the formation of an absorption band in the region of the244 Reactivity of Zn-Cr Mixed Oxides 1 Cr (atom %) 100 80 60 40 20 0 Zn (atom %) Fig. 7. CO chemisorptive capacity as a function of sample composition. Open symbols: total adsorption at 60 Torr. Full symbols: adsorption with qdiff 2 60 kJ mol-'. Table 2. Infrared frequencies for CO adsorption onto the whole series of R samples sample-Zn : Cr v/cm-' (298 K) vlcm-l(l70 K) 33:67 - 2170 38:62 2202 (ii) 2195 (i)-2205 (ii) 44: 66 2195 (it2202 (sh) 2195 (i)-2205 (sh) 50: 50 2192 2192 75 : 25 2192 2192 metal carbonyl, also present on C samples. Such bands have been observed at room temperature on all samples except the stoichiometric spinel (Zn:Cr = 33:67).If the spectra are carried out at 170 K, even in the case of ZnCr,O,, a small i.r. band appears, and on some of the non-stoichiometric samples a better resolution of the band in two component is visible. The i.r. frequencies recorded for the adsorption of CO at room temperature and at 170 K on the various samples are reported in table 2, and the corresponding i.r. spectra at 170 K are shown in fig. 8. The CO pressure was kept at 100 Torr in all cases. Three main facts can be outlined by inspection of the i.r. results : (i) the intensities of the spectra roughly follow the same order observed for the amounts adsorbed and reported in fig.6; (ii) the stoichiometric ZnCr,O, spinel exhibits at low temperatures a CO stretching band at 2170 cm-', whereas all the bands related to the non-stoichiometric spinels are at frequencies > 20 cm-I higher; (iii) in the case of the two samples exhibiting the highest adsorption capacities (Zn : Cr = 38 : 62 and Zn : Cr = 44 : 56) the low-temperature spectra reveal the presence of two distinct bands in the carbonyl region.E. Giamello et al. 245 1 - 100 2200 2100 ! 3 I 5 300 2200 2100 2300 2200 2100 2300 2200 2100 2300 2200 2100 vim-' Fig. 8. Infrared spectra in the carbonylic region of adsorbed CO. T = 170 K. (1) Zn : Cr = 33 : 67, (2) Zn:Cr = 38:62, (3) Zn:Cr = 44:56, (4) Zn:Cr = 50:50, ( 5 ) Zn:Cr = 75:25. Discussion Nature of the Interaction of CO with the Zn/Cr Samples The investigation of CO adsorption on calcined samples (C) has identified the presence of two types of interactions with the surface, i.e.redox reactions, with the consequent formation of carbonates, and CO coordination. The former phenomenon is due to the presence of chromates at the surface of the samples, easily observed by i.r. and X.p. spectroscopy. The reduction of the chromates by CO (very slow at room temperature) is highly exothermic, but involves a relatively low number of CO molecules. In the case of C-Zn : Cr = 75 : 25 for instance, the number of reactive chromate centres present at the surface is CQ. 25% of the total number of sites reacting with CO. The reversible adsorption of CO on NSS is characterized by heterogeneity in the adsorption sites.Inspection of the differential heat plot in fig. 6 suggests the presence of two distinct families of sites: the first, with a high differential heat (8MO kJ mol-'), is more abundant than the second, with a heat of adsorption of ca. 50 kJ mol-l. This interpretation is supported by i.r. data which show, at least in the case of R-Zn : Cr = 38 : 62 and R-Zn : Cr = 44: 56, the presence of two distinct absorptions (table 2 and fig. 8). The adsorption of CO at the surface of the non-stoichiometric spinels is thus characterized by a family of active sites capable of a strong but still reversible interaction with the CO molecule, having an energy of interaction in the range 8MO kJ mol-'. A frequency value higher than that of the free molecule indicates that the chemical bonding is mainly based on the interaction between the 50 orbital of CO and an acceptor site.This entails a net increase of the bond order between C and 0. Nature and Number of Active Sites Stoic h iome t r ic So lids The Cr3+ ions are thought to be present in octahedral coordination in both stoichiometric and Zn-excess they are also present in the same coordination in Cr,O,, which, however, has the corundum structure. The pure chromia has a chemisorptive capacity similar to that of ZnCr,O, (at least with the pretreatment adopted in the present work) in the adsorption of CO at room temperature (fig. 5). Infrared work carried out on a- chromia microcrystals" has shown that the frequency of adsorbed CO is 2185 cm-'246 Reactivity of Zn-Cr Mixed