摘要:

GENERAL DlSCUSSIONS OF THE FARADAY SOCIETY Date 1907 1907 1910 191 1 1912 1913 1913 1913 1914 1914 1915 1016 1916 1917 1917 1917 1918 1918 1918 1918 1919 1919 I920 1920 1920 1920 I921 1921 1921 1021 I922 1922 1923 I923 I023 1923 1923 1924 I924 1924 1924 1924 1925 I925 1926 1926 1927 1927 1927 Subject Osmotic Prcssure Hydrates in Solution The Constitution of Water High Temperature Work Magnetic Properties of Alloys Colloids and their Viscosity The Corrosion of Iron and Stcel The Passivity of Metals Optical Rotary Power The Hardening of Mctals The Transformation of Purc Lron Mcthods and Appliances for the Attainmcnt of High Tcmpcraturcs i n a Refractory Materials Training and Work of thc Chcmical Enginccr Osmotic Pressurc Pyrometers and Yyronictry Thc Setting of Cements and Plastcrs Electrical Furnaces Co-ordination of Scientific Publication The Occlusion of Gases by Metals The Present Position of the Theory of Ionization The Examination of Materials by X-Rays Thc Microscope : Its Dcsign, Construction and Applications Basic Slags : Thcir Production and Utilizaticm i n Agricullurc Physics and Chemistry of Colloids Elcctrodcposition and Electroplating Capillarity The Failure of Metals under Intcrnal and l'rolongcd Strcss Physico-Chemical Problcms Rclating to the Soil Catalysis with spccial refcrcnce to Newcr l'hcorics of Chemical Action Some Propcrties of Powders with spccinl rcfcrcncc to tirading by The Generation and Utilization of Cold Alloys Resistant to Corrosion The Physical Chcrnistry of the Photographic Process The Electronic Theory of Valcncy Electrode Reactions and Equilibria Atmospheric Corrosion.First Report Investigation on 0 p pa u Ammon i 11 m Sul p ha tc-N it ra t c Fluxes and Slags in Metal Melting and Working Physical and Physico-Chemical Problems relating to 'Textile Fibrcs The Physical Chemistry of Igncous Rock Formation Base Exchange in Soils The Physical Chemistry of Stccl-Making Proccsscs Photochemical Reactions in Liquids and Gases Explosive Reactions in Gascous Media Physical Phenomena at Interfaces, with special refcrencc to Molecular Atmospheric Corrosion. Second Report The Theory of Strong Electrolytes Cohesion and Related Problems Laboratory Elutriation Orientation VO/ldJtlC! Trans. 3 3 6 1 8 9 9 9 10 10 11 12 12 13 13 13 14 14 14 14 15 15 16 16 16 16 17 17 17 17 18 18 19 I!, 19 19 19 20 20 20 20 20 21 21 22 22 23 23 24GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Dctte 1928 I929 L 929 1929 1930 1930 1931 1932 1932 1933 1933 1934 1934 1935 1935 I936 1936 1937 1937 1938 1938 1939 1939 I940 1941 1941 1942 1943 1944 I945 1945 I946 1946 I947 1947 1947 1947 1948 1948 1 949 1949 1949 1950 1950 I950 1950 1951 1951 1952 I952 1952 1953 1953 1954 Subject Homogeneous Catalysis Crystal Structure and Chemical Constitution Atmospheric Corrosion of Metals.Molecular Spectra and Molecul? r St ructure Optical Rotatory Power Colloid Scicnce Applied to Biology Photochemical Processes The Adsorption of Gases by Solids The Colloid Aspects of Textile Materialc Liquid Crystals and Anisotropic Melts Free Radicals Dipole Moments Colloidal Electrolytes The Structure of Metallic Coatings, Films and Surfaces The Phenomena pf Polymerization and Condensation Disperse Systems in Gases : Dust, Smoke and Fog Structure and Molecular Forces in (a) Pure Liquids, and (6) Solutions The Properties and Functions of Membranes, Natural and Artificial Reaction Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry The Electrical Double Laycr (owing to the outbreak of war the meeting The Hydrogen Bond The Oil-Water Interface The Mechanism and Chemical Kinetics of Organic Reactions in Liquid The Structure and Reactions of Rubber Modes of Drug Action Molecular Weight and Molecular Weight Distribution in High Polymers.(Joint Meeting with the Plastics Group, Society of Chemical Industry) The Application of Infra-rcd Spectra to Chemical Problems Oxidation Dielec trics Swelling and Shrinking Electrode Processes The Labile Molecule Surface Chemistry.Colloidal Electrolytes and Solutions The Interaction of Water and Porous Materials The Physical Chemistry of Process Metallurgy Crystal Growth Lipo-Proteins Chromatographic Analysis Heterogeneous Catalysis Physico-chemical Propcrties and Bchaviour of Nuclex Acids Spectroscopy and Molecular Striicture and Optical Methods of In- Electrical Double Layer Hydrocarbons Thc Size and Shape Factor in Colloidal Systems Radiation Chemistry The Physical Chemistry of Proteins The Reactivity of Free Radicals The Equilibrium Properties of Solutions of Non-Electrolytes The Physical Chemistry of Dyeing and Tanning The Study of Fast Reactions Third Report was abandoned, but the papers were printed i n the Transactions Systems (Jointly with the Societi: de Chimie Physique at Bordeaux.) Published by Butterworths Scientific Publications, Ltd.vest iga t ing Cell Structure Volunie 24 25 25 25 26 26 27 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 35 36 37 37 38 39 40 41 42 42 A 42 B Disc. 1 2 Trans. 43 Disc. 3 4 5 6 7 8 Trans. 46 Disc. 9 Trans. 47 Disc. I0 1 1 12 13 14 15 16 17 1954 Coagulation and Flocculation 18I h t c I955 I955 I956 1956 1957 I957 1958 1958 959 959 960 G E N E R A L DISCUSSJONS OF T H E FARADAY SOCIETY Sihject Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Proccsses at High Pressures Molecular Mechanisni of Rate Processes in Solids Interactions in Ionic Solutions Configurations and Interactions of Macromolecules and L,iqiii(l Crystals Ions of the Transition Elements Energy Transfer with special refcrcnce to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents Volirtne 19 20 21 22 23 24 25 26 27 28 29 For current availability of Discimion volirmes, see inside of hack cover.