Oxides Fig.9. Schematic representation of an ideal (1 00) face of the ZnCr,O, spinel. The lattice parameter is ( a ) Taking as a reference the plane of external ions (Cr3+, 02-: open symbols) the other ions lie below this plane at distances of a/8 (Zn2+, full symbols) and a / 4 (02-, dashed symbols), respectively . (0 = 0), which shifts at high coverage to 2170 cm-l. This latter value is exactly the same as that measured by us on the zinc chromite at high coverage ( p = 100 Torr, table 1). The carbon monoxide adsorption on chromia has been assigned to the coordination onto coordinatively insaturated Cr3+ octahedral ions at the (0001) faces.ll The fact that ZnCr204 and Cr203 show similar trends in the differential heat of CO adsorption and exactly the same infrared frequency at high coverage, suggest that, on these two solids, the active sites for CO adsorption are the same, i.e.the coordinatively unsaturated octahedral Cr3+ ions. The absence of adsorption of CO onto zinc ions in the stoichiometric spinel can be explained by taking into account that, in AB204, the (100) and (1 11) are the most exposed crystal faces.12 In the former case the surface-exposed ions are exclusively Cr3+ and 02-, whereas the Zn2+ ions lie under the first surface layer with a complete tetrahedral coordination sphere (fig. 9). With regard to the ( 1 11) faces, it has been clarified12 that, although they could in principle assume two distinct configurations, only the one exposing octahedral sites is present at the surface.The previous description agrees with the very low value of Zn : Cr found by X.P.S. surface analysis in the case of the zinc chromite (table 1) and also with the lack of detection, on the same solid, of zinc hydrides observed by some of us on the non-stoichiometric solids. l 3 Non-stoichiometric Spinels In these solids the chromium ions are expected to maintain the same octahedral coordination typical of ZnCr,O,, but the presence of an excess of Zn2+ ions also in octahedral coordination4* implies that each Cr3' is surrounded by a 'mixed ' cationic sphere (at 2/2a/4) composed of both chromium and zinc ions. At the NSS surface, therefore, two kinds of coordinatively unsaturated ions of octahedral origin are exposed : Zn2+ ions and Cr3' ions 'modified ' by the presence of the former. The unambiguous identification of the nature of the site adsorbing CO at the surface of NSS, on the basis of the i.r.frequency only, is practically impossible because the observed frequency values are in agreement with those reported in the literature forE. Giamello et al. 247 adsorption either on Zn2+ or Cr3+ centres."' 14, l5 Some hypothesis can thus be made only considering the coupling between spectroscopic and energetic data. If CO were adsorbed onto Zn2+ the simple model of o-donation would apply for the chemical bond. In this model the CO stretching frequency and the heat of adsorption must both increase with an increase in the electrostatic field of the cation, which is related to the degree of coordinative unsaturation of the cation itself.The existence of a parabolic correlation law between the heat of adsorption and frequency has recently been proposed on the basis of the results obtained for various solids containing 'non-d' cations.l6 From an inspection of the correlation curve one can deduce that in the case of the Zn2+ cations of unreduced ZnO a frequency of ca. 2188 cm-' is associated with a heat of adsorption of 45 kJ mol-', while frequencies in the range 2192-2205 cm-l, like those monitored in the case of non-stoichiometric spinels, correspond to an energy in the range 50-55 kJ mol-'. If the zinc ions coordinate CO on non-stoichiometric spinels, they should have a higher coordinative insaturation than in ZnO. A typical example of highly exposed Zn2+ is that of the Zn2+ partially exchanged Y zeolites : in this system Angel1 and Shaffer found a stretching frequency for adsorbed CO at 2214 cm-', which was unambiguously assigned to CO adsorbed on highly uncoordinated zinc ions typical of the zeolite framework." As no energy data were available for this system, an ad hoc experiment was performed to measure the heat of adsorption of CO and the related frequency on a partially exchanged Zn/Y zeolite.The results will be reported elsewhere in detail;'* they confirm the frequency value from ref. (1 7) (2214 cm-l) and indicate a heat of interaction, due to CO coordination onto zinc