ISSN:0366-9033    

DOI:10.1039/DF960290X001

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

1. OXIDATION-REDUCTION REACTFIQNS IN IONIZING SOLVENTS INTRODUCTORY PAPER ELECTRON-TRANSFER REACTIONS BY J. HALPERN* AND L. E. QRGEL Dept. of Theoretical Chemistry, University Chemical Laboratory, Lensfield Road, Cambridge Received 20th April, 1960 The papers in the first section of this Discussion are largely devoted to the consideration of reactions of the type : Cr2 + + co3 + +Cr3 + + Co2 +, (1) Co(NH3);' + Eo(NH3):+ *Co(NH3):+ + >o(NH~);+, (2) * * TI+ +TI3++Tl3' +T1+, (3) 2Fe2+ +TI3+-+2Fe3 i- +T1", (4) in which the overall change, apart from sometimes subtle rearrangements in the co-ordination shells of the reacting metal ions, corresponds simply to the transfer of one or more electrons between the ions. These are, at least superficially, among the simplest oxidation-reduction reactions and the ones in which the widely recog- nized, but sometimes artificial, connection between electron transfer and oxidation- reduction emerges most clearly.In view of this, it is a curious fact that tho study of such reactions, apart from considerations of stoichiometry and thermodynamics, was almost completely neglected until a few years ago; once started it has been pursued intensively by many workers. Thus a recent and fairly exhaustive com- pilation 1 lists more than a hundred simple redox reactions bctween metal ions or complexes, the kinetics of which have now been examined. With one or two exceptions these refer to work published within the last ten years and in well over half the cases within the last five. The study of electron transfer processes has thus increased very greatly in scope and taken on an entirely new emphasis since the Faraday Society last considered this subject at the Discussion on Oxidation in 1945.The elucidation of the mechanisms of electron transfer reactions between metal ions presents a problem of much greater difficulty and complexity than is sug- gested by the simplified equations by which we usually represent such reactions. The problem has been approached at various levels, both experimental and theoretical, and some of the most important studies relate to the following themes. (i) The nature and sequence, if more than onc, of the elementary steps which (ii) The composition and configuration of the activated complex in the electron * on leave from the Department of Chemistry, University of British Columbia, Van- comprise the overall reaction mechanism. transfer step.couver 8, B.C., Canada. 7ELECTRON-TRANSFER REACTIONS The atomic rearrangements accompanying the electron transfer process. Whether multi-electron redox reactions such as (3) and (4) occur in a single step or through successive one-electron steps. The significance of the large variations in rate which are observed in series of related electron transfer reactions in which the metal ions or the ligands are varied. Examples are the Cr2+-Cr3+, V2+-V3+, Fe2+-Fe3 I-, Fe(CN)% - -Fe(CN)i - and Fe( o-phen) $+-Fe( o-phen); -I- isotopic exchangc reactions whose bimolecular rate constants at 0" are of the order, < 10- ', Other examples of such variations are listed in table 1. 1, lo2 and >lo5 1.mole-' sec-', respectively.' TABLE 1 .-LIGAND EFFECTS IN VARIOUS ELECTRON-TRANSFER REACTIONS (bimolecular rate constants, 1. mole-1 sec-1) (HgN)gCo3 +X-I- Cr2 + (20") (H20)&r3+X+ Cr2+ (OO) (bridged) (bridged) H20 0.9 2 x 10-5 (250)~ F- 2.6 x 10-3d N5 > 1 -2d OH- 1-7 x 106a 0.7 (25" )c c1- > 103b 9d Br- > 6Od NCS- 1.8 x 10-4 (27")d ref. (16). b Anderson and Bonner, J. Amer. Chem. d SOC., 1954, 76, 3826. e Silverman and Dodson, J. Physic. Chem., g 1952, 56, 846. ref. (7). i Laurence, Trans. Faraday SOC., 1957, 53, 1326. Our understanding of these problems is still EXPERIMENTAL 2 x 103e 0.87f 1 x 103e 1 x 103~ 9*7g 1XlW 9.7s > 1.6 x 104e 4.9h 12-2i 2~ 103i ref. (15). ref. (24). ref. (28). Hudis and Wahl, J. Amer.Ciiem. SOC., 1953,75,4153. Bunn and Dainton, Truiu. Furuduy Soc., 1959, 55, 1267. far from complete, ASPECTS Conventional kinetic measurements have been widely used in the study of electron transfer reactions and account for much of our knowledge about their mechanisms. In most cases this approach yields information about the nature of the rate-determining step and the gross composition of the activated complex but not about its detailed configuration or about the participation of the solvent, which is normally present in large and constant excess. Sometimes the values of AH+ and, particularly, of AS* provide indirect information about these, but such information is subject to considerable uncertainty. The paper of Higginson et al.2 is of interest in this connection, Determination of the volume of activation from the pressure-dependence of the rate constitutes another potentially useful extension of the kinetic method; this has yielded information about the role of solvent and the configuration of the activated complex in a ligand exchange reaction 3 but has not so far been applied to oxidation-reduction reactions.The extension of kinetic measurements to non-aqueous solvents offers another poten- tially useful field of investigation. A number of studies of this type have recently been reported including the CeIII-PbIv and Corr-PbIV reactions in acetic acid 49 5 and the FelI-FeTI1 exchange in nitromethane and in alcohol^.^ The Fell-FelllJ . HALPERN AND L. E. ORGEL 9 reaction is much slower in these solvents than in aqueous solution, and is markedly accelerated by the addition of small amounts of water, suggesting that the latter plays a critical role in the reaction.However, these measurements also emphasize the limitations of our general knowledge about ionic reactions in non-aqueous solvents ; considerably more experience with systems of this type will be required before they can be interpreted with confidence. In many cases, kinetic measurements are limited by the high rates of electron- transfer reactions but this limitation is gradually becoming less important as various new methods for the measurement of fast reaction rates are being developed and applied. Flow methods, capable of measuring the rates of reactions with half- lives down to about 10-3 sec have been used to study the kinetics of the Mn0;- MnOi-, and Ag+-Ag2+ reactions ' 9 whose rate constants are of the order of lo3 1.mole-1 sec-1. The rate of Cu+-Cu2+ exchange (kz50 = 5 x 107 1. mole-1 sec-1 in 12 M HCI) has been estimated 10 from the broadening of the n.m.r. signal of Cu+ which occurs when Cu2-t is added and the rate of electron exchange between naphthalene and its mononegative ion (k-107-109 1. mole-1 sec-1) by a corres- ponding e.s.r. measurement ; 11 these techniques will undoubtedly find many other applications. Relaxation methods 12 which have been used to measure the rates of very rapid proton transfer and ionic association reactions (k up to 1011 1. mole-1 sec-I-) also offer possibilities which have not so far been exploited for the study of oxidation-reduction reactions.The introduction of isotopes into common laboratory use has often been cited as one of the most important factors responsible for the recent awakening of interest in the study of electron transfer reactions. One widespread use has been in the study of isotopic exchange reactions between different oxidation states of the same element. Such reactions often have the advantages of being slower than those involving a net chemical change and of providing more convenient models on which to base theoretical treatments, since there is no overall energy change. Isotopic labelling of ligands can also provide valuable information about the detailed mechanism of electron transfer and the configuration of the activated complex. An example of this is the recent demonstration by Kruse and Taube 13 that the oxidation of Cr2+ by (H~N)~CO(OH~)~+ is accompanied by transfer of oxygen from the cobalt complex to chromium.Since both the CO~+ complex and the Cr3+ produced are substitution-inert, this implies that electron transfer proceeds through the bridged intermediate 1 5 + . H (H~N)~CO-O-C~(OH~)~ II H Another important example, involving isotopic labelling of the ligands in the study of the PtT*-PtrV exchange, is described in the paper by Morris, Basolo and Pearson.14 Finally, reference should be made to the measurement of kinetic isotope effects in the study of electron-transfer reactions.15-18 Such measurements may provide information about the extent to which bonds involving the isotopically substituted atoms (0, N and H in the cases examined) are weakened in the activated complex, but unfortunately their interpretation is not always free from ambiguities. This is particularly the case for kinetic isotope effects arising from the substitution of ordinary water by D20 as solvent.MECHANISMS The resolution of complex reaction mechanisms into a sequence of elementary steps can frequently be accomplished by kinetic measurements. The paper of Higginson el aZ.2 deals particularly with this theme and only a few examples will be noted here. Most commonly this problem arises in connection with reactions in which the stoichiometric ratio of oxidant and reductant differs from unity, e.g. the10 ELECTRON-TRANSFER REACTIONS oxidation of Fe2+ by TP+ (eqn. (4)). can be written as The rate-law for this reaction 19 which kl k2 [Fe2 '1 [T13 +I/( k - [Fe3 '1 + k2 [Fe2 '1) implies the mechanism, Fe2 + + TI + k* Fe + T1 ' .( 6 ) The kinetics of simple bimolecular reactions such as (l), (2) and (3) are usually of first order in each of the reactants implying that electron transfer occurs by direct reaction between the oxidant and reductant through an activated complex involving both. However, indirect paths are sometimes found even in such cases. Thus the rate-law 20 for the reaction points to the mechanism, k i Hgi +Hg2 + Hg"(aq), k- i Hg"(aq) +TI3 + 3Hg2+ + T1+, (9) k2 (106 1. mole-1 sec-1 at 25") being at least 106 times greater than the rate con- stant for direct reaction between the Hgif and T13+. The Ag+-Ag2+ isotopic exchange 9 is another example of a simple reaction, in this case a 1-electron transfer, for which an indirect path is preferred.The rate law, Ic[Ag2+]2 suggests that the main exchange path is k 2Ag2'+Ag+ +Ag3+ with k(1 x lo3 1. mole-1 sec-1 at 0") being at least 100 times larger than the rate constant for direct electron transfer between As+ and Ag2+. While the elucidation of the steps involved in complex redox reactions continues to be an important area of investigation, it is on the detailed mechanisms of the elementary electron transfer steps themselves that much of the current interest in this field is focused. An important advance in our understanding of these has been the recognition of at least two types of electron-transfer mechanisms-" outer- sphere " and " inner-sphere " (or & & bridged ").In the first of these electron transfer between the metal ions occurs without disruption of their first co-ordination shells and in the second through an intermediate in which the two metal ions are linked by a bridging group which forms part of the co-ordination shells of both. The distinction between the two is not always sharp and many reactions cannot at this stage be assigned with certainty to either class.21 OUTER-SPHERE ACTIVATED COMPLEX In these reactions there is no change in the first co-ordination shells of the exchanging ions. Examples are the MnOZ-MnOi-, Fe(CN): --Fe(CN)z', Fe(o-phen) ;+-Fe(o-phen) $+ and Co(en) 3 +-Co(en) :+ is0 topic exchanges and theJ . HALPERN AND L. P,. ORGEL 11 oxidation of Cr(dipy)i 1- by Co(NH&+.The evidence for this typc of mechanism is based in most cases on (i) a rate-law which corresponds to an activated complex containing all the ligands in the co-ordination shells of both ions, and (ii) the demonstration that electron-transfer is fastcr than substitution into the co-ordination shells of either of the metal ions. Neither of these criteria is readily applicable to reactions between aquo-ions which can thus rarely be demonstrated to be of this type. In many instances therc is a marked dependence of the rates of such reactions on the nature and concentrations of ions of opposite sign (e.g. the Mn04 -MnOi- exchange is accelerated by cations in the order Cs-'->K+>Na+I Li+).8 One possible interpretation is in terms of an outer-sphere bridged complex such as INNER-SPHERE BRIDGED ACTIVATED COMPLEX Typical of the reactions in this class is the oxidation of Cr2f by complexes of the type (H3N)gCo3+X where X may be one of a largc number of ligands, e.g.H20, OH-, C1-, Br-, acetate, fumarate, etc.22s 23~16. In each case it is found that X appears in the co-ordination shell of the Cr3+ formed. Since both the Co3+ complex and Cr3-t- product are substitution-inert this must mean that electron- transfer occurs through a bridged intermediate of the type in which X is simultaneously co-ordinated to both metal ions. Other examples include electron exchange between Cr2f and Cr3+ complexes of the type (H20)5Cr3+X24 and (E&N)~Cr3fX25, as well as the Pt(en);+-Pt(en)2Cl;+ and related exchange reactions discussed by Morris, Basolo and Pearson.14 For reactions of most metal ions, mechanisms of this type, even if applicable, cannot be demonstrated unequivocally because of the substitution lability of the reactants and/or products.Several points connected with this type of mechanism are worthy of special mention. (i) Although the bridging ligand is generally transferred from the oxidant to the reductant it is not clear that this transfer is an essential feature of the mechanism since in the cases noted it follows simply from a consideration of the relative affinities for the ligand of the two product ions. It has been suggested 26 that the oxidation of Cr2+ by IrClg- also occurs through a C1' bridged mechanism but in this case the products are IrC1;- + Cr(OH2)i-'-. The description of such mechanisms as atom-transfer (as distinct from electron-transfer) processes may thus be somewhat mislcading ; this point is emphasized by the C1--bridged PtII-PtIv exchange re- actions 14 which involve the transfer of two electrons and are thus not equivalent simply to the transfer of a C1 atom from PtrV to Ptn.(ii) Neither catalysis by anions nor incorporation of anions into the co-ordin- ation shell of the oxidized metal ion necessarily reflect the participation of the anion as a bridging ligand. Thus SO:- and P20;- accelerate the oxidation of Cr2+ by (NH3)5Co(OH2)3+ and both are incorporated into the product Cr3+ complex.25 Similarly, during the oxidation of Cr3+ by (H3N)5CoC12+ in the presence of P20$-, both C1- and PzO$' are incorporated into the Cr3+ product.The effect of these anions as non-bridging ligands is, however, much smaller than as bridging ligands. On the other hand, C1- exerts a large catalytic effect on the oxidation of Cr2+ by C O ( N H ~ ) ~ ~ ; the product of the Cl--catalyzed reaction which pre- sumably proceeds by an outer-sphere mechanism, is CrC12-1-.27 The observation (H3N) ~CO~+-X-CO~+(OH~)~12 ELECTRON-TRANSFER REACTIONS by Zwickel and Taube 28 of a large dependence of the rate on the naturc of X in the outer-sphere oxidation of Cr(dipy): + by (H3N)SCo3+X should also be men- tioned in this connection. (iii) Fumarate and p-phthalate are of special interest as bridging ligands in the oxidation of Cr2'- by (H3N)&03+X since the rates for these are much higher than for other carboxylic acids.23 This has been interpreted in terms of a bridged intermediate in which the two metal ions are co-ordinated to different carboxylate grou PS , O-Cr(OH& 4f r (H3N)sCO-O // \ // \ C-CH=CH-C OH I 0 the electron being transferred between them by " conduction " through the con- jugated z-electron system.Strong support for this is provided by the observation that in the corresponding oxidation of Cr2+ by (H3N)5 C03+-0 \ 0 // 'c--cH=cH--c' // \ 0-Me 0 electron transfer is accompanied by hydrolysis of the ester and incorporation of both the methyl group and the acid into the co-ordination shell of the Cr3+ pr~duct.~' Hydrolysis is not observed when Cr(dipy)$+ or V(dipy);'+ is used as the reducing agent, the reaction in these cases being of the outer-sphere type.27 With maleate or monomethyl maleate ester (but not the corresponding fumarates) as the bridging group cis-trans isomerization and hydrogen exchange with the solvent (D20) also occurs as a consequence of electron transfer from V2+ or Cr2+ and this has been construed as evidence that an electron passes into the maleate group during the reaction.30 The possibilities afforded by the use of such con- jugated bridging groups for distinguishing between the two types of mechanisms and for the systematic variation of structural parameters makes these systems extremely valuable and their study will undoubtedly play an important role in the future development of the subject.HYDROGEN TRANSFER AND BRIDGING MECHANISMS The suggestion, first made by Dodson and Davidson,31 that redox reactions between metal aquo ions may occur through transfer of a hydrogen atom between their hydration shells, has continued to receive serious attention, particularly with reference to the F&+-Fe3+ exchange.A simplified representation is * * 11 11 H * l Fe2+-OH+HOFe3f-> r Fe2+-0 . . . H . . . O--Fe3+ 5+-tFeOH2-'-+H30Fe3+ * Fe3++ OH- Fez++ H30+ 1 3 H A I L H or, for the hydrolyzed ion (1 1) 8 * Fe2+0H+HO-Fe3+-+ (12) I H H the intermediate, in the latter case, being symmetrical.J . HALPERN AND L. E. ORGEL 13 Several lines of evidence have been advanced in support of this suggestion. (i) A surprisingly large number of diverse redox reactions between metal aquo ions have activation energies close to 10 kcal/mole and entropies close to -25 cal/mole deg., suggesting that they proceed by a common mechanism which probably involves water.329 1 (ii) In a number of redox reactions of metal complexes there seems to be a requirement that at least one of the inner shell ligands be a water molecule,32 e.g.one of the CN- ions must be replaced by a water molecule before Fe(CN);' is oxidized by hydroperoxide. Similarly, the electrolytic reduction of Cd(CN): - proceeds through the aquotricyano complex. The slowness of Fe2+-Fe3+ exchange ion non-aqueous solvents such as nitromethane 6 and alcohols 7 has also been attributed to this factor. (ii) The rates of the F&+-Fe3+ and Fe2+-FeOH2+ exchange reactions are re- duced by a factor of two on changing from H20 to D20 as solvent.33 This is consistent with the isotope effect expected for breaking of an 0-H bond but is not conclusive evidence for this since even larger H2O-D20 isotope effects have been observed in the oxidations of Cr2 + by (H3N)sCoOH?- and (H3N),CoOH2 I- which are known to proceed through oxygen-bridged mechanisms.16 Even Cl- bridged reactions exhibit appreciable, though somewhat smaller isotope effects in the same direction.25 Until differences in the solvent characteristics of H20 and D20 are better understood the interpretation of such effects must be approached with great caution.On energetic grounds the suggestion of a net H atom transfer between water molecules in a reaction such as (1 1) does not appear too attractive since the endo- thermicity of this process is expected to approach that of the self-ionization of water (-13 kcal).This is difficult to reconcile with an overall AH+ of 10 kcal and with the relatively small difference (2-5 kcal) in AH+ between the reactions of Fez+ with Fe(OH&+ and with Fe(OH2)50H2f. H atom transfer thus seems unlikely in reaction (1 l), although it may occur in (12), in reactions between aquo ions involving a large free-energy decrease or in the oxidation of aquo ions by free radicals, i.e. ' MOH;j+ +*R*MOH"+ +HR. (13) A related view 1 on the role of water in these reactions, which probably has more validity, emphasizes the formation of hydrogen-bridged intermediates, e.g. H 1 I Fe2+-0 . . . H-O-Fe3+ I H H or Fe2+-0 . . . H-O-Fe3+ I H I H in which coupling of the hydration shells by hydrogen bonding lowers the energy of the activated complex and improves orbital overlap thus providing a more effective conducting path for electron transfer.In this context hydrogen transfer is incidental to the bridging role of the proton and might accompany electron exchange of Fez+ with FeOH2+ but not with Fe3+. The analogy between the role of the bridging proton in such a mechanism and that of bridging groups in the inner- and outer-sphere bridged mechanisms already considered is readily ap- prec i a t ed.14 ELE C T R 0 N - TK A N S FER RE A C T 10 N S REACTIONS OF UNCERTAIN MECHANISM The uncertainties concerning the detailed mechanism of the Fe2+-Fe3+ exchange extend also to the redox reactions of most other aquo ions and labile complexes. In some cases the mechanism of a reaction which cannot be directly elucidated may be inferred with some confidence from a comparison between it and reactions of known mechanism.For example, similarities between the oxidation of Cr2+ and V2+ by (H3N)Co3+X complexes strongly suggest that the latter reaction also proceeds by an inner-sphere bridged mechanism.30 Similarly, the fact that C1- is incorporated into the co-ordination shell of the Cr3+ product during oxidation of Cr2+ by Fe3+ in the presence of C1-, while not conclusive evidence for a C1-- bridged mechanism (in view of known instances of incorporation of non-bridging ligands) makes this seem rather likely.26 The special role of the bridging ligand in the inner-sphere mechanism might be expected to give rise to a different pattern of dependence of the rate on the nature of the ligand from that observed for outer-sphere reactions, thus providing a diagnostic tool for distinguishing between the two types of mechanism. Un- fortunately the patterns observed so far, for the few reactions of known mechanism (table 1) are not sufficiently distinctive to permit a confident assignment for, say, the Fe2+-Fe3+ reaction, to be made.The value of this approach will undoubtedly be enhanced by the accumulation of data of this type for more systems of known niechanism; the papers by Stranks 30a and by Zwickel and Taube 28 represent important contributions to this field. TWO-EQUIVALENT REDOX REACTIONS The transition metals generally exhibit stable oxidation states differing by one clectron and react with each other by 1-equivalent steps.On the other hand, the stable oxidation states of the post-transition elements generally differ by two electrons, e.g. TI '-TI3' ; Sn2+-Sn4' ; Hgi'-2Hg2+, etc. The question thus arises as to whether oxidation or reduction of these ions occurs in a single step or by successive 1-equivalent steps. Two classical principles dominate much of the earlier thinking on this theme. (i) Michaelis' principle of " compulsory univalent oxidation steps ".34 This hypothesis invokes the second alternative for all reactions. It evolved from a Consideration of a restricted field of redox reactions, of which oxidation of hydro- quinones to quinones through semiquinone intermediates is typical, and is now gcnerally recognized as being without universal validity.Apart from reactions involving metal ions, many two-equivalent redox reactions are now known which proceed in one step through the transfer of a hydride ion or an oxygen atom ( e g NOT + OCl--+NOT + C1-).35* 36 (ii) Shaffer's principle of " equivalence change ".379 38 This refers to the observation that non-conplementary reactions (i.e. those between 1-equivalent oxidants and 2-equivalent reductants, or vice versa) are often slow compared with complementary ones (those between 1-equivalent oxidants and 1 -equivalent reductants, or between 2-equivalent oxidants and 2-equivalent reductants). Examples are the slow reduction of Tl3+ by Fe2+ or of Ce4-k by T1+ compared with the rapid reduction of Tl3f by Sn2+ and of Ce4f by Fez+. This is interpreted in terms of the following types of mechanism for a typical non-complementary reaction in which A is oxidized to A+ and B2+ reduced to B.2A + B2 +-+2A -I- + B, (1 Sa) ( I 51,)J. HALPEKN A N D L. E. OKGEL 15 The first of these mechanisms is expected to be slow because it involves a ter- molecular step and the last two because they involve the formation of unstable intermediates (B+ or A2+). Onc of the implications of the comparison on which the principle of equi- valence change is based is that reactions between 2-equivalent oxidants and 2- equivalent reductants occur by a concerted 2-equivalent step. This may well be the case for reactions such as the Tl+-TP+ exchange and the oxidation of Hg" and U44- by Tl3f whose rates secm too high to be reconciled with an initial 1-electron step in which two unstable intermediates (Hg+, TP+, etc.) are formed.20.389 39 It should be noted that the entropy correlations discussed by Higginson2 are also more dificult to reconcile with an initial 1-electron transfer for the Tl+-Tl3+ exchange than with a 2-electron transfer. Some reactions between 2-equivalent oxidants and 2-equivalent reductants, however, do proceed by 1-electron steps.The oxidation of V3+ by TI,+ is apparently such a case2 as is the oxidation of U4+ by 0 2 for which the following chain mechanism has been demonstrated,40 U'V+02+Uv+H0,, (174 Uv+ 02+UV'+H02, (176) t17d U IV + HQ2-+UV + H202. For non-complementary reactions the three types of mechanisms considered above have all been observed. The " termolecular " mechanism (type 1) is readily distinguished kinetically from the other two.Probable instances are the oxidation of Fe2+ and Pu3-f- by 0 2 and thc reduction of Ag+ by H2, for which the rate-laws k[Fe2+]2[02], k[Pu3+]2[02] and k[Ag+]2[H2] have been observed.41-43 One of the paths in the oxidation of CoI1 by Fblv in acetic acid, corresponding to the rate-law k[PbIV][Co1*]2, apparently is also of this type.5 In aqueous solution, however, there is no known instance of a reaction involving three metal ions which proceeds by this mechanism. A kinetic distinction between the two bimolccular inechanisms (types I1 and IlI), is normally possible only in those favourable cases where reversal of the first step is fast enough to compete with the second step, for inhibition by one of the products is then observed.Initial 1-electron steps have been demonstrated in this way for several reactions, 2Fe2++T13+ (eqn. (5) and (6)),19 Tl++2Co3+,44 and 2V4++ T13+2, and are considered likely for many others, e.g. U4++ 2Fe3f745 Hg2++2Co3+.46 On the other hand, inhibition by PbK suggests that one of the paths in the oxidation of Col' by Pblv in acetic acid involves an initial 2-equivalent step with the formation of Colv as an intermediate.5 The observation47 that Cr2+ is oxidized to Cr3f by 1-electron oxidants such as CU~+ and Fe3-1- by 1-electron oxidants such as Cu2f and Fe3-i- but to a binuclcar species (probably Cr-O-Cr4f) by 2-electron oxidants such as Tl3-f- suggests that the latter reaction also proceeds through an initial 2-electron transfer, is., Cr2 + + Ti3 + -+ Cr4 + +TI c r 4 + + Cr2 + -+(cr3 +I2.(18) (19) The factors which influence the choice of mechanism in these systems are still not well understood. THEORETICAL CONSIDERATIONS The theoretical problems associated with the mcchanisnis of clectron-transl'r reactions are of great complexity. To simplify 0111' discussion we divide i h e16 ELECTRON-TRANSFER REACTIONS process into three successive stages ; the initial approach of the, reactants, the surmounting of the Franck-Condon barrier, and the electron-transfer process itself. The paper by Marcus48 deals particularly with the first two of these themes, and that by Halpern and Orgel49 with the last. This division of the problem is somewhat artificial ; it is convenient since it permits a simple treatment or many of the most important features of the reaction mechanisms but it does not necessarily form the best starting-point for quantitative calculations, THE INITIAL APPROACH The approach to an intermolecular distance which permits electron transfer, of a pair of reactants one or both of which is uncharged, is presumably governed by the normal diffusion Iaws and can be calculated from collision theory.More often we are concerned with transfer between pairs of ions carrying the same charge, and then we have to consider the electrostatic repulsion which tends to keep them apart. The only treatments which have been attempted so far are based on classical electrostatic theory.50-52 It is supposed that the solvent can be treated as a continuous dielectric medium and the interionic potential energy estimated in terms of an effective dielectric constant. This treatment should be adequate for large intermolecular distances but must clearly break down when the inter- molecular distance becomes small, in particular when ions approach to the point of contact of their hydration shells. It is difficult to assess its validity for typical reactions between metal ions. In a general way we expect the rates of reaction to decrease as the charges (of the same sign) on the reactants increase.No doubt this repulsion between charges is important, but its significance should not be overestimated. The re- action between Fe(WG3- and Fe(CN)64-, for example, is very rapid.53 It is not unlikely that the incorporation of ions of opposite sign into the activated complex contributes to the reduction of the electrostatic barrier in this and similar reactions.The marked cation dependence of the MnO;; -MnOt- exchange, for example, is probably related to this.8 In the particular case of reactions involving bridged activated complexes there is a further stage in the initial approach, namely, the step leading to the formation of the binuclear species, e.g., C O ( N H ~ ) ~ C ~ ~ + +Cr(H,0)~+-+[(H3N)5C~-CI-Cr(H20)5J4'+ +H,O. (20) The rate of this step is presumably governed by the same factors as control simpler substitution reactions of inorganic complexes. .It has been noted, however, that the AS+ values of reactions of this type are considerably more negative than those of non-redox reactions which proceed through analogous bridged intermediates and this has been attributed to the more stringent requirements in the way of simultaneous bond readjustment in the activated complex in the case of the electron-transfer reaction.25 THE FRANCK-CONDON BARRIER The Franck-Condon principle was first proposed in connection with the analysis of molecular spectra.It states that it is extremely improbable that a large change of the nuclear configuration of a molecule will occur during an electronic transition. The physical basis of this generalization is simple ; electrons move so much faster than nuclei that an electronic transition is completed before much nuclear motion can occur. As pointed out by Libby,W the same general considerations apply also to electron-transfer reactions and they have important consequcnces. We first consider the transfer of an electron between two molecular or ionic species which differ only in the number of electrons which they contain, for example, bctweeiiJ .HALPERN AND L. E. ORGEL 17 benzene and the benzene negative ion or between Fe(H20), and Fe(H20)62+. At first sight it might seem that there can be no barrier to electron transfer since the products of the reaction are the same as the reactants. The Franck-Condon principle shows that this is not the case. The structure of each of the reactants depends on its state of ionization, for example the metal-oxygen bonds are longer in Fe(H20)62 than in Fe(H20)G3i-. If an electron is transferred between the reactants without any change in the inter- nuclear distance, as is required by the Franck-Condon principle, then the products are formed in inappropriate configurations. Thus in the ferrous-ferric exchange, one would obtain a compressed ferrous ion and an extended ferric ion.Thus direct electron exchange between partners in their equilibrium configurations leads to products which are vibrationally excited and therefore requires electronic activation energy. The same electron-transfer process can be brought about without electronic excitation energy, by following a different route. The two partners in the reaction are first symmetrized, that is they are deformed to a common configuration inter- mediate between their equilibrium configurations. This involves the expenditure of Vibrational energy, but now an electron can be transferred without further electronic activation energy.It is readily seen that the vibrational activation energy involved in this indirect route is always less than the electronic activation energy needed for direct transfer, since in the former case deformation to an intermcdiate configuration is sufficient while in the latter both products are pro- duced in extreme mismatching configurations. (We may expect the factor involved to be close to 4 in many cases.55) We shall refer to the vibrational excitation energy as the Franck-Condon rearrangement energy. Clearly the Franck-Condon barrier is most likely to be important where the oxidized and reduced forms of the reagents differ greatly in molecular geometry. For example, the Cr(H20)~~' ion has a regular octahedral structure while the Cr(H20)62' ion is extensively distorted and has a greater mean bond-length.This may be a cause of the slow electron exchange-rate observed in an aqueous system containing Cr2+ and Cr3+ ions. In general, a smaller Franck-Condon barrier is anticipated for electron-transfer between tzg orbitals than between eg orbitals.55 The Franck-Condon barrier is less likely to be important in oxidation-reduction reactions associated with large decreases in free energy, for then an electron can be transferred without extensive vibrational activation although the products are obtained in excited vibrational states. The excess vibrational energy of the products is lost as part of the process of dissipating the excess free energy. The Franck-Condon principle also applies to electron transfer between molecular species in the gas phase (e.g.H2-H$, N2-N$) although it appears that the effect in these cases is not large.56 ELECTRON CONDUCTION MECHANISMS In the gas phase there is little probability of electron-transfer between species except in collisions sufficiently close to allow the occupied orbitals of the donor molecule to overlap appreciably with the unfilled orbitals of the acceptor. Solu- tion reactions may proceed in another way, namely, by transferring electrons through intervening molecules which are not themselves permanently oxidized or reduced. The transfer between a hydrocarbon and its negative ion may be by direct contact, but many of the reactions between pairs of metal ions are known to proceed via bridging mechanisms.In very many metal ion reactions then, we are faced with the problem of electron conduction through ligands; stated in another way we must find out how the " outside " of a complex ion such as Fe(phenanthroIine)33+ receives information about the valency of the metal ion at its centre. The detailed quantitative answer to this question is not at present available, but a number of qualitative observations may be useful.18 ELECTRON-TRANSFER REACTIONS Extensive work of the paramagnetic resonance spcctra of transition-metal complexes has shown unambiguously that electrons which we are accustomed to think of as isolated on a metal ion are in fact more or less delocalized on to the ligands.57 Thus, even in fluorides such as MnF2, the unpaired d electrons are partly concentrated (perhaps 5-10 %) on the fluoride ions.It is natural to suppose that the same is true in all complex ions. This enables one to understand the transfer of electrons through small ligands such as the halide ions or the water molecule ; the electrons and unoccupied valence orbitals are partially located on the periphery of the complex ion and hence can interact with those of contiguous molecules. The ability of a ligand to facilitate electron transfer would be expected to fall off very rapidly with the number of saturated single bonds which must be traversed by the electron. On the other hand conjugated systems might be expected to con- duct electrons over longer distances on account of their extensive delocalized systems of n-orbitals.@ There is some evidence for the validity of these suggestions for reactions proceeding both by inner- and outer-sphere activated complexes. The higher rates of electron transfer gcnerally observed for complexes contaiiiing unsaturated ligands, such as cyanide and o-phenanthroline, than for those con- taining saturated ligands such as water and ammonia, are in line with these pre- dictions.However, it also appears that the geometrical configurations of the two oxidation states often differ less in the former case than in the latter so that there is also a contribution to the difference in rate from differences in the Franck- Condon barriers. The relative importance of these factors is difficult to assess. The theoretical treatment of Marcus,51 which is particularly appropriate for reactions of the outer-sphere type, assumes that the probability of electron transfer in the transition state is sufficiently high for the rate to be wholly determined by the electrostatic repulsion and Franck-Condon barrier ; this is probably valid for many reactions.TWO-ELECTRON TRANSFERS Two-electron transfers such as A+Az++A2++A are known to occur in the gas phase although their cross-sections, in accord with theoretical predictions, are somewhat lower than (+ to 3) those of corresponding resonant one-electron transfers.56 It is thus reasonable to expect similar reactions to occur in solution. They will, however, be subject to considerably larger Franck-Condon barriers 51 and this is likely to bereflected in more drastic atomic rearrangcments accompanying electron transfer.It is possible that such reactions will show a greater preference for bridged mechanisms both because a higher " electron conductivity " is more impor- tant in their case than for one-electron transfer and because of the reduction of the Franck-Condon barrier resulting from strong coupling between the metal ions and from displacement of the bridging anion from the oxidant to reductant. Unfortunately, there is still considerable uncertainty about the detailed mechanism of the Tl2+-Tl3+ and related 2-electron transfer reactions.58~ 59 SPIN-SELECTION RULES One special feature of certain reactions of metal ions and of the oxygen molecule is that they do not conserve the total spin. Thus the decomposition of anthracene peroxide involves a conversion of a singlet state to a triplet state 4 0 2 + singlet t r i p l e t s i n g l e tJ .HALPERN AND L. E. QRGEL 19 while the reaction between a cobaltic complex and a reducing agent often involves a similar departure from spin-conservation. While the significance of this selection rule is not yet understood in detail, there can be little doubt that it influences profoundly the rates of many reactions of molecules which contain more than one unpaired electron. The widespread tendency for reactions involving the reduction of 0 2 or oxidation of H202 to proceed by free-radical mechanisms rather than in a single step may be related to this. 1 Stranks, Modern Co-ordination Chemistry (Interscience Publishers Inc., New York, 2 Higginson, Rosseinsky, Stead and Sykcs, this Discussion.3 Hunt and Taubc, J. Amer. Chem. Soc., 1958, 80, 2642. 4 Benson and Sutcliffe, Trans. Faraduy Soc., 1960, 56, 246. 5 Benson, Proll, Sutcliffe and Walldey, this Discussion. 6 Maddock, Trans. Faraday Soc., 1959, 55, 1268. 7 Horne, Microfilm Diss. Abstr., 1957, 17, 1673. 8 Shcppard and Wahl, J. Anzer. Chem. Soc., 1957, 79, 1020. 9 Gordon and Wahl, J. Amer. Chem. Soc., 1958, 80, 273. 10 McConncll and Weavcr, J . Chem. Physics, 1956, 25, 307. 1 1 Ward and Weisman, J . Amer. Chem. Soc., 1957, 79, 2086. 12 Eigcn, Faraday Soc. Discussions, 1954, 17, 194; 1957, 24, 25. 13 Kruse and Taube, J . Amer. Chem. SOC., 1960, 82, 526. 14 Morris, Basolo and Pearson, this Discussion. 15 Murmann, Taube and Posey, J. Amer. Chem. Soc., 1957, 79, 262.16 Zwickcl and Taube, J. Amer. Chenz. SOC., 1959, 81, 2915, 1288. 17 Mudis and Dodson, J. Amer. Chern. Soc., 1956, 48, 91 1. l8 Newton and Rabideau, J. Physic. Clzem., 1959, 63, 365. 19 Ashurst and Higginson, J. Chem. Sac., 1953, 3044. 20 Armstrong, Halpern and Higginson, J. Physic. Chem., 1956, 60, 1661. Armstrong 21 Taube, Advances in Inorganic Chemistry and Radiochemistry (Academic Press, New 22 Taube, Myers and Rich, J . Amer. Chenz. Soc., 1953, 75, 4118. 23 Taubc, J . Amer. Chem. Soc., 1955, 77, 4481 ; Can. J . Chem., 1959, 37, 129. 24Taube and King, J . Amer. Chem. Soc., 1954, 76, 4053. 25 Ogard and Taubc, J. Amer. Cheni. Soc., 1958, 80, 1084. 26 Taube and Myers, J. Amer. Chenz. Soc., 1954, 76, 2103. 27 Taube, Chem. Soc. Spec. Publ., 1959, 13, 57. 28 Zwickel and Taube, this Discussion. 29 Fraser, Sebera and Taubc, J . Amer. Chem. SOC., 1959, 81, 2906. 30 Fraser and Taube, J. Amer. Chem. Soc., 1959, 81, 5514. 31 Dodson and Davidson, J . Physic. Chem., 1952, 56, 866. 32 Reynolds and Luniry, J. Physic. Chem., 1955, 23, 2460. 33 Hudis and Dodson, J. Amer. Chem. Soc., 1956, 78, 91 1 . 34 Michaelis, Trans. Electrochcm. Soc., 1937,71, 107; Cold Spring Harbor Symp. Quant. 35 Anbar and Taube, J. Arner. Chem. Soc., 1958, 80, 1073. 36 Stewart, Experientia, 1959, 15, 401. 37 Shaffer, J . Amer. Chem. SOC., 1933, 55, 2169; J. Physic. Chem., 1936, 40, 1021 ; 38 Halpern, Can. J . Chem., 1959, 37, 148. 4o Halpern and Smith, Can. J . Cltem., 1956, 34, 1419. 41 George, J . Clieni. SOC., 1954, 4349. 42 Baker and Newton, J . Physic. Cheni., 1957, 61, 381. 43 Webster and Halpern, J. Physic. Cheni., 1957, 61, 1239. 44 Ashurst and Higginson, J . Cheni. Soc., 1956, 343. 45 Dctts, Can. J . Cheni., 1955, 33, 1780. 1960), p. 78. Gjertsen and Wahl, J . Amer. Chem. Soc., 1959, 81, 1572. and Halpern, Cun. J . Chem., 1957, 35, 1020. York, 1959), 1, 1, and rcferences thcrein. Ball and King, J . Amer. Chem. Soc., 1958, 80, 1091. Chia and King, this Discussion. 300 Stranks, this Discussion. Biol., 1939, 7, 33. Cold Spring. Harbor Symp. Quant. Biol., 1939, 1, 50. Harkness and HaIpern, J . Anrer. Chem. Soc., 1959, 81, 3526.20 ELECTRON-TRANSFER REACTIONS 46 Rosseinsky and Higginson, J. Chem. SOC., 1960. 47 Arden and Plane, J. Amer. Chem. Soc., 1959, 81, 3197. 48 Marcus, this Discussion. 49 Halpern and Orgel, this Discussion. 50 Marcus, Zwolinski and Eyring, J. Physic. Chem., 1954, 58, 432. 51 Marcus, J. Chem. Physics, 1956, %I, 966 ; 1957, 26, 867, 872. 52 Laidler, Can. J. Clzem., 1959, 37, 138. 53 Wahl and Deck, J. Amer. Chem. SOC., 1954, 76,4054. 54 Libby, J. Physic. Chem., 1952, 56, 863. 55 Orgel, Report X Conseil Chimie Solvay, Brussels, 1956, 289. 56 Gurnee and Magee, J . Chem. Physics, 1957,26, 1237. 57 Owen, Faraday SOC. Discussions, 1958, 26, 53. 58 Jilks and Waind, this Discussion. 59 Carpenter, Ford-Smith, Bell and Dodson, this Discussion.