ions, of 58 kJ mol-l, i.e. lower than that measured on NSS. These two values fall very close to the correlation curve in ref. (16). The hypothesis whereby zinc cations are the strongest active sites in CO adsorption at the NSS surface must therefore be disregarded.To explain the high heat of adsorption observed in correspondence with frequencies around 2200 cm-', it is necessary to consider the role of chromium ions as adsorption centres. It is generally accepted that the interaction of CO with a transition-metal ion bearing a high electric charge, like Cr3+, is based on simple o donation typical of those ions, without the possibility of d-n back-bonding.lg However, in a recent paper by Zecchina and co-workers this problem was reinvestigated on the basis of the results obtained for CO adsorption on pure a-chromia." The authors observed relevant frequency shifts of the CO stretching band of both the static and dynamic types, indicating, respectively, the existence of inductive effects and vibrational couplings in the CO/Cr203 system.This behaviour can be explained by a bond model involving in addition to a strong interaction between the 50 orbital and a suitable d orbital, a non- negligible contribution by d-n* delocalization. l1 The frequency value at zero coverage found on Cr20, (2185 cm-') is therefore determined by the balance of two opposite tendencies: a strong c interaction, which tends to increase the C-0 frequency, and back-bonding, which contributes to its reduction. The correlation between heat and frequency, typical of simple o coordination, does not apply in this model, and a lowering of the zero-coverage frequency by the n contribution corresponds to a higher heat of adsorption, as the latter value monitors the strength of the whole interaction.Therefore the heat and frequency values cannot fall on the correlation curve reported in ref. (16), which is typical of pure o coordination. In the case of NSS we thus assign the extended CO adsorption with a heat of interaction between 80 and 60 kJ mol-1 to Cr3+ ions present at the surface of the spinel-like system, thus modifying our previous a~signment.~ The heat of adsorption has the same initial value as that observed for stoichiometric oxides (fig. 6), indicating that the nature of the interaction is basically the same in the two cases and involves both a-bonding and n-backbonding. The assignment of the main fraction of CO adsorption to the surface chromium ions present on NSS is also in agreement with the data for chemisorptive capacity (fig.7), indicating that the adsorption of CO decreases on increasing the zinc content of the samples. For the248 Reactivity of Zn-Cr Mixed Oxides second, less abundant, family of sites exhibiting a heat of interaction < 60 kJ mol-1 and observed at the surface of non-stoichiometric spinels only, two hypotheses can be proposed. In the first the active sites are still Cr3+ ions in a different environment from those constituting the main fraction of adsorption sites : this is the case, for instance, of the ions located on a different crystal plane. In the second hypothesis the sites are constituted by surface Zn2+ ions: the frequency values corresponding to a heat of 50-55 kJ mol-' are expected to fall around 2200 cm-l,18 on the basis of the v us.AH relationship. l6 Finally, the remarkable increases observed on passing from ZnCr,O, to NSS, both in the amount and in the stretching frequency of the adsorbed CO, must be discussed. First of all, as already mentioned, the adsorbing Cr3+ ions in NSS are different from those of zinc chromite because of the presence of neighbouring octahedral zinc ions which can induce, by electrostatic effects, variations of the actual cationic charge at the adsorption sites, thus influencing the adsorption behaviour. We basically think, however, that the origin of this behaviour mainly stems from the different 'collective' properties of the systems investigated. It is well known, on the one hand, that Cr,03 and ZnCr,O, show similar conductivity behaviour.'" On the other hand we have recently reported5 the following.