ISSN:0366-9033    

DOI:10.1039/DF9602900007

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

EXCHANGE REACTIONS AND ELECTRON TRANSFER REACTIONS INCLUDING ISOTOPIC EXCHANGE THEORY OF OXIDATION-REDUCTION REACTIONS INVOLVING ELECTRON TRANSFER PART 4.-A STATISTICALWCHANICAL BASIS FOR TREATING CONTRIBUTIONS FROM SOLVENT, LIGANDS, AND INERT SALT BY R. A. MARCUS Dept. of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn 1 , N.Y. Received 28th January, 1960 The mechanism for electron transfer is discussed in terms of an atomic motion on a potential-energy surface in many-dimensional atomic configuration space. In the absencc of electronic coupling between the reactants, a surface for the reactants intersects one for the products. Electronic coupling causes the usual removal of this degcncracy and permits the products to be formed adiabatically or nonadiabatically by an atomic motion across the " intersection " surface.The properties of a system on this latter surface are formulated in terms of statistical mechanics, in order to treat in a consistent manner the ligands microscopically and the exterior solvent macroscopically. A concept of " equivalent equilibrium distribution " is introduced to evaluate the surface integral. A macroscopic quantity is invoked only in the last step of the derivation, replacing its statistical-mechanical equivalent. A relatively simple expression is obtained thereby for the reaction rate, which rcduces to that obtained in part 1 when ligand and salt contributions are omitted. Applications can be made to a number of problems, such as prediction of non-isotopic electron-transfer rates from isotopic ones, relation between chemical and electrochemical electron transfers inert salt effects and possibility of an inverted chemical effect.1. INTRODUCTION In a recent series of papers, the writer has formulated and applied a quanti- tative theory of the rates of electron transfers in solution.1-3 In that work the need for reorganization of configuration of the solvent molecules before and after electron transfer was discussed. The free energy of solvent reorganization was then computed using a macroscopic treatment 4 for such a system having " non- equilibrium dielectric polarization ". In some electron transfers there are also changes in distances in the co- ordination shell as well (cf. ref. (947)). Clearly, this contribution needs to be estimated in microscopic terms. In order to include both contributions in a consistent manner, we first formulate the entire discussion of the reaction rate in terms of statistical mechanics and only in the last step we replace, for ease of calculation, one of the quantities by its macroscopic equivalent.2. MANY-DIMENSIONAL POTENTIAL ENERGY SURFACES (i) No ELECTRONIC INTERACTION In discussions of electron transfer, problems which have frequently arisen and have occasioned some uncertainty and confusion concern the charge distribution 2122 ELECTRON TRANSFER THEORY in the transition state, the mode of calculating its interaction with surrounding molecules, and the mcchanism of the electron transfer itself. To treat these prob- lems, we first consider a hypothctical case where no elcctroiiic coupling between the redox orbitals of the reactants occurs, so that no clectroii transfer is possible.To anticipate, conclusions reached in 5 2 include those reached somewhat more intuitively in part 1 (cf. ref. (8). In this case, we have two distinctly different electronic states-one having the electronic structure of the reactants, the other having that of the products. The lowest electronic state of each chemical pair has its own potential-energy surface in a many-dimensional atomic configuration space, whose co-ordinates are those of all the atoms of the two reactants, of the solvent, and of any electrolyte. The two surfaces each have their own valleys but the two sets of valleys occur in quite different regions of the space, reflecting differenccs in stable bond lengths, solvent orientations, etc.The surfaces intersect, usually along some upper reaches of each, and form thereby a surface of one less degree of freedom. A cross- section of the surfaces and of their intersection is indicated in fig. 1. atomic configuration FIG. 1 .-Profile of N-dimensional potential energy surfaces plotted against an atomic configurational co-ordinate of the entire system. Curve R denotes reactants (ox1 +redz) ; curve P, products (redl -FOX& Dotted lines show intersection of surfaces (zero electronic interaction case) and solid lines indicate the splitting for the case of weak interaction. The intersection surface can be reached by any suitable fluctuation of atomic co-ordinates to produce some atomic configuration which is usually a compromise between the stabler ones of the two electronic states.Because of the absence of electronic interaction of the redox orbitals, such a fluctuation does not cause any electron transfer. The system merely stays on the surface corresponding to the original electronic configuration on passing through the intersection. Fluctuations of this nature involve simultaneous changes in orientation, position and atomic polarization of the solvent molecules, in internuclear distances in the co- ordination shell, in relative motion of the reactants and in configuration of the ionic atmosphere. (ii) ADIABATIC AND NON-ADIABATIC MECHANISMS FOR ELECTRON TRANSFER Consider next the weak electronic interaction between the redox orbitals which occurs, for example, when the reactants are not too far apart.Their interaction leads to the usual splitting of the surfaces, as indicated in fig. 1.R . A . MARCUS 23 For sufficient electronic interaction, a system passing across the intersection during a fluctuation will always stay on the lowest surface. We see from fig. 1, therefore, that the products have been formed from the reactants adiabatically (in the quantum-mechanical sense) as a result of this atomic motion. This motion, then, is one which produces an atomic configuration of the system more favourable to the electronic charge distribution of the products. When the electronic interaction is extremely weak, on the other hand, for example when the reactants are far apart, the system tends to retain its original electronic configuration on passing across the intersection, i.e., the system " jumps " to the upper surface at such times and jumps back on its return.Each time no electron transfer tends to occur. There is, nevertheless, in such cases a small proba- bility of " transition ", For this system, we have thereby a " non-adiabatic " mechanism for electron transfer. As long as the interaction is not too strong, the splitting is relatively small, and little error is made in regarding the correct potential energy at the " intersection " surface as being essentially equal to that for the zero-interaction system. Thus, both the potential energy and the probability distribution on the intersection surface can be computed for the weak interaction system by the simple expedient of regarding the system as being the conceptually simpler zero-interaction one.Moreover, it may be emphasized here that in the computation, the charge distribution for the zero- interaction case should be used. It is the one for the reactants (or products) and not some compromise. In both cases, adiabatic and non-adiabatic, it is necessary for the system to pass through the intersection surface. In the first approximation the theoretical rate expression deduced below for the adiabatic mechanism will apply to a non- adiabatic one if, in the latter case, it is multiplied by some factor denoting an average transition probability per passage through the intersection region. (Nuclear tunnelling through the barrier in fig. 1 is neglected here in both cases.) 3.QUANTITATIVE FORMULATION OF THE THEORY (i) EQUATIONS FOR RATE AND FOR INTERSECTION SURFACE We shall use an equation for rate of passage through a surface in many- dimensional space, in our case the intersection surface. It is similar to the usual transition state theory equation (e.g. ref. (9) and unpublished results). If Apt denotes the difference in free energy of the reactants when they are constrained to exist on this (N-1) dimensional surface as compared with their existing in all atomic configurations, the rate constant, kr, is kr = (kT/h) exp (-AF$/kT). (3.3 .l) For defining the intersection surface in terms of molecular properties, we /c = any atomic configuration of the entire system in N-dimensional space, p = superscript to designate throughout a property of the products (a change introduce the following notation : of notation from part l), Z'k = potential energy of reactants in configuration k, A 8 = difference between electronic energy of the lowest electronic state of the products and that of the reactants when each is at its own zero of potential energy.Since the electronic energies of the reactants and products are equal along the intersection surface, the latter obeys the relation, gk = 8; + A&' at the intersection. (3.1.2)24 ELECTRON TRANSFER THEORY The potential energy of the reactants on the intcrsection surface, Z'i, say, equals Ek and because of (3.1.2) could also be written as (3.1.3) where rn is any constant. The usefulness of (3.1.3) will be shown in tj 3.4. (ii) POTENTIAL-ENERGY EXPRESSION two contributions : We assume that the potential energy of the reactants is essentially the sum of (3.2.1) where 8'ki depends on the internal co-ordinates, k i , of the co-ordination shells alone (gki being defincd as zero at the equilibrium values of these co-ordinates), and g,p depends on all other co-ordinates, k", of the entire system.Thus, k, the totality of all co-ordinates,* is an abbreviation for ki plus k" ("inner" and " outer "). We treat thejth particle as possessing a permanent dipole moment pj, an iso- tropic polarizability aj, and a charge el, some of which may be zero. We introduce the following additional notation : E = electric field strength at any point, arising from all the ionic charges $ = potential arising directly from all ionic charges = Zjej/rj.D = contribution to E arising solely from the charges. D = -@. and from the permanent and induced dipoles. D, = contribution to E arising solely from the permanent dipoles. Qk0 =I van der Waals' potential energy of interaction of all the particles (repulsive, dispersive, permanent dipole-dipole). Qko is taken to depend only on k", i.e. f&' = @o. j = subscript to also denote fields at yarticlej, minus the latter's contribu- tion. It can then readily be shown that 8 k o is given by (3.2.2) To establish (3.2.2), arguments related to those in appendix IV of ref. (4) may be used (cf. ref. (10)). The second term is the interaction between the charges. The third is that between the charges and the permanent dipoles. The remainder is a composite one.It includes ion-induced dipole interactions, - CjajEj . Dj ; an induced-permanent dipole term, - CjajEj . D,j ; induced-induced, - 3CjajEj . (Ei- Dj-D,j) ; and the energy stored up in the induced dipoles ZjajE? /2. The R,,o term includes the permanent dipole-dipole term, - Zjpj . Dpj/2. Ej obeys the relation : (3.2.3) (Cf. ref. (11) for non-polar and ref. (10) for polar molecules between parallel elec- trodes in a non-electrolyte system.) Unlike the D in ref. (ll), say, ours is not the dielectric displacement, a quantity with little molecular significance here, but is the microscopic equivalent of 4 EF). * There would be no real loss of generality if one now omitted from k", k and further consideration those co-ordinates whose behaviour is entirely the same in each of the two electronic states (e.g.some solvent vibrations).R . A. MARCUS 25 (iii) POTENTIAL ENERGY FOR TRANSITION STATE Introducing the above quantities into (3.1.3), an expression is obtained for 8i which simplifies considerably when the linearity property of (3.2.3) is applied.” We obtain where 8i = a;i+(.f,a+c, (3.3.1) 8; = fiko+Zj[e;+j+/2--pj. Dj’-cxjEf .(Df+DPj)/2]. (3.3.2) 47, D;, Ej’- and are abbreviations for functions of the type X + = X+m(X-XP); (3.3.3) C = m(m + 1)C j[aj(Ej - Ey) . (Dj - Ds) + ( e j - ep)($ - 49/21 - mA6. (3.3.4) C depends esscntially only on the positions of the two reacting species : for Dj-Df and related factors depend only on these co-ordinates, while Ej-E! is independent of molecular orientations and of positions of atmospheric ions.Because a liquid is closely packed, the energy term invoIving Ej-E! can be taken as effectively independent of the much less important variables, the positions of the solvent molecules. (iv) EQUIVALENT EQUILIBRIUM DISTRIBUTION (e.e.d.) : It is instructive, for evaluating AFJ, to first compare the transition state, in which exp (- g$/k?’) is integrated over the intersection surface, with a state in which this factor is integrated over all of space. We shall term the configurational dis- tribution of the latter state the “ equivalent equilibrium distribution ” (e.e.d.). Comparison of (3.3.1) with (3.2.1.) and of (3.3.2) with (3.2.2) reveals that the e.e.d. is one which would be obtained in a corresponding equdibrium system in which the charges on the two central ions were enf, i.e. e,+m(e,-e;), (n = 1,2), and which had tFli as a potential function for the co-ordination shell.The transition state of the zero-interaction system differs from this system in only two respects : the charges of the two central ions are those of the reactants, and it has one less dimension of freedom than an N-dimensional system. 4. EVALUATION OF THE REACTION RATE CONSTANT (i) GENERAL For exact evaluation of the surface integral, we should examine in detail the motion along the surface, for example, by examining the atomic motion normal to it, i.e., the reaction co-ordinate. We hope to analyze this dynamical problem at a later date. For the present, we use instead the following procedure. By a suitable choice of m (see 5 4.4. and appendix l), the e.c.d.is made to centre on the intersection surface, and thercby to die away fairly rapidly along the normal. Since (3.3.1) applies both to e.e.d. and to the transition state, we may then set the surface integral over exp (-tfi/kT) equal to the volume integral for the e.e.d., divided by a partition function along the normal, as found in appendix 1. (If some of the motions along the surface are quantized, this statement could be expressed * For any given j and k”, Ej is the same function of the D,,-+-Dp, as ET is of the DL+Dpm and as E,-EP, is of the Dm-D1’. This relationship becomes evident when :hc n simultaneous vector eqn. (3.2.3) are written in matrix form and inverted to obtain a formal cxplicit expression for the matrix of EjS. (The procedure is analogous to that cmployed in eqn.(4) of ref. (10) for a simpler system.) A similar procedure is then used to obtain Epand, by subtraction, Q-Ef.26 ELECTRON TRANSFER THEORY in terms of equating corresponding free energies of the two systems.) Most of thc likely motions along the normal to thc transition state surface, such as some of those mcntioned in 5 2.1 have a " frequency " of motion of about 1013 sec-1. We anticipate, therefore, that the partition function just noted, which may be written as kT/hv, will be of the order of unity, and that the procedure just outlined makes the rate constant uncertain only by a small numerical factor. (ii) APPLICATION OF e.e.d. The e.e.d. was seen to have " inner " co-ordinates which behave as though the potential function were 8'; (or as we shall now denote it, 8'$. Let the latter's minimum rchtive to the zero of 8'ki be called A8/ and the corresponding vibrational energy levels be 2?: (totality of quantum numbers, u).Let Fdenote the free energy of the reactants. Using (3.3.1.) we then deduce for AFT : exp ( -AFtjkT) = $LkT)J. . Jf exp - (a: + As! v = O +.