(a) All NSS are antiferromagnetic and show a resonant line in their e.s.r. spectra at the same g value observed for ZnCr,O,. The linewidth of the e.s.r. spectrum of NSS, however, is always larger than that of zinc chromite and regularly varies with composition, indicating a progressive variation of the magnetic coupling between Cr3+ ions. (b) Non-vibrational absorption bands are observed in the i.r. region in the case of NSS, whose maxima vary slightly with composition. This behaviour indicates the presence of semiconductivity phenomena, which are likely more pronounced than in the case of ZnCr,O,. It is therefore not surprising that CO adsorption, which involves electron donation towards the bands of the could occur at different extents on NSS and ZnCr,O,.Similar considerations explain the variation of ca. 30 cm-l of the frequency values at 100 Torr between stoichiometric and non-stoichiometric oxides : the delicate balance between electron donation and back-donation, which determines the value of v, basically depends on the capacity for transmission through the solid of the adsorbate-adsorbate interaction. The latter, in its turn, must be related to the electron distribution in the bands of the solid. Conductivity measurements are needed to confirm relationships between electronic properties and surface reactivity of the solids. Conclusions The investigation of the interaction of CO with the surface of Zn-Cr non-stoichiometric spinels has provided evidence of both the oxidation of the CO molecule to surface carbonates and the reversible coordination of the molecule mainly onto surface Cr3+ ions.The latter ions are able to form stable, but reversible, complexes with CO based on the mechanism of a-donation and n-back-bonding. The zinc-excess solids are able to chemisorb CO in larger amounts than the stoichiometric zinc chromite. The total amount adsorbed is related to the chromium content and therefore decreases with increasing zinc excess. The increase of the chemisorptive capacities towards CO is basically due to the unusual collective properties of the non-stoichiometric spinels, which contain Zn2+ ions in the B positions of the lattice. The Zn2+ ions (responsible for the hydrogen dissociation on non-stoichiometric spinels13 but not for the main fraction of CO adsorption) therefore play a fundamental role in determining the general properties of these solids.Like other systems active in the synthesis of methanol from carbon monoxide and hydrogen, the activation of CO consists of the 'carbon-down' coordination of theE. Giamello et al. 249 Helpful discussions with Prof. F. Trifiro’ are gratefully acknowledged, as well as financial support by the Italian Ministry of Education (Progetti di rilevante interesse Nazionale : Gruppo Struttura e reattivita’ delle superfici). References 1 G. Natta, in Catalysis, ed. P. H. Hemmet (Reinhold, New York, 1953), vol. 111, chap. 8. 2 M. Di Conca, A. Riva, F. Trifiro’, A. Vaccari, G. Del Piero, V. Fattore and F. Pincolini, Proc. 8th Znt. 3 G. Del Piero, M. Di Conca, F. Trifiro’ and A. Vaccari, in Reactivity of Solids, ed. P. Barret and L. C. 4 G. DelPiero, F. Trifiro’ and A. Vaccari, J . Chem. Soc., Chem. Comrnun., 1984, 656. 5 M. Bertoldi, G. Busca, B. Fubini, E. Giamello, F. Trifiro’ and A. Vaccari, J. Chem. SOC., Faraday 6 F. Trifiro’, L. Mintchev, G. Busca, A. Vaccari and A. Riva, J. Chem. SOC., Faraday Trans. 1, 1988, 84, 7 E. Giamello and B. Fubini, J . Chem. Soc., Faraday Trans. 1 , 1983, 79, 1995. 8 E. Giamello, B. Fubini and P. Lauro, Appl. Catal., 1986, 21, 133. 9 E. Giamello, B. Fubini and V. Bolis, Appl. Card., 1988, 36, 287. 10 B. Fubini, Rev. Gen. Thermodyn., 1979, 297. I 1 D. Scarano, A. Zecchina and A. Reller, Surf. Sci., 1988, 198, 11. 12 J. L. Hutchison and N. A. Briscoe, Ultramicroscopy, 1985, 18, 435. 13 G. Busca and A. Vaccari, J. Catal., 1988, 108, 481. 14 A. Zecchina, S. Coluccia, E. Guglielminotti and G. Ghiotti, J. Phys. Chem., 1971, 75, 2774. 15 D. A. Seanor and C. H. Amberg, J. Chem. Phys., 1965, 70, 2967. 16 C. Morterra, E. Garrone, V. Bolis and B. Fubini, Specfrochim. Acfa, Part A , 1987, 43, 1577. 17 C. L. Angel1 and P. Shaffer, J. Phys. Chem., 1966, 70, 1413. 18 V. Bolis, B. Fubini and E. Giamello, to be published. 19 Yu. A. Lokhov and A. A. Davidov, Kinet. Katal., 1980, 21, 1523. 20 J. F. Garcia de la Banda, J. Catal., 1962, 1, 136. 21 G. L. Griffin and J. T. Yates Jr, J. Chem. Phys., 1982, 77, 3351. 22 K. Klier, Adv. Catal., 1982, 31, 243. Congr. Catal. (Dechema, Frankfurt am Main, 1984), vol. 11, p. 173. Doufur (Elsevier, Amsterdam, 1985), p. 1029. Trans. I , 1988, 84, 1405. 1423. Paper 8/00566D; Received 15th February, 1988

ISSN:0300-9599    

DOI:10.1039/F19898500237

出版商:RSC    

年代:1989

数据来源: RSC