&lo + C + K)/kT]dz,, (4.2.1) where K is the kinetic energy of the NO outer co-ordinates and dzo is their volume element in phase space. Summation over all 2, immediately yields the vibrational partition function, Qtib, for the inner co-ordinates, and integration over the No momenta cancels a corresponding momentum integral in an expression for F (as does the hNo factor). The residual integrand depends only on the relative " outer " co-ordinates (position and orientational) of all the particles.We next hold all of these relative co-ordinates fixed within two fairly large spheres, one about each central ion (large enough so that the long range ion-ion-solvent interactions are negligible on their surfaces). We then integrate over the co-ordinates of the centre of gravity of these two ions and over the orientations of their line of centres, translating and rotating, respectively, the entire system within the large spheres to ensure constancy of the important relative co-ordinates during integration. Holding the distance Y between the ions fixed, we next integrate over all other outer co-ordinates, the integral being denoted later by exp (-F&r)/kT). In integrating finally over Y, we first note two factors which favour small YS in spite of any coulombic repulsion : the solvent reorganization barrier is smaller there (cf.below) and, at the larger YS, the electronic interaction becomes so weak that out there the integral should be multiplied by some small non-adiabatic transition probability. We presumably err relatively little if we simply take Y as the distance of closest approach and set the corresponding r-partition function equal to unity, i.e. kT/hvr-l (cf. also 5 4.1). We obtain after some cancellation : (4.2.2) where k, = Z exp [ -(A.F! +AF;)/kT], AFy = A@ - kT 111 Qti,,/Qvib, (4.2.3) AFi+Fo = F&(r) = -kT In exp (-b"i.[kT)dkb. (4.2.4) s-s In these equations, Qvib, the vibrational partition function of the inner co- ordinates of the reactants, was extracted from F: F&r) is the configurational free energy of the reactants due to all ion-solvent-ion interactions in (3.2.4), at fixed positions of the central ions ; dk', is the configuration volume element of the remaining (N-6) outer co-ordinates.2 is the same as the usual collision frequency of two non-polar molecules in solution (probably about 1011 l./rnole sec rather than the value suggested in ref. (2) and (12)).R. A . MARCUS 27 (iii) EvaLrrArIoN OF AFi AND AF,? It follows from $ 3.4 that (4.2.4) for F&) is simply the free energy of a system having the charges of the reactants a distance r apart but a distribution of orienta- tions of solvent molecules and of positions of ions in the ionic atmosphere which would be in equilibrium with the hypothetical charges, e,+rn(e,-e{), (n = 1, 2), on the two central ions.It is at this point that we introduce the macroscopic expression4 for the frec energy of this type of non-equilibrium system. We obtain * A F ~ = w + m2L, (4.3.3) (4.3.4) where w is the coulombic work required to bring the reactants together at the prevailing salt concentrations and equals ele2/D,r at infinite dilution; Ae is the charge transferred; a1 and a2 are the ionic radii of the ions (including their co- ordination shells) ; we take r = al+ a2 ; n and D, are the refractive index and static dielectric constant, respectively. We evaluate the contributions to AFf when the vibrations are harmonic, the anharmonic values being somewhat more complex. If q, denotes a bond co- ordinate of the reactants, having equilibrium value q: and force constant K,, we havc F k i = CsKs(q,- 43'12.(4.3.5) Upon finding the minimum of for the transition state : and evaluating i%'~,/aq, there (at qd), we deduce (4.3.6) qzt = [(m + l)K,q,P - mK,Pq:]K:, K; = (m + S)K, - mK:, (4.3.7) A€! = (m2/2)ZsK,(Aq~)2(K~/K,?)2, (4.3.8) where Aq," = q:'-q;. In appendix 2, these equations are obtained approximately for a normal co- ordinate treatment, the qs-qi then becoming normal co-ordinates and the 1/KS/2n becoming vibration frequencies of the normal modes. (iV) EQUATION FOR Vl The equation for rn is obtained by equating the difference between free energies of activation for the forward and reverse reactions to the standard free energy of reaction at the prevailing electrolyte concentration, AF"'.In the process, we tacitly set the free energy of the reactants on the intersection surface equal to that of the products there (by making both equal F f ) and so satisfy the energy condition (Al) in appendix 1, sincc the entropies of two systems similarly distributed on the * Eqn. (25) and (2%) of ref. (4) wcre used in conjunction with certain macroscopic properties (Pu and ci) of the c.e.d. system. Two minor approximations were madc: " image effects " were neglected. We estimate 13 that their inclusion would raise AFA by less than 10 % (see also ref. (14)). In calculating the salt effect, an additional approximation was made but leads to no error in the Debye-Hiickel region and is probably unimportant otherwise. Incidentally, the ions are not treated as conducting spheres, as suggested on p.986 of ref. (4). The mathematical details of these calculations will be dcscribed else- where.28 ELECTRON TRANSFER THEORY same surface are also equal. Thereby the e.e.d. is made to centre on the inter- section surface. The term ( F Z - P ) can cither be calculated directly or simply by using the following transformation property to obtain it from FS-F; any property of the transition state is invariant with respect to a simultaneous replacing of -m by m+ 1 and interchange of " p " and " no p " superscripts (the property can be established from (3.1.3)-valid now for all k of the e.e.d.-with some caution, remembering that t??i is relative). We obtain for m : - (2m + 1)A +Ad'! - Abft = AF"'- AF& + wp - w, (4.4.1) where At??:' is A.8: with m+ 1 and K, replaced by -in and Kf, and where - AF& is defined as kT In Qtib/Qvib.When Ks = Kf, A8)- A8fS becomes simply - (2m+ I)X&(Aq;)2/2. 5. CONCLUDING REMARKS Eqn. (4.2.2) and (4.4.1) reduce to those of part 1 when any effects from co- ordination shell distances and from electrolyte are omitted. Eqn. (4.2.3) for the contribution of the " inner " co-ordinates reduces to that obtained by George and Griffith 15 if AF" is set equal to zero, the partition function omitted and the normal co-ordinates replaced-by bond co-ordinates. Among the topics to which the results of the present analysis could be applied are the following : (i) Relation between chemical and electrochemical electron transfer rates : cf.ref. (3) for solvent reorganization only. This discussion could now be generalized. (ii) Prediction of electron transfer rates of non-isotopic exchanges from iso- topic ones : e.g., taking K s g K f , one finds from (4.2.2) that when correc- tions are made for any differences of coulombic repulsion, the mixed rate constant is related to the isotopic ones (kl and k2) and to the equilibrium constant K in the given electrolyte medium by k12~(klk2K)* if AFo is not too large. (iii) Numerical estimate of contribution to activation free energy from the co-ordination shells when the necessary force constants and internuclear distances are available * (cf. ref. (7)). (iv) Inert salt effects (subject to an assumed treatment of the ionic atmosphere as a continuous distribution, however).(v) Possibility of "inverted" chemical behaviour. If AF" becomes too negative, intersection of the two surfaces becomes possible only at high potential energies, unless in such cases a more favourable reaction mech- anism is found. In (4.3.3) and (4.3.8) m2 eventually increases with in- creasing - AF", and the rate constant decreases. (vi) Analysis of assumptions made when electron transfers are interpreted in the terms of the Franck-Condon principle (cf. analysis in ref. (8)). APPENDIX 1 PROPERTY OF THE e.e.d. If the e.e.d. is indeed " centred " on the intersection surface, a system having the e.e.d. and the electronic configuration of the reactants would have the same * A similarly made estimate for D20fH20 effects using (4.2.3) would be valid only if the contribution of the OH frequencies to thc reaction co-ordinate were negligible (cf.discussion of uncertainty in kr in 9 4.1) and only if one added to AFS any additional con- tribution from changes in hydrogen bonding as the charged reactants approach each other, if any.R. A . MARCUS 29 average energy as a system having the same e.e.d. and the electronic configuration of the products. That is, it would satisfy each averaged over the e.e.d. (They would also have the same free energy too,) It is easy to show that such an e.e.d. exists. Consider the expression -kT In J . . exp (-8'#T)dzk, as a function of rn and minimize it with respect to rn. One obtains immediately, using (3.1.3) : ' (Al) J . . J exp (- bi/kT)b,dz, - $ . . S exp (- &$/kT)(&;+A&)dz, - J .. J exp (- bi/kT)dz, J . . J exp (- €i/kT)dr, This is the desired property. Thus, there is an e.e.d. centred on the intersection surface. It has the property that the In term, i.e. the free energy, is a minimum with respect to rn. (4.4.1), the equation in the text for m, satisfies the above equation. We now examine in more detail the approximation of replacing the (N- 1)- dimensional surface integral by an N-dimensional volume integral over the e.e.d., N being large. We note first that the intersection of the two potential surfaces in fig. 1 defines a surface of (N-1) degrees of freedom and that shifting the potential-energy surface of the products vertically by an amount I? without change of shape, pro- duces a different intersection which defines a new (N- 1)-dimensional surface parallel to the first one.In this way a family of parallel surfaces can be generated, each member associated with a particular value of r and obeying (A2) (cf. 9 3.1). Let CT denote the totality of (N- 1) orthogonal curvilinear co-ordinates defining position on any given surface and let y be the co-ordinate normal to the family of surfaces, so that k in 8 k consists of 0 and y. Let the origin of y be at the actual intersection surface, for which I? = 0. T(y) is a strictly monotonic function of y and r(0) = 0. A co-ordinate system is introduced as follows. &, = Gc+A&+I'. (A2) Consider now the volume integral over the e.e.d., 1. . . { exp (- &t,/kT)dody, where 8'& satisfies (A3) (cf. 3.1.3)) and rn was selected so that (A4) is satisfied (cf.(Al), using A2)). In the vicinity (A4) thus becomes where F!, the free given by (A6) : of y = 0, I? equals y(fl/dy)o, the derivative being non-zero. 03 [ -a2 yexp(-F:,,/kT)dy = 0, (4 energy of a system constrained to exist on the surface y, is exp (- Ft,,/kT = J . . . [ exp (- &.&/kT)da. (A61 Since (A5) is applicable to all T, we infer that F$ is an even function of y and write therefore the Taylor's series (A7), retaining only terms up to y2 for physical reasons based on fig. 1 : F l y ) = F t 0 ) + ( y 2 / 2 ! ) F { 6 ) + . . . . (A7130 ELECTRON TRANSFEK THEORY Using (A7) the N-dimensional volume integral becomes But exp (-Ft0)/kT) equals $ . . . $ exp (-ikbo/kT)da, using (A6) and (A3) at y = 0, and so equals the desired (N- 1)-dimensional surface integral.Thus, if the " vibrational-like partition function " 2/27ckT/F& is of the order of unity, the basic approximation enunciated in 9 4.1 is seen from (A8) to be justified. We next estimate F& and incidentally investigate the significance of rn. Diflerentiating (A6) with the aid of (A3), we find q o ) = m(dr/dy),=o + <(d~u,/WO)O, q l ) = <(d26,/dr2)o>o + [(d&:,ldY)o); - <(d@y/dY);)ol/w (A9) (AW where (f)o denotes any function f averagcd over the intersection surface, 1. . . Jjcxp (-C,,/kT)do//. . . J exp (-Buo/kTda. Sincc F& = 0, wc find It can thereby be seen that for any fixed shape of the two potential energy sur- faces (i.e. for fixed AS"), rn is the increase in activation energy per unit increase in standard energy of reaction.Accordingly, if m were 0, the activated complex would resemble the reactants. It would resemble the products if in were - 1 and would be as much like one as the other if rn were -3. These remarks can also be inferred from (3.3.3). F(d, contains first an average force constant term ((dz8':y/dr2)o)o. The sum of the second and third terms is found from approximate calculations based on (4.3.5) to be of a magnitude comparable with the first. Accordingly, it seems reasonable to expect that the results of more detailed calculations will show that the value of F& is of the order of that of a typical force constant, and that there- fore the partition function is of the order of unity. The results for the calculated free energy of activation are, it follows from (AS), relatively insensitive to the exact value of F;;;.APPENDIX 2 NORMAL CO-ORDINATES AND AFf As before, 8'ii is minimized and AT! and the vibration frequencies v6 are then computed. A reactant whose structure has a similar syrnmctry in the two rcdox states will also have similar types of normal co-ordinates, Qs. The dependcnce of certain of these co-ordinates (particularly stretching co-ordinates) on the internal co-ordinates of displacement, St = xt-x;), will also be essentially the same in spite of any changes in equilibrium bond lengths. Moreover, comparing molecules of similar geometry, it may be deduced from the pertinent transformation equations 16 that cach Qs is unaffected by changes in corresponding force constants when only one type of force constant contributcs appreciably to that Q, or when all contributing ones change by the same factor.The former appcars to be true for many vibrations, its inferrcd from the valcncy forcc field approximation ' 7 and pcrhaps from theR. A . MARCUS 31 relative constancy of vibration frequencies associated with the relative motion of two atoms or of two groups. We shall, for simplicity, make this approximation here. Thus, writing Qs =CtZ,t(~.t - $1 and Q," =CJ,",(.t - x,OP>7 we shall let Ift = I,*. Denoting 4n2v: by A,, we also have We next define a new set of coordinates qs (equilibrium values q i ) : 4 s = CtlstXto7 4: = ZtLtC Therefore, Q, = qS- 4; alld Qf = 4,- 4;". Regarding 8'$ as a function of the qs now, we may expand it about its minimum at qs = qil say) by the usual process of computing derivatives with respect to the qs. Eqn. (4.3.6) to (4.3.8) are then obtained, with the Ks replaced by As and the q3s having the above meaning. The A: are related to the frequencies v: by the equation, A: = 4x2v:2. The author is pleased to acknowledge the support of this research by the Office of Naval Research and the National Science Foundation. * Marcus, J. Chem. Physics, 1956, 24, 966 (part 1). 2 Marcus, J. Chem. Physics, 1957, 26, 867, 872 (parts 2 and 3). 3 Marcus, Can. J. Chem., 1959, 37, 155. 4 Marcus, J. Chem. Physics, 1956,24, 979. 5 Orgel, Tenth Int. Solvay Conf., Brussels, 1956, p. 289. 6 H U S ~ , Farday Society Discussions, 1958, 26, 145. 7 cf. Marcus, Trans. N. Y. Acad. Sci., 1957, 19, 423 for numcrical estimate. 8 Marcus, Trans. Symp. Electrode Processes, E Yeager, ed. (McGraw-Hill Book Co., 9 e.g. Horiuti, Bull. Chem. Japan, 1938, 13, 210 (cf. eqn. (2)). 1" Mandel and Mazur, Physica, 1958,24, 11 6. 1 1 Kirkwood, J. Chem. Physics, 1936, 4, 592. 12 Frost and Pearson, Kinetics and Mechanism (John Wiley and Sons, Tnc., New York, 1953), p. 118. 1 3 cf. Stratton, Electror.nagnetic Theory (McGraw-Hill Book Co., Inc., New York, 1941), p. 204. 14 Levine, Faraday SOC. Discussioiis, 1957, 24, 43. 15 George and Griffith, The Enzymes, Boyer, Lardy and Myrback, ed. (Academic Press Inc., New York, 1959), p. 364 (cf. ref. (5)). 16 cf. Wilson, Decius and Cross, Molecular Vibrations (McGraw-Hill Book Company Inc., New York, 1955), p. 72 ff. 17 cf. Herzberg, Infra-red and Ramaiz Spectra (Van Nostrand and Co., Tnc., New York, 1945), for calculations. New York, 1960).

ISSN:0366-9033    

DOI:10.1039/DF9602900021

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

THE THEORY OF ELECTRON TRANSFER BETWEEN METAL IONS IN BRIDGED SYSTEMS BY J. HALPERN” AND L. E. ORGEL University Chemical Laboratory, Lensfield Road, Cambridge Received 4th February, 1960 The role of bridging groups in promoting electron transfer between metal ions in solution is discussed. Interactions between orbitals of the metal ions through those of the bridging groups give rise to two possible exchange mechanisms-double exchange and superexchange. Expressions for the exchange frequencies associated with these are derived and their dependence on various factors such as orbital symmetry, overlap and redox potentials is discussed. Particular consideration is given to electron transfer through bridging groups containing conjugated n-electron systems. Electron-transfer reactions between metal ions in solution have been shown 1 in many cases to proceed through intermediates in which the two metal ions are coupled by a bridging group which forms part of the inner co-ordination shells of both.Examples are the oxidation of CrII by CrIII and CoIII complexes through the bridged intermediates (H20)5CrIIIXCrII(OH2) 5 and (H3N) 5 CoIIIXCrII( OH2) 5 , respectively. A characteristic feature of these reactions is the very marked sensi- tivity of their rates to the nature of the bridging group. Thus the rate of the first of the above reactions decreases by a factor of 107 along the series X = Br->NY, Cl->OH->F->NCS->H20,2 and that of the second by a similar factor along the series X = OH- >C1- >p-phthalate >fumarate, H20 >acetate, succinate, m- phthalate, o-phthalate.1 The higher rates of electron transfer with p-phthalate and fumarate (/’‘bi-40 and 0-5 M-1 sec--1 respectively) than with other carboxylic acids (kbi4.1-0.2) are of special interest and have been interpreted in terms of bridged intermediates, such as (H,N),co~~~ .. . o- Y O . . . Cr”(OH,), \c-CH=CH-C OY \OH in which the two metal ions are co-ordinated to different carboxyl groups. Transfer of an electron between the separated CrII, and CoIII ions presumably occurs through the conjugated n-electron system of the bridging group. In all these reactions the overall electron-transfer process is accompanied by transfer of the bridging ligand from the oxidant to the reductant and, in some cases, by reaction of the ligand itself (e.g.hydrolysis of methyl fumarate 2 and cis-trans isomerization of maleate 3). All of these observations emphasize the important role of the bridging group in relation to the mechanism of electron transfer in these systems. Bridged inter- mediates are undoubtedly important also in many other electron-transfer reactions, although the substitution lability of most ions makes this difficult to demonstrate unequivocally. Various theoretical aspects of electron transfer processes in solution have been considered by Libby,s Zwolinski, R. J. Marcus and Eyring,6 R. A. Marcus,7 * on leavc from tlic Chemistry Department, University of British Columbia, Vancouver 8, Canada. 32J . HALPERN AND L. E. ORGEL 33 Orgel 8 and George and Grfith.9 Nearly all these treatments have emphasized the dependence of the rate on the following factors.(i) electrostatic interactions between the overall charges of the reactants ; (ii) the reorganization energy of the ligands and of the surrounding medium prior to and during electron transfer, associated with the Franck-Condon restriction, and (iii) the rate of the electron-transfer process itself in the transition complex. Considerable progress has been made, .particularly by Marcus 7 in the quantitative treatment of the first two of these and although the models employed for this purpose approximate more closely to reactions of the " outer-sphere activated complex " type 1 (i.e. those in which electron transfer occurs without disruption of the first co-ordination shells of the ions) many of the results are at least quali- tatively relevant also to bridged systems, The role of the last factor, however, is still not well understood, although some attempts have been made to treat it both from the standpoint of the time-dependent perturbation theory 5 and of electron tunnelling.6910 For many reactions, the system may pass through a con- figuration in which the electron-transfer probability is sufficiently high for the rate to be determined completely by other factors (i.e.the free energy of activation for attainment of this configuration). On the other hand, it seems likely that some of the variations in rate found in bridged systems, such as those for the oxidation of Cr11 by Con1 through conjugated carboxylic acid bridges, are associ- ated with differences in the rate of the electron-transfer process itself.The concept, based on analogy with similar processes in the gas phase, that electron transfer in solution occurs directly between the orbitals of the exchanging ions, has led to emphasis on the overlap of the latter as a critical factor in deter- mining the electron transfer probability. Calculations based on this approach lead to the conclusion that the probability of electron transfer between ions is indeed appreciable even at distances of the order of lOA and larger.5 However, failure to take into account the effect of the intervening medium renders this, and similar results based on electron-tunnelhg models,6 of doubtful significance for most electron-transfer processes in solution and, in particular, for reactions of the bridged type.For such systems it is probable that direct interaction between orbitals of the metal ions is unimportant relative to interactions through orbitals of the bridging groups. Various possible detailed mechanisms of electron transfer involving such mediated interactions have been considered by Taube and Myers 11 and by George and Griffith.9 In this paper we attempt to examine these suggestions in greater detail, with particular emphasis on their application to electron transfer through conjugated systems. KINETIC CONSJDERATIONS We consider the problems of electron transfer within the framework of the general reaction scheme formulated by Marcus.7 Thus, taking account of the Franck-Condon restriction, we assume that electron transfer occurs through an intermediate atomic configuration of the system, achieved through suitable ad- justment of the ligands and surrounding solvent, such that the electron configur- ations corresponding to the reactants and products (I and 11, respectively) have the same energy.The overall reaction is thus represented formally by the series of elementary steps, ki A+X-B++(Ax-B+) (AX-B +)+(A+x- B) k- I k2 I1 I k - 2 B34 ELECTRON TRANSFER IN BRIDGED SYSTEMS (A+x-B)~A+x- +B 11 and the usual steady-state approximation for (I) and (11) yields for the overall bimolecular rate-constant, k b i = k,l[1 +(I + k-zlk3)k- 1/k2]* (4) For simplicity we assume that A and B are the same and that the structure of the bridged intermediate is symmetrical. Its formation from the reactants involves a substitutional step whose rate constant is included in kl.k2 and k-2 refer to the actual electronic transitions, that is the rate constant for the transition during the period in which the configuration of matching energies is maintained, and k3 and k-1 to disorganizing motions of the ligands or solvent which destroy the energy equivalence. In a symmetrical system such as we are considering, k 2 = k-2 and k-1 = k3. Two limiting cases may be, noted. (1) When the probability of electron-transfer during the lifetime of the sym- metrical intermediate is high (k2 >k-l) then k b i z i k l . ( 5 ) Under these conditions the rate does not depend directly on the electron-transfer probability although it may do so indirectly since, as pointed out by Marcus 7 large electronic interactions lead to relaxation of the Franck-Condon restriction.(2) When the probability of electron transfer is small (k-lbkz) then kbix klk,/k,,. (6) Under these conditions the intermediate (I) is essentially in equilibrium with the reactants and its lifetime is of the order of l/kdl. The transition probability during this lifetime then determines the rate. The transition probability may be computed using the time-dependent per- turbation theory which gives,12# 14 P , = sin2 nut, (7) where P I , I I ( ~ ) is the probability of the system, initially in state I, undergoing a transition to 11, in time d. v is given by in the case where @I and @u (the 11) are orthogonal, and otherwise unperturbed wave functions for the states I and (to first order in overlap) by where and Thus, according to (7) if the system is initially in configuration (I) it will “ oscillate ” between the two configurations (i.e.the electron will exchange between A and B) with the frequencyv. For times z, small compared to l/nv, (7) may be expanded to give P , I,(Z) = I nvz 12. (10)J . HALPERN A N D L. E . ORGEL 35 Under these conditions the transition probability is seen to be proportional to the squares of both v and z, the lifetime of the intermediate.* The latter is of the order of 10-13-10-12 sec and thus it is likely that the electron-transfer probability, in the sense implied here, will be an important rate-determining factor only if v < 1013 sec-1 (HI 11<0.5 kcal). Although, as emphasized by Marcus,7 this con- dition is more likely to apply to electron-transfer reactions of the outer-sphere type, it may also be realized in bridged systems, where coupling of the metal ions by the bridging group is very weak.We proceed to examine the nature of the interactions which give rise to such coupling. DIRECT AND DOUBLE EXCHANGE We consider first a simple model system comprising a one-electron atom A and the corresponding ion, Bf, coupled symmetrically through a bridging ion, X- containing a closed shell of two electrons. If we represent the unperturbed states I and 11, corresponding to the electron being located on A and B, respectively, by the determinental wavefunctions (in which 4~ and & refer to electrons with different spins), I then the exchange frequency is given by 2 or, in the approximation which neglects overlap terms relative to 1 and which we also subsequently use, by Expansion of HI I and HI 11 gives, H I I = (4A(1)$X(2)4X(3) I 1 $A(1)4X(2)4X(3)) - (4A(1)4X(2)4X(3) 1 I 4X(1)4A(2)4X(3)) HI I1 = (4*(1)4X(2)4X(3) 1 H I4d1)4x(mx(3)) - (4A(1)4X(2)4X(3) I I 4X(1)4B(2)4X(3)), The forms of the two terms in the expression for I3111 suggest that the first may be loosely identified with direct exchange of an electron between A and B * It should be noted that the earlier use of the ordinary form of the rate-law for the electron-transfer step in the steady-state kinetic treatment is not strictly consistent with (7) and (10).However, provided that encounters are sufficiently frequent and that the probability of transition per encounter is sufficiently small then the macroscopic rate law is still linear in the time, but the rate constant is dependent on the variation of PI II(T) with T, the lifetime of the “energy-matched” intermediate.It should also be noted that while PI 11 is a quadratic function of YT in the model which we have adopted, the nature of the dependence in a more realistic theory is by no means obvious, and may indeed be linear.36 ELECTRON TRANSFER IN BRIDGED SYSTEMS and the second with a " double exchange " mechanism corresponding to con- certed transfer of an electron from A to X and from X to B. This type of inter- action was first invoked by Zener 14 to account for the electrical conductivity and ferromagnetic properties of mixed valence metal oxides (e.g.those containing Mn3f and Mn4f ions) and Taube and Myers 11 have drawn attention to its possible relevance for electron-transfer processes in solution. Eqn. (11) may be compared with the corresponding result 5 for the unmediated electron transfer frequency (i.e. in the absence of X-) Approximate values of v1 and v2, computed using hydrogen 1s orbitals for C)A, C)X and 4~ are listed in table I. As expected, v2 falls off more rapidly than v1 (roughly as SAB and SAXSAB, respectively) with increasing A-B separation. TABLE 1 .-IS ELECTRON-EXCHANGE FREQUENCIES A-B separation V1 v2 (Bohr radii) sec-1 seC-1 5 3 x 1015 3 x 1014 10 7 x 1013 4 x 1012 15 2 x 1012 4 x 1010 20 3 x 1010 3 x 108 A similar result is obtained if the bridging group contains more than one closed shell, Thus, if there are N filled orbitals, 4xl, #xZ, .. . J(2N + l)! (1 - Six,) i = 1 and, again neglecting overlap terms relative to 1, we get Expansion of HI 11, neglecting terms higher than second order in overlap, givesJ . HALPERN AND L . E. ORGEL 37 The terms in this summation correspond to contributions to double exchange through the various occupied orbitals of the bridging group and may either rein- force or oppose each other depending on the symmetries of the orbitals. We now proceed to apply this result to a system in which A and B are linked through a conjugated bridge. We introduce the following notation and simplifying assumptions, have the same product form as previously (eqn. (14)) but &,, &,. . . . 4 x N now correspond to the N occupied molecular orbitals of the conjugated bridge.We approximate these by wave functions of the Huckel type, (i) @I and where Xk is the atomic p-orbital of the kth atom. All the Xks are assumed to be equivalent. The atoms to which A and B are attached are identified by the subscripts r and s respectively. (ii) In the expression for v (eqn. (17)) we neglect terms involving overlap of non-adjacent orbitals. This makes both H a x i , x i ~ and SAXiSXiB pro- portional to CirCis and thus The coefficients, j ; are approximately, but not strictly, independent of i, Y or s, but it is of interest to note that in the approximation where this dependence is neglected, v becomes proportional to the mobile bond order,l5 prs between the rth and sth atoms of the conjugated system (defined by prs = 2 ClrCis). This result is readily reconciled with the concept of electron transfer by n-electron " conduction " through the conjugated system.To examine some consequences of this result we list in table 2 mobile bond order values for a number of conjugated systems computed from the coefficients all electrons TABLE 2.-MOBILE BOND ORDERS IN CONJUGATED SYSTEMS * 1 A -0.50 - 0.02 - 0.42 B 1 --- * 0.88 0 C -0.07 0 -0.58 -0.21 D P * 0.87 0 -0.39 0 0.30 E lk ak 1 G38 ELEC'I'RON TRANSFER I N BKIDGEL) SYS'I'EJMS TABLE 2. -con t in ucd J K L trends. (9 (ii) The M N of the Huckel orbitals of the corresponding hydrocarbon molecules or anions. The value (whose sign is not relevant in this connection) refers in each case to the bond order between the designated atom and the starred one.We note the following A general tendency for the bond order to fall off with increasing length of the conjugated path. In many cases there is superimposed upon this an alternation effect such that the bond order between atoms separated by an odd number of atoms is zero. (This is a general result for alternant molecules but not necessarily for ions.) introduction of hetero-atoms (e.g. 0 or N) which are normally present in the systems of actual interest as bridging ligands will undoubtedly modify this pattern but is unlikely to alter it qualitatively. Thus the alternation of bond orders is probably relevant to the differences noted between m- and p-phthalate as electron transfer mediators (cf. K and L, table 2).Of related interest is the observation 1 that the fumarate and p-phthalate medi- ated oxidations of CrII by CoIII are accelerated by acids. This has been interpreted in terms of the improved conjugation of the path connecting the two metal ions, resulting from protonation of the carboxyl oxygen adjacent to CoIII, e.g., In terms of our model this explanation finds an analogy in the increase in bond order in going from M to N (table 2). The bond order patterns in some of the aromatic molecules listed in table 2 are also of interest in relation to electron transfer reactions of metal complexes of dipyridyl, o-phenanthroline, porphyrins, etc. Such reactions are generally of the outer-sphere type, but it is likely that electron transfer through the ligands (e.g. the relative effectiveness of different positions of the aromatic system) is governed by similar considerations.SUPEREXCHANGE George and GrBth 9 have drawn attention to another possible detailed mechan- ism of mediated electron transfer which may be important in these systems. This is the mechanism of superexchange first suggested by Kramers 16 also to account for magnetic interactions between transition metal ions in oxide crystals. It1. IiALPEKN AND L. E. OKGCL 39 arises from mixing with the ground states, @I and QI, of excited configurations such as A+X"B+ and AXB (111) (IV) corresponding to transfer of an electron in the first case from A to one of the un- occupied orbitals 4xtj of X and in the second from one of the occupied orbitals through (111) leads to additional contributions to v $xi, of X to B.Interaction of @I and in eqn. (15) of the form where the energy of the excited configuration. The principal which extends over all the unoccupied orbitals of X, are Similarly interactions through (IV) give rise to a term, containing contributions from each of the occupied orbitals, Xi, of the form, - (4A(1)4Xi(2)6Xi(3) 1 I $A(1)4X,(2)48(3>)(~A(1)4Xi(2)4B(3) I I 4Xi(1)4Xi(2)4B(3))* EI-EIv, The magnitude of the superexchange interactions, like those of double exchange, are of the order of the overlap product, SAXSXB. However, because of the energy term in the denominator, it is to be expected that contributions from superexchange will arise principally from interactions through the highest occupied and lowest unoccupied orbitals and that both their absolute and relative importance will be related to the ease of oxidation or reduction of the bridging ligand by the metal ions.The magnitude of the transition frequency, v, is determined by the algebraic sum of the contributions from these simultaneous interactions, i.e., Thus the contributions from the various superexchange interactions may either reinforce or interfere with each other as well as with those from double exchange. A factor of importance in relation to both the double exchange and super- exchange mechanisms is the matching of the symmetries of the metal ion and bridging orbitals. Thus electron transfer between t2g d-orbitals will be favoured through n-bridging orbitals and transfer between eg orbitals through a-bridging orbitals.It should be noted that on the basis of this criterion, neither the CrII+CrIn nor Cra+ CoIII systems, both of which involve electron transfer between eg orbitals, represent favourable cases for mediation by n-bridging orbitals. However, this40 ELECTRON TRANSFER IN BRIDGED SYSTEMS rcstriction may be partly removed by a number of factors (e.g. distortion from planar configuration) and its importance is difficult to assess. In this connection the possibility of participation of excited configurations of the metal ions should also be considered, particularly in reactions involving a net free-energy decrease. CHEMICAL MECHANISMS In addition to these quantum-mechanical interactions it is possible for net electron transfer to be effected through chemical mechanisms in which the bridging group is first reduced by one of the metal ions and subsequently reoxidized by the other (or vice versa).In contrast to superexchange this type of mechanism in- volves the participation of configurations such as 111 and IV as actual chemical intermediates in the reaction and depends on the attainment of such configurations through thermal activation. Thus it is likely to be important only when the redox potential for the oxidation or reduction of the bridging group is very favourable. The limiting case of this type of mechanism involves participation of only one of the metal ions in the rate-determining step (e.g., A+X-->A+ X ; X+ B+X-+ B+) and is readily distinguishable kinetically. This is not commonly encountered in redox reactions between metal ions but possible instances are the oxidation of T1+ by CeOH3+ 17 and the TlBrlfTl+ electron exchange.18 In general, however, even this type of mechanism is likely to be favoured by concerted interactions of both metal ions with the ligand and hence to proceed through an activated complex of the bridged type.Redox mechanisms19.20 involving the transfer of an H atom (i.e. the intermediate reduction of a water molecule) between the hydration shells of the metal ions may be included in this class. Conjugation in the bridging group is important also in relation to this type of mechanism since an electron transferred from the reducing ion to a conjugated bridging group is in a delocalized orbital and can pass readily to the oxidant. Thus the process is analogous 9 to the mechanism of ordinary semiconduction in solids involving thermal excitation of electrons into a conduction band.That an electron passes into the maleate bridge in the oxidation of Vn and CrII by maleato- pentammine-cobaltIII has been inferred from the observation that the maleate group undergoes cis-trans isomerization and deuterium exchange with the solvent during the reaction.4 Also relevant to this theme are recent studies21 on the oxidation of the organic ligand in complexes such as oxalatopentammine cobalt111 by Ce*V and other oxidants. CONCLUSIONS In this paper we have attempted to examine various types of interaction which may be of importance in promoting electron transfer across bridged systems. At this stage neither the theoretical nor experimental evidence appears adequate for quantitative assessment of the importance of these relative to each other or to other factors which may influence the overall rates of such reactions.Among the latter are the rate of the substitutional step leading to the formation of the bridged intermediate, the ligand displacements (particularly that of the bridging ligand) associated with the Franck-Condon restriction and the lifetimes of configurations appropriate for electron transfer compared with frequency of the electron transfer process itself. Qualitatively we have noted a number of factors (bond orders, redox potentials, orbital symmetries, etc.) which may serve as distinguishing criteria for some of the interactions we have considered and these suggest further experiments whereby their importance might be tested.The study of conjugated bridging groups offers a particularly promising approach for it permits the various parameters of interest to be varied in a systematic manner. Thus it would be of interest to compare the effectiveness as electron-transfer mediators of a series ofJ . HALPERN AND L. E . ORGEL 41 dicarboxylic acids connected through conjugated paths of varying length, or of a series of diaza-aromatic compounds varying the relative positions of the two N atoms. Comparison of reactions of VII and CrII which have similar redox poten- tials, but involve transfer of electrons from orbitals of different symmetry, should also be of interest in assessing the importance of the latter factor. Such measure- ments appear to lie within the scope of present experimental methods. We are grateful to Prof. H. C. Longuet-Higgins, Prof. S . Golden and Mr. J. S . Griffith for valuable discussions. One of us (J. H.) also thanks the Nuffield Foundation for a Travelling Fellowship and the University of British Columbia for a leave of absence. 1 Taube, Advances in Inorganic Chemistry and Radiochemistry (Academic Press, New 2 Ball and King, J. Amer. Chem. SOC., 1958, 80, 1091. 3 Fraser, Sebera and Taube, J. Amer. Chem. Soc., 1959, 81, 2096, 3000. 4 Fraser and Taube, J. Anrer. Chem. SOC., 1959, 81, 5514. 5 Libby, J. Physic. Chem., 1952, 56, 863. 6 Zwolinski, Marcus, R. J. and Eyring, Chem. Rev., 1955, 55, 157; J. Physic. Chem., 7 Marcus, R. A., J. Chem. Physics, 1956,24,966; 1957,26, 876, 871. 8 Orgel, Report X ConseiZ Chim. SoZvay (Brussels, 1956), p. 289. 9 George and Griffith, The Enzymes (Academic Press, New York), 1959, 1, 347. 10 Laidler, Can. J. Chem., 1959, 37, 138. 11 Taube and Myers, J . Amer. Chem. SOC., 1953, 76, 2103. 12 Slater, Quantum Theory of Matfer (McGraw-Hill, New York, 1951), p. 81. 13 Gurnee and Magee, J. Chem. Physics, 1957, 26, 1237. 14 Zener, Physic. Rev., 1951, 82,403. 15 Coulson and Longuet-Higgins, Proc. Roy. Soc. A, 1947, 191, 39. 16 Kramers, Physica, 1934,1, 182. 17 Armstrong and Halpern, unpublished. 18 Carpenter, Ford-Smith, Bell and Dodson, this Discussion. 19 Reynolds and Lumry, J. Chem. Physics, 1955,23,2460. 20 Hudis and Dodson, J. Amer. Chem. SOC., 1956, 78, 91 1. 21 Taube, Chem. SOC. Spec. Publ., 1959, 13, 57. York), 1959, 1, 1. 1954, 58, 432.

ISSN:0366-9033    

DOI:10.1039/DF9602900032

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

THE RATES AND MECHANISMS OF REACTIONS OF Cr(bip):+ WITH Co(JII) COMPLEXES * BY A. M. ZWICKEL? AND HENRY TAUBE George Herbert Jones Laboratory, University of Chicago, Chicago 37, Illinois, U.S.A. Received 18th January, 1960 Cr(bip):+ is shown to react with complexes of the type CoIII(NH3)sL (L = NH3, OH2, OH-, C1-, Br-) by an outer sphere activated complex. Salt, ligand, and isotope effects have been investigated and are discussed. A useful criterion for classifying and, through this, for improving the under- standing of mechanisms of electron transfer reactions is provided by the geometry of the activated complex. Some activated complexes are characterized by inter- penetration of the first coordination spheres of the reactants in the activated com- plex. These, which have been named the bridged activated complexes, have been demonstrated in the reactions of chromium(I1) with a great variety of oxidants inert to ligand substitution.1 This demonstration is made possible by the behaviour of chromium toward substitution when reduced and when oxidized.Chromium is perhaps unique among aquo ions in that it is labile to substitution when reduced but inert when oxidized. Thus, progress with other aquo ions as reducing agents awaits the development of less direct means of classifying the mode of attack. A second activated complex, which has been called the outer sphere activated complex, is defined by the requirement that the number and identity of the ligands in the first coordination spheres of the reactants remain unchanged when the reactants enter the activated complex.Since this activated complex perhaps must of necessity operate in reactions where both reactants are inert to substitution, it has been found in more systems than has the bridged activated complex.1 One method of attack on the systems which have thus far resisted classification may be a discrimination on the basis of the chemical and isotopic effects characteris- tic of the two activated complexes. Some effects of this kind have been elucidated for reactions involving the bridged activated complex. Analogous effects have now been in part determined for the outer sphere activated complex by study of the reactions of Cr(bip);+ (bip = a&-bipyridine) with various complexes of cobalt(I1I). These oxidants were chosen for study in order to provide comparisons with the data which have been observed for the reactions which they undergo with Cr:.In all the reactions studied thus far using oxidizing agents of the class of present interest, except when L = NH3, C r l l reacts by means of the bridged activated complex. EXPERIMENTAL Due to the air-sensitivity of the reductant, all work was done in an atmosphere of nitrogen scrubbed with Ce; to remove traces of oxygen. The reductant was generated by addition of C<$ (electrolytically produced) to a solution of a,a’-bipyridine. The reductant was added to the deoxygenated solution containing oxidant, neutral salts to * Contribution from the George Herbert Jones Laboratory, University of Chicago. -f present address : Department of Chemistry, Florida State University, Tallahassee, Florida.42A . M. ZWICKEL AND 11. TAUBB 43 fix the ionic strength, and miscellaneous reactants (e.g. acid). 'The mixture was stirrcd by bubbling with nitrogen and pumped into a deoxygenated spectrophotometer cell. The cell and the mixing vessel wcre thermostatted by immersion in a water bath. After mixing, the cell was isolated, dried, and transferred to the thermostatted cell compartment of a Cary model 14 spectrophotometer, and the optical density of the solution as a function of time was recorded. At 562.5 mp, the extinction coefficient of the reductant, 4340 cm-1 mole-1 l., was ca. 100 times that of any other speciesIpresent. Thus, the sccond-order rate law could be used in the form where D is the optical density of the subscripted time, E the extinction coefficient of the reductant, and I the optical path length of the cell.The differentiation with respect to time was performed graphically. Linearity of the above plots under widely varying initial conditions of concentration was taken as proof of the validity of the treatment of the data and specifically of the assumed second-order rate law. RESULTS THE FORMULA OF THE C ~ ~ + - B ~ ~ I D I N E COMPLEX Evidence that the predonlinant form of Cr(U) in the reactant solutions is a complex containing 3 molecules of bipyridine for each atom of chromium was provided by a mass-action analysis of the colour of solutions containing 1.0 x 10-4 M Cr(II), 5 x 10-4 M HC1 and various concentrations of bipyridine. The extinction coefficient of the terminal complex at high bipyridine concentration was determined using a solution containing a large excess of the base.Using the extinction coefficient thus determined, the concentration of the terminal complex was calculated from the measured optical density of the intermediate solutions, the concentration of Cri: then being obtained by difference. The concentration of free bipyridine was also determined by difference, using the value of Harkins and Freiser2 for the acidity of the bipyridinium ion. The data and the results of the calculations are shown in table 1. TABLE ~.-D~ERMINATIoN OF THE COMPOSITION OF THE Cr(II) COMPLJX temp., 23" total bip., M 2.2 x 10-4 3.7 x 10-4 5.6 XlO-4 Cr(bip);', M 2-26 x 10-5 5.32 x 10-5 8-75 x 10-5 Cr:gf, M 7.74 x 10-5 4.68 x 10-5 1.25 x 10-5 calc.for n = 1 2.4 x 10-5 5.9 ~ 1 0 - 5 1.2 x 10-4 n = 2 2.1 x 10-5 3.8 ~ 1 0 - 5 7.4 x 10-5 n = 3 1.6 x 10-5 2.6 x 10-5 4.6 x 10-5 free bip, M 0.8 x 10-4 1-51 x 10-9 1-40 x 10-14 0 . 5 2 ~ 10-4 1 a26 X 10-9 0.17 x 10-4 0.83 x 10-9 1-28 x 10-14 It is apparent from the results shown in table 1 that the assumption that the formula of the complex is Cr(bip)z+ does account satisfactorilyfor the data, and that44 REACTIONS OF Cr( bip)z+ WITH Co(I1 I ) COMPLEXES it is the only simple assumption that does. In the solutions used in the rate experiments, the total concentration of bipyridine was at least 9 times as great as in the experiments outlined in table 1 so that it can safely be assumed that unless the acidity is too great the predominant form of Cr(1I) in the solutions is the com- plex Cr(dip)g+.EVIDENCE ON THE GEOMETRY OF THE ACTIVATED COMPLEX The reaction of Cr(dip):+ with the Co(1II) complexes studied was found to be nicely first order in the reducing agent and in the oxidizing agent at least for all the oxidants with which it was possible to get fairly extensive kinetic data. The rate of reaction of Cr(dip):+ with Co(NH&+ was also shown to be independent of total bipyridine concentration over a considerable range from 0.002 M total to greater than 0.01 M total (Cr(I1) total at ca. 5 x 10-5 initial, pH approximately 4). With Co(NH3);' as reactant, and with bipyridine in good excess, the rate of reaction was shown to be independent of pH in the range 3.5 to 5.6; with the aquo complex as reactant, the rate of reaction was shown to be independent of pH in the range 3.0 to 5.0.For both systems it can therefore be taken as proved that the reactant is Cr(dip):+ rather than an ion containing less bipyridine per Cr(I1). (It should be mentioned, however, that an increase in the rate of reaction is noted when the pH is lowered to 1.5. Presumably a species such as Cr(dip)2+ or Cr(dip)g+ is present at low pH, and it reacts more rapidly with Co(NH&+ than does Cr(dip):+.) TABLE ~ . - c o ( N H ~ > ~ + AS OXIDIZING AGENT Total [bip] 0.002 or greater ; [initial Cr(II)] ca. 5 x from 5 x 10-6 to 1 x lO-3M [Co(NH,)3,+], temp. 25 25 25 25 25 25 4 4 4 25 24 24 24 23 4 24 0.01 (NaCl) 0.05 (NaCl) 0.096 (NaC1) 0.20 (NaCl) 0 2 0 (NaCl) 0 2 0 (NaCl) 0.01 (NaCl) 0.05 (NaCl) 0-20 (NaCl) 020 (NaCl) 0-01 (NaC104) 0.05 ( N ~ C I O ~ ) 0.10 (NaC104) 0-20 (NaRr) 0.20 (NaBr) 0.20 (KCl) k x 10-3 M-1 min-1 2.4 6.8 10.8 14.9~ 15*2b 11-oc 0.43 1-48 3.9d 20.0e 5-6 21.3 41 36 9.6 15.6 a average of 5 determinations, with an average deviation from the mean of 5 %. b using 94.8 % D20 as solvent, mean of two values.c using Co(ND3);' in 93.8 % D20, mean of two values. dmean of 3 values, average deviation, 5 %. e 0.005 M Na2SO4. The kinetic evidence cited implies that the chromium reaction product is Cr(dip)i+, for bipyridine is not lost from the Cr(II) complex prior to reaction, andA . M. ZWICKEL AND H . TAUBE 45 since Cr(II1) is usually quite inert to substitution, the base is probably not lost after the electron transfer reaction is consummated.This prediction based on kinetic considerations is supported by the following evidence. The spectrum of the reaction product is identical with that obtained for a solution of Cr(dip)z+ which has been oxidized by air, and that of a solution prepared by prolonged heating of Cr(HzO);+ in the presence of excess bipyridine. The reaction product cannot be eluted from a column of Dowex-50-X4 ion exchange resin by 1 M HC104, but is eluted by 4 M HC104 so that it probably has a charge of +3. The arguments just presented show that the coordination sphere of the Cr(I1) complex is not disrupted when it reacts. The well-known inertia to substitution of the Co(II1) complex studied ensures that the oxidizing agents also keep the co- ordination sphere intact, so that the mode of attack is limited to that corresponding to the geometry of the outer-sphere activated complex.SUMMARY OF KINETIC DATA The results of experiments with Co(NH&+ as oxidizing agent and covering a range of conditions are summarized in table 2 and for certain other oxidizing agents in table 3. Table 4 shows the activation parameters computed from the data obtained on the reaction of Co(NH3>;+ with Cr(dip)i+ at different temperatures. TABLE 3.-REA(=TION OF Cr(dip)$+ WITH A VARIETY OF OXIDIZING AGENTS Concentrations in the range used for experiments of table 2, NaCl to maintain p, pH-4 oxidant temp., O C P k, M-1 min-rx 10-3 Co(en$+ 25 0.10 2.2 Co(en): + 25 0.20 3.8 CO(NH~)~(OH~)~-~ 4 0.05 126* CO(NH3)5(OH2)3 + 4 0.05 486 CO(m3)5(OH2)3 + 4 0.05 73= Co(NH3)5(OH2)3+ 4 0.01 39 Co(NH3)5Br2+ 4 00001 > 103 CO(NH~)~CP+ 4 0.01 630 a mean of 9 values (variable pH), average deviation from mean of 4 %.b In 93.8 % D20, making a linear extrapolation to 100 % D20. In D20 deuteration of the H20 molecule on Co(NH3)sH203+ takes place, but not immediate deuteration of NH3. An additional experiment using completely deuterated aquopentamminecobalt (111) showed the rate to be the same as that with only H20 deuterated. c at pH = 7.25. TABLE 4.-AcTIVATION PARAMETERS FOR THE REACTION CO(NH3);' WITH Cr(dip);+ medium AH+, kcal AS+, cal/molc deg. 0.20 (NaCl) 9.9 - 14 0.05 (NaCl) 11.3 -11 0.01 (NaCI) 13.0 - 10 0.20 (NaBr) 10.8 - 9 DISCUSSION The actual mechanism of the reactions investigated is most probably a quantum- mechanical tunnelling process.In support of this hypothesis may be cited the46 REACTIONS OF Cr( hip):+ WITH Co(ll1) COMPLEXES result that Cr(bip);+ reacts with Co(en):+ several times less rapidly than it does with Co(NH3):'. The decreased rate observed with ethylenediamine as compared to NH3 as ligand on the oxidant can on this basis be ascribed to the greater size of the ethylenediamine rnoleqle resulting in greater tunnelling distance and consequently lowering the probability for barrier penetration. It is interesting that even for the outer-sphere activated complex, the rates of reaction are very sensitive to the nature of the groups associated with the oxidizing agent. The comparison of the reaction rates for two ions of like charge, namely Co(NH3);' and Co(NH3)5Hz03+ is particularly significant.The increased rate when H20 is substituted for NH3 implies that the electron transfer process makes particular use of Iigands in these reactions also, and that the electron transfer proceeds through the ammonia ligand only when it has no other choice. Results then for ions of fixed charge type, can be interpreted as measuring the " conduc- tivity " of each ligand, or on the tunnelling model, the permeability of each ligand for electrons. The rate of reaction of Cr(bip):+ with Co(NH3)50H2+ may be calculated as 6 x 10 4 M-1 min-1 from the experiment with the aquopentammine system done at pH 7.25 under which conditions ca. 80 % of the aquo complex is dissociated to the hydroxy form. The comparison of the relative rate of reaction of Co(NH3)50H2+ and Co(NH3)50Hi+ with Cr(bip);+ on the one hand and with Crzl on the other is particularly significant.When Cr: is reactant, with both oxidizing agents a bridged activated complex is involved,3 and the hydroxo ion reacts at least 106 times more rapidly than does the aquo.4 But by the " outer-sphere " mechanism, the hydroxy ion in fact reacts less rapidly than the aquo. This implies that in the many systems in which the hydroxy form of the oxidizing agent reacts more rapidly than the aquo, the hydroxy ion is serving as a bridging group. In the bridged activated complex, it performs two functions, acting as a binding ligand, and conducting the electron. Its superiority over H20 in stabilizing a binuclear com- plex apparently far outweighs its somewhat lessened conductivity. The result for OH- as ligand observed in the system under present study is consistent with the observations made for the halide ions as ligands.By extrapolating the specific rates observed for Br- and C1- as ligands, the rate for (NH3)5CoF2+ reacting with Cr(dip):' is expected to be of the same order as it is for (NH3)5CoOH2+, and OH- and F- are perhaps expected to resemble each other in permeability to electron transport. It is also profitable in the context of these remarks to draw attention to the great increase in reactivity that takes place when H20 on Cr2+ is replaced by bipyridine. The rate of reaction of Crx,* with Co(NH&+ at 25" and p = 0.40 (NaC104) is 5-3 x 10-3 M-1 min-1.5 This reaction presumably also proceeds through an outer-sphere activated complex. Thus it is known that a proton is not lost from the oxidizing ion when it enters the activated complex, as would be required to expose an electron pair for use in bridging.The reaction has an activation enthalpy of 14.7 kcal and activation entropy of - 30 cal/mole deg. Part of the reason for the greater speed at which Cr(dip>g+ compared to C<$ reacts with Co(NH3);+ is the more fwourable entropy associated with the formation of the activated com- plex. On the tunnelling model, the entropy of activation may be interpreted as the sum of the classical entropy of formation of the activated complex from the reac- tants, and a term - R Ink,, where k , is the probability of barrier penetration.6 The function of the bipyridine molecule can in part be construed as being to bring the electrons to the surface of the molecule, thereby increasing the probability of barrier penetration.However, it must be recognized that the electronic con- figurations of Crz: and Cr(bip>:+ differ, the former having three d electrons in orbitals of t2g symmetry and one in an e, orbital 7 while the latter has four t2g electrons.8 Thus the electron which transfers from the bipyridine complex is inA. M. ZWICKEL AND H . TAUBE 47 an orbital which can overlap the 7r orbitals of the ligands, and thus can be brought to the surface of the molecule with consequent enhancement of reactivity to electron transfer. That such 7r orbitals areused as indicated by the result of George and lrvine 9 showing that the 5-nitro - 1,lO-phenanthroline complex of Fe(I1) reacts with Ce(IV) less rapidly than does the 1 ,lo-phenanthroline complex.This dif- ference presumably appears because the use of the ligand 7r orbitals by the nitro substituent renders them less available for use by the d electrons of the metal. The absence of a solvent isotope effect for the reaction of Co(NH3);' with Cr(dip):+ is interesting and implies that electron transfer occurs, at best, through the solvent and not to it. Indeed, it appears unlikely that the solvent plays any role at the mimediate site of attack, electron transfer most probably occurring directly from complex to complex without intervening layers of solvent.10 But even granting this, it is still surprising that there is no detectable solvent isotope 11 effect associated with rearrangement of the solvent about the ions.12 The isotope effect found on deuteration of the coordinated ammonia molecules, a decrease in rate by a factor of 1.36, probably does not arise from a stretching of N-H bonds, but from stretching the Co-NH3 bonds. Before electron transfer can take place, excitation of the breathing modes of the complex is likely necessary, in order to set up a potential field in whcih the energy of the electron is the same before and after transfer, as discussed by Libby.13 The Franck-Condon principle requires that the electron transfer process be adiabatic.The isotope effect accompanying deuteration in the first sphere of coordination in Co(NH&+ (diminution in rate by a factor of 1-36) is markedly different from that accompanying deuteration of the water molecule in Co(NH3)50Hi+ (diminution in rate by a factor of 2.6).This again is evidence that particular use is made of special groups also when electron transfer takes place by the " outer-sphere " mechanism. The specific implication is that it is expeditious to distort the co- ordinated water molecule. Since the diminished rate observed when OH- rather than H20 is the conducting group indicates that it is not helpful to remove the proton from water, the most reasonable distortion is a bending rather than a stretching mode. It should be noted that the isotope effect associated with replacing H20 in Co(NH&OH;+ by D20 when attack occurs via an outer-sphere activated complex is not much different from that observed for the bridged activated complex.In the latter case (Cr2+ as reducing agent) a total diminution in rate by a factor of 3.8 is observed.4 Part of the factor of 3.8 is undoubtedly to be attributed to substitution of D20 for H20 in the first sphere of coordination about Cr2+. From the H-D solvent isotope effect observed in 14 the reaction of Cr2+ with (NH3)5CrC12+, this is estimated as contributing a factor of 1.3, so that the effect associated with sub- stituting D20 for H20 in the oxidizing agent is a factor of 2.9 by the bridged activated complex. This comparison for the two kinds of mechanism makes it seem all the more unlikely that the H-D effects can be used in a simple way to distinguish between the two kinds of mechanisms although the results are still of great importance in defining the mechanisms of the processes. The salt effects are in accord with the general ideas discussed by Marcus 10 and by Libby.13 The smallest anion used, C1-, presumably interacts most strongly with solvent and therefore the rearrangement of the ionic atmospheres of the reactants in the activated complex is least easily effected with it.As may be expected for an activated complex formed from cations, substitution of K -I- for Na -I- has a negligible effect on reaction rate at least when the cations are at low concentration. Sheppard and Wahl15 have demonstrated the great sensitivity of the electron exchange re- action between MnO, and Mn0;- to the nature of the cation present in solution. We wish to thank the Atomic Energy Commission (Contract AT(11-1)-378) for support of the reaserch described in this paper.48 REACTIONS OF Cr(bip)g+ WITH Co(1II) COMPLEXES 1 Taube, Can. J. Chem., 1959,37, 129. 2 Harkins and Freiser, J. Amer. Chem. Soc., 1955,77, 1374. 3 Kruse and Taube, J. Amer. Chem. Suc., 1960, 82, OOO. 4 Zwickel and Taube, J. Amer. Chem. SOC., 1959,81, 1288. 5 Zwickel and Taube, to be published. 6 Marcus, Zwolinski and Eying, J. Physic. Chem., 1954, 58, 432. 7 Orgel, J. Chem. Physics, 1955, 23, 1004. 8 Hein and Herzog, 2. anorg. Chem., 1952,267, 337. 9 George and Irvine, J. Chem. SOC., 1954, 587. 10 Marcus, J. Chem. Physics, 1956,24,966. 11 Baker, Basolo and Neumann, J. Physic. Chem., 1959, 63, 371. 12 Marcus, J. Chem. Physics, 1957, 26, 867. 13 Libby, J. Physic. Chem., 1952, 56, 863. 14 Ogard and Taube, J. Amer. Chem. SOC., 1958, SO, 1084. 15 Sheppard and Wahl, J. Amer. Chem. Soc., 1957,79, 1020.

ISSN:0366-9033    

DOI:10.1039/DF9602900042

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

MECHANISMS OF SOME OXIDATION-REDUCTION REACTIONS BETWEEN METAL CATIONS IN AQUEOUS SOLUTION BY W. C. E. HIGGINSON, D. R. ROSSEINSKY,* J. B. STEAD AND A. G. SYKES Chemistry Dept., The University, Manchester, 13 Received 21st January, 1960 The main features of the kinetics of the following reactions in aqueous perchloric acid are briefly described : FeIII+ VIIbFeIIf VIV ; the preceding reaction, catalyzed by catalyzed by AgI ; 2HgII+ZVIII-+(Hg1)2+2VIV. The mechanisms of these and related reactions are discussed. The significance of the positive entropies of activation found for some bimolecular oxidation-reduction processes occurring between metal cations is discussed. CUII ; TIIII+2VIv+TlI+ 2VV ; TlII~+2VII~+TlI-t 2VIv ; 2Cew+ (Hg92+2CeIII+ 2HgI1, Much of the interest in oxidation-reduction reactions between metal cations in solution relates to the nature of the electron-transfer process itself.Many of the reactions already studied, especially those of the isotopic-exchange type, involve only a single oxidation-reduction process. In this paper, however, we report our findings, in several cases of a preliminary nature only, concerning some reactions in which more than one oxidation-reduction step contributes to the total chemical change. Our emphasis is primarily upon the overall oxidation-reduction mechanism. EXPERIMENTAL Reactions were followed spectrophotometrically, as described previously,l except for the CeIv+(HgI)z+AgI system in which CeIv was estimated by titrating samples of the reaction solution with FeI4 All reactions were in dilute perchloric acid unless otherwise stated.Reaction solutions which included VIII were kept under nitrogen. The ionic strength I was made 3.0 M by the addition of NaC104, except in certain experiments with the CeIv+(HgI)z+AgI system in which I = 4.5 M, and in mixing experiments with the TlIIIf VIII system in which I -rr 6 M. The concentration equilibrium constant of the reaction V02++Fe3+ +H20 +VOl+ Fe2++2Hf Pt 1 Fe3+, Fe2+, H+ 11 VO,’, V02+, H’ 1 Pt, the concentrations and ionic strength being similar to those in the related kinetic experi- ments. was found by e.m.f. measurements using the cell RESULTS AND DISCUSSION THE REACTION BETWEEN IRON(@ AND VANADTUM(III) The reaction, Fe”‘+ V1lr+FeII+ VrV at first appeared to involve a single-stage oxidation-reduction process, similarly to the reaction, Conr+ CeT1I+Cou+ Ce1V,2 * present address : Chemistry Department, University of the Witwatersrand, Johannes- burg, Union of South Africa.4950 SOME OXIDATION-REDUCTION MECHANISMS because preliminary experiments in the initial absence of the products showed the kinetic equation to be -d[Fe'"]/dt = -d[V"']/dt = Ic,[Felll][V1'l]. However, further work has shown 3 the full kinetic equation to be -d[Fe"']/dt = -d[V"']/dt = k,[Felll][V*ll]+ k'[ Fe '"1 [V I ''1 [V'"]/[ Fe"] . (1) If the products, FeII and VIv, are absent at the beginning of the reaction, then at any time during the reaction [Fe"] = [VIV] and so ko = kl+k'; hence the simple form of the kinetic equation under these conditions. In experiments at a high initial concentration of FeI1 the contribution of the term in k' (eqn.(1)) is negligible and kl can be found. We consider that this term relates to a single- stage process, analogous to that of the ColI1+CeI1* reaction. The dependence of ki upon the hydrogen-ion concentration in the range 0.50-2.40 M is but although individual values of kl are subject to relatively small errors, corres- ponding values of b, c and d are of low precision. From experiments at 15, 20, 25 and 30°C with I - 3.0 we find that b = antilog,, (1143&2.9) x exp -((17.3f4.1)1O3/RT)M-' min-', c = antilog,, (16.4k3.9) x exp - ((23.2_+5.4)103/RT}minA', d = antilog,, (17*1*2-0) x exp -((24~5~2-8)103/RT)M rnin-'. The entropy of activation A S corresponding to the velocity constant b is - 15 ;G 13 cal mole-1 deg.-1 It is not possible to obtain k' satisfactorily by finding ko from experiments in which neither Ferl nor VIV is present initially and then subtracting kl, since this constant is several times larger than k'.We have found k' from experiments using a high initial concentration of VfV. The term involving this constant in eqn, (1) is interpreted as indicating a sequence of two reactions : k2 k-2 Fe I * I + V IV+- Fe + Vv The stationary-state approximation, dwv]/dt = 0, leads to -dCFe"'] -d[V"'] k,k,[Fe"'JrV"'J[V''] dt dt k-,[Fel1] + i3[V11ij-' =-= and if k-2[Fer1]>k3[V111] this corresponds to the second term in eqn. (l), with k 5 kzk31k-z == k& where K2 is the concentration equilibrium constant for the reaction : Fe3 + -I- V02+ -+ H2 0 + Fe2 + VO; 4- 2H'.W e have measured K2 at temperatures corresponding to those of the kinetic experi- ments and so we obtain k3. (The value, K2 - 8-0 x 10-6 M2 at 25°C and I = 3.0 M may be compared with the value, 1 . 6 0 ~ 10-5 M2 recently obtained 4 at 25" and I = 1.0 M. The thermodynamic constant is 9 . 0 2 ~ 10-5 Mz at 25°C.) At 25°CHIGGINSON, ROSSEINSKY, STEAL) A N D SYKES 51 in 1 M perchloric acid, k3 fi 1.7 x 104 min-1, thus it would be difficult to investigate the reaction between Vv and VII1 directly by conventional methods. The depend- ence of k3 upon the hydrogen-ion concentration in the range 060-2.40 M at 15-30°C is k, = e+j/[H+] and e = antilog,, (16.2+_ 1.3) x exp - ((16.6+ l-8)lO3/RT)M-' mill-' ; from the pre-exponential term, AS+ = 5 5 6 cal mole-1 deg.-1 Values of f are about two-thirds those of e at corresponding temperatures, but are subject to rat her large errors.CATALYSIS OF THE IRON(1II) + VANADIUM(II1) REACTION BY COPPER(I1) The oxidation-reduction reaction between CulI and VrlI cannot be investigated directly, but can be studied by following the FerI1+V1I1 reaction in the presence of CuII.3 At sufficiently high concentrations of CUT', the rate of reaction is inde- pendent of the concentrations of FeIII, FeI1 and VIV, the rate equation being -d[Fe"'J/dt = -d[V'"]/dt = kk[V"'] = k4[V'"][Cu1']initial. This is consistent with a 2-stage mechanism : c u I 1 + v I I I k " - , c u I + v IV, Fe I I I + Cu I rap!$ Fe I I + Cu I I. The alternative possibility for the slow step, CuT1+ VrlI+C~~tom+ Vv, is regarded as improbable on energetic grounds. In most experiments it was convenient to use concentrations of CuI1 such that the rate of the uncatalyzed reaction, although small, was not negligible compared with the rate observed.However, knowing ICO, k4 can be obtained from such experiments. At 10-2S°C, 0-7-2-6 M hydrogen ion and I = 3.0 we find that k, = 9 + h/[H+I, g = antilog,, (16*1_+ 1-1) x exp - ((2100f 1-5)103/RT)M-' min-', h = antilog,, (15.1 f0.4) x exp -((19~0+0~6)103/R7)min-1. The value of AS+ corresponding to the velocity constant g is 5 f5 cal mole-1 deg.-1 SOME REACTIONS INVOLVING 2-EQUIVALENT CHANGES IN OXIDATION STATE IN A SINGLE PROCESS The FerIr+ VII1 system is abnormal since reactions in which the change in oxida- tion number is unity for each reactant usually involve only one stage.However, in reactions in which at least one of the reactants changes its oxidation state by more than one unit, several steps are always to be expected. There is one major exception to this generalization, the system in which both reactants change their oxidation number by two units, since here a single-stage process may occur. Unfortunately, it is difficult to prove the occurrence of 2-equivalent (2-eq.) changes by straightforward kinetic methods. For example, the reaction T P f UIV-+T1l+ Uvl follows the rate law ; 5 This equation is to be expected for a single-stage, 2-eq. process. However, it is possible that if initially the 1-eq. reaction Tlln+UIV+Tlll+UV were to occur, the subsequent reactions of the relatively reactive intermediates, Tlrl and Uv, so formed would be sufficiently rapid that the overall kinetics would follow the same52 SOME OXIDATION-REDUCTION MECHANISMS simple law.In systems of this sort a possible approach would involve the prior demonstration of a reaction characteristic of an intermediate which would be formed if the initial reaction were of the 1-eq. type, e.g. the irreversible oxidation of a substrate, inert to reactants and products taken separately, in a system in which this intermediate is known to be produced. The presence or absence of this characteristic reaction on adding the substrate could then be sought in the system under investigation. Nevertheless, the indication of a l-eq. reaction would be a more certain conclusion than that of a 2-eq.process based upon a negative result. Occasionally a more positive indication of a 2-eq. change is possible, as in the reaction Tlm+ 2Cr11+T11+ (Cr1I1)2, the mechanism being : 6 T1"' + Cr" -+Tl'+ Cr Ivy CrIv+ Cr11-+(Cr111)2. The observation that almost all the CrlI1 appears in a dimeric form provides the evidence for the intermediate formation of CrrV and hence makes the 2-eq. first stage probable. A review of the reactions of chromic acid 7 has shown that 2-eq. changes are common between oxidation states of chromium. Another reaction believed to involve a 2-eq. change, TllI1+ (Hgl)z+Tll+ 2Hg11, does not proceed by a single step, but follows the mechanism : 8 T1'" + HgtOm+Tl' + Hg" . Again, although the second reaction is probably a single-stage 2-eq. reaction, the evidence is not conclusive.THE REACTION BETWEEN THALLIUM(III) AND VANADIUM(IV) Although the examples quoted above suggest that Tlrn can act as a 2-eq. oxidant in its reactions with metal ions, the reactions, TPr+ 2Feu-+T11+ 2Fe111 and T11U+2V1V-+T11+2VV, follow 1-eq. steps. The mechanism of the former reaction is 9 Tl"'+ Fe" s Ti"+ Fe"' T1" + Fe" +Tll + Fe"' . The study of the TIU1+Vv'v reaction in dilute perchloric acid presents difficulties, since temperatures of 60-80°C are necessary to obtain a satisfactory rate of reaction and under these conditions TllI1 slowly decomposes to TI1 and molecular oxygen. The rate equation is probably 3 -d[V"]/dt = .k,[T11''J[VLV]2/(k~[VV] + [V"]}, where k~fi1.34 M-1 min-1 and k6-2 at 80"C, 1.8 M hydrogen ion and I = 3.0. This is consistent with a mechanism similar to that of the TllI1+ FeT1 reaction : TP + v IV + TI + vV, TI + V IV -+Tl I + Vv.The alternative reaction sequence, 2v'" + VI'l+VV, T1"'+V"'+Tl'+VV, can only occur to a minor extent, if at all.HIGGINSON, ROSSEINSKY, STEAD A N D SYKES 53 THE REACTION BETWEEN THALLIUM(KII) AND VANADIUM(LII) The alternative mechanism mentioned above was considered owing to the rapidity of the second stage, the TllI1+VII1 reaction. When solutions 0,009 M in each of these species and 6 M in perchloric acid were mixed rapidly at ca. 5"C, reaction was complete 3 within the time of sampling, 45 sec. The products of this reaction were TI1 and VIV ; no Vv was detected. Plausible mechanisms are : A: TI'" +V"'~Tl"+V'V, (1-eq. change) ~i I1 + v I I I - + T I I + Vv.B : T1"' + V I I 'ST1 ' + Vv, (2-eq. change) vv+ V"'22V'V. Under the conditions of the mixing experiment k3, the velocity constant of the last-quoted reaction, cannot exceed 3 x 103 M-1 min-1. (T.his value is obtained by extrapolation from the values of k3 obtained as described earlier in this paper.) It can be shown that if the reaction follows mechanism 23, k7 must exceed 3x 102 M-1 min-1 if 95 % of the initial concentration of VII1 has been oxidized 45 sec after mixing. If (k3/k7)<1OY it can also be shown that at least 5 % of VII1 will have been oxidized to Vv when the reaction is complete. This is contrary to the experimental evidence and we conclude that mechanism A is dominant. We have not observed the formation of Vv in dilute perchloric acid, but in similar experiments with dilute sulphuric acid as solvent and with excess of present up to 3 % of VII1 was converted to Vv.This proportion could be increased to 10 % in experiments in which VIV was present initially. We are unable to interpret this observation in terms of mechanism B, but it is consistent with mechanism A if the following steps are added : T I ~ ~ + V ~ ~ - + T I ~ + V ~ , VV+V"'+ 2v IV. We originally expected the first stage of the T1IU+V1I1 reaction to be of the 2-eq. type. However, if this were so, either extensive hydrolysis would occur owing to the formation of VO;, or a less hydrolyzed and hence less stable form of Vv would be produced. In either case, a relatively high activation energy is likely and so the occurrence of the alternative 1-eq.reaction seems less surprising. In theT1lll+UIV reaction, which is probably of the 2-eq. type,s the alternative l-eq. initial step should not offer an easier route according to this interpretation, since Uv and Uvl are hydrolyzed to the same extent in their most stable forms (UOt and UO;+), unlike VIV and Vv (V02+ and VOS). CATALYSIS OF THE CERIUM(IV) + MERCURY(I) REACTION BY SILVER(I) The CeIV+Agl system is similar to the Cull+V1ll system in that no reaction is observed in the absence of a suitable substrate. In the presence of (Hg1)2 or TI1 a reaction occurs and has been identified 10 as the oxidation of the one or the other of these species, catalyzed by Agr : 2Ce" + (Hg1)$$2Ce ' I r + 2Hg", 2Ce IV + T11EBI!2Ce ' ' I + TI 'I! Under the conditions of our experiments, the direct reactions between CeIV and (Hg1)2 or Tll could be neglected. In the presence of a sufficiently large excess of (Hg1)2, the reaction followed the rate law : - d[CeIv]/dt = - 2d[(Hg'),]/dt = 2k',[Ce1"] = 2k,[Ce'V][Ag'Jinitial, (2)54 S 0 ME OX I D AT I 0 N - R ED U C T I 0 N ME C 1-1 A N 1 S M S the rate of reaction being independent of the concentration of (Hg1)2.If Cell1 is present initially and (HgT)2 is only in small excess, the plot of logl~[C&~] against time is curved so that k; decreases as the concentration of CelI1 increases. We conclude that the mechanism of the reaction is k 8 Ce"+Ag'+ Ce"'+Ag", k-8 ks Ag"+(Hg'),--+Ag'+Hgl+ Hg", Ce 1v + Hg I rapid --+Ce"'+Hg", and, by assuming d[AglI]/dt = 0, we can deduce that The integrated form of eqn.(3) is in good agreement with the results of a series of kinetic experiments in which different concentrations of were present initially. The value of k_8/k9 (0.198 at 1.50 M hydrogen ion, I = 3-0 M and 20°C) is such that the term in [Ce111]/[(Hg1)2] is negligible if (Hgl)z is in large excess; eqn. (3) then reduces to eqn. (2). If Tll is used as the substrate, the sequence of reactions is thought to be similar ; From this mechanism we similarly deduce that The value of k+/klO, 35.7, is very much larger than that of k-8/k9 under the same conditions and the term in [Ce1I1]/[TI1] cannot be neglected. Thus k8 cannot be obtained from plots of logl~[@~] against time. By using the integrated form of eqn. (4) both k-8/k10 and k8 can be found and the latter is in good agreement with the corresponding value obtained when (Hg1)2 is the substrate.From k-8/k9 and k-S/klO, we find k9/klo = 180 at 1.50 M hydrogen ion and 20°C. This quan- tity is the ratio of the rate constants for oxidation of (Hg1)2 and of Tll by AgI1. Under the same conditions, the ratio of the rate constants for oxidation of these two reductants by ColI1 is 185.11 The dependence of k8 upon the concentration of hydrogen ions has been in- vestigated over the range 022-4.2 M with Z == 4.5 M at various temperatures from 9.8 to 30.0"C. The form of this dependence is complex and there is evidence for the presence of dimeric CeIV species in appreciable proportions in the less acid solutions. In the range 1.0-42 M hydrogen ion we find that ks =j[H'I2/{[H+I2 +K,[H'] +KJ4)' This result is most simply interpreted in terms of a bimolecular reaction between the least hydrolyzed monomeric CeIV species present and Ag+.At 24*95"C, the rate constant for this reaction, j , is 6.2 f0.7 M-1 min-1 and the first hydrolysis constant of this CeTv species, K3, is ca. 10.6 M. We fmd that j = antiloglo (15-4f0-9)x exp-{(20.0f.l*2)103/RT)HIGGINSON, ROSSEINSKY, STEAD A N D SYKES 55 and AS+ = 1.8 f4 cal mole-1 deg-1. Values of the first and second hydrolysis constants of Ce4f have recently been obtained l l a and by comparison we conclude that K3 is the first hydrolysis constant of this ion. Hence j is the velocity constant for the bimolecular reaction between Ce4+ and Agf. THE REACTION BETWEEN MERCURY(II) AND VANADIUM(III) The reaction 2HgT1+ 2V1I1-t(Hg1)2+ 2VIv follows a complex rate equation : 10 - d [V' I '1 - [ Hg 'I] [V I' I] + [Hg I '1 [ V " 'J - dt p[V"] + q[V"'] r[V'v] +s[Hg"]' where p = 2.52f0.15, q = 0.20fO.05, r = 3.4f0.6 and s = 6.04~13 M min at 15"C, 0.20 M hydrogen ion and Z = 3.0 M.It was not possible to vary the con- centrations of reactants and products as much as is desirable in a case where four constants are necessary to describe the rate of reaction. The form of the term in p and q in eqn. ( 5 ) seems certain, although the form of the second term, which contributes only 10-20 % of the total rate, may be erroneous. The first term is in accordance with the mechanism : k-1 1 k-11 Hg"+V"' + Hg'"'', The second term may indicate an alternative sequence of reactions : k13 2v"' f v'v+v", k--13 Hg I' + Hg&,mzp% (Hg I), .The relations between the bimolecular velocity constants defined in these equations and the constants p , q, r and s are : k l l = 1/2q; k-ll/k12 = p / q ; kl, = 112s; k+JkI4 = rls. COMMENTS ON THE FORMULATION OF REACTION MECHANISMS As shown above, a complex form of the rate law may be sufficient to indicate the essentials of a reaction mechanism. Such complexity often occurs if the first stage in the sequence of reactions involves a positive change in free energy. A highly reactive species produced in this stage may either react further, ultimately yielding a final product, or may react in the reverse sense with the re-formation of the reactants. If the rates of these competing reactions are similar, kinetic complexity is observed and the overall mechanism of reaction is usually obvious.If, however, this reverse reaction is relatively slow and can be neglected, a simple form of kinetic equation is likely. Some reactions following a several-stage mech- anism show simple kinetics which may be consistent in form with two or more reaction sequences. In certain cases of this type the probable mechanism can be inferred from the stability of the oxidation states adjacent to those of the reactants. For example, the reaction 2Fe"I+ U1v+2Fe11+ Uvl follows the rate law,l2 -d[Fe"']/dt = k[Fe'll][U'V]56 SOME OXIDATION-REDUCTION MECHANISMS which is formally consistent with the rate-determining initial reactions, and Fe"'+ U'v+Fel+Uv'. The latter can be excluded owing to the lack of evidence for Fel in dilute acid solu- tions. Thus, in discussing mechanisms of oxidation-reduction reactions in solu- tion it is helpful to consider the electronic structures of simple cations and other evidence about the stability of the parent elements in their various oxidation states.We may conclude that for homogeneous reactions in acid solutions monomeric forms of, e.g., CelI1, CeIV, Ti"', FeTIr, CoII, ColI1 are very unlikely to undergo 2-eq. reactions as also are oxidizing agents including VIIr, CrlI1, MnlI1 9 , UIV Np'v, PuIV and reducing agents including Vlv, Uv, Npv, Puv. On the other hand, the stable ionic oxidation states of non-transition metals usually differ by 2 units, so that 2-eq. changes are favoured.13 Nevertheless, in reactions with reagents re- stricted to 1-eq.changes and in certain other cases, e.g., the T1I1I+V1I1 reaction, intermediate oxidation states, usually of low stability, can be produced with com- parative ease from non-transition metals. Chromium, although a transition element, is also known to form unstable oxidation states.aS7 Such intermediate states, particularly those of non-transition metals, are analogous to the free radicals of the chemistry of non-metallic elements. In this connection, intermediate states produced in the reduction of Crvr have been shown to initiate vinyl polymerization.14 In the reactions mentioned in this paper, a series of bimolecular reactions seems adequate in formulating reaction mechanisms and the corresponding transition complexes contain only two metal ions.Examples are known in which three species undergo oxidation-reduction in a single transition complex,15 but although two may be metal ions, the case in which all three species are metallic does not appear to have been observed. Such a threefold transition complex may be possible if anions are also incorporated. Many partly-hydrolyzed metal ions form dimeric species 16 and it is conceivable that a dimeric ion, formed from a simple cation capable only of a 1-eq. change, may react in a single process with a cation favouring a 2-eq. change. For example, the reaction, 2Fe11T+ Sn11-+2Fe11+ SnrV has been studied 17 under conditions in which dimeric FelI1 18 is almost cer- tainly present. In any re-interpretation of the complicated behaviour observed in this system, the possibility should be considered of the reaction (Fe111)2+ S n l b 2Fe'I+ Snxv, where (Fe111)2 represents Fe2(OH)i+ or a related dimeric ion.ENTROPIES OF ACTIVATION OF SOME BIMOLECULAR OXIDATION-REDUCTION REACTIONS In table I we summarize entropies of activation AS+ for bimolecular reactions between metal cations in dilute perchloric acid solutions and for two reactions of anionic complexes. Since the reaction paths to which these entropies apply do not involve a dependence of rate upon hydrogen-ion concentration, the corresponding transition complexes can be regarded as composed of the two reactants and water molecules; in the cationic reactions, perchlorate ions may also be present. In group Athe reactions are of the isotopic-exchange type and there is no net chemical change; the entropy of reaction AS can be taken as zero. In reactions in group B, chemical change occurs and AS is usually not zero. It can be seen that in group B there are several cases in which AS+ is positive. This seems surprising since there are experimental and theoretical reasons for expecting negative values of AS+ in bimolecular reactions between ions of like charge.19~ 20 A suggestion 21 that the positive value of AS+ observed in the Co3++Tl+ reaction is due to the incorporation of perchlorate ions in the transition complex has been shown to be incorrect and this interpretation is also unlikely for others of the reactions cited .I1 A recent interpretation 22 of entropies of activation in the oxidation-reduction reactions of uranium, neptunium and plutonium has shown that the entropies ofHIGGINSON, ROSSEINSKY, STEAD A N D SYKES 57 the transition complexes are related simply to their charge. The reactions in table IB conform rather poorly with this type of relation, possibly because in many of them the transition complexes, lacking bridging groups between the metal atoms, are less compact.Following a similar approach to that of Halpern,ls we suggest this type there may be a relation between AS* and AS. Re- the free energy of activation and the free energy of reaction, that in reacfions of lationships between TABLE 1 react ants A NpO$++NpOt MnOZ-I- MnOi- Fe3 + +- Fez+ ~ 1 3 + + ~1 -t- V3 ++ V2-1- charge on complex 4 cal mole-1 AS9 deg.-l transition ref. mole/l.3-0 -11.7 + 3 22 0.16 - 9 -3 30 3-68 - 20 -I- 4 31 0.55 - 25 +5 32 2.0 - 25 +5 33 Fe(CN)2-$- Fe(CN)$- 0.01 -41 -7 34 B vo,++v3+ c03 ++TI .t- Cc4+ + Ag + Co3 ++Hg,” + CO~+-I-VO~+ cu* + -1- v3 + PuO,”++Pu3+ TP++ Fe*+ C03+-t- V3+ Fe3 .I- + V3 + 3.0 3.0 4.5 3.0 3.0 3.0 1.0 3.0 3.0 3.0 + 5 f 6 +13f6 3. 2 f 4 + 9 f 6 + 1 2 f 9 + 5f5 - 40.4 f 0.6 -5*6 >o -15f13 $4 +4 t 5 +5 $ 5 3-5 +5 + 5 +6 +6 3,35 11 10,35 1 1 3,35 22 -t 11 3,35 t calculated from Johnson’s results 36 by using Biedermann’s value 37 for the first hydrolysis constant of Tl3-‘-. and between the activation energy and heat of reaction are well known.23-25 Particularly for ionic reactions, in which entropies are largely determined by ionic charge, similar relationships may apply between the corresponding entropies.We therefore propose the relation, AS’ = AS&, +aAS where AS+ and AS refer to the reaction under consideration, AS& represents the entropy of activation of a reaction of similar nature and the same charge-type for which A S = 0, and O<a< 1. From the values in table lA, we assume ASP,, = - 19, - 25, - 32 cal mole-1 deg.-1 when the charge of the transition com- plex is 4, 5, 6, respectively. We cannot assign a value to a since, for a given re- action, this parameter presumably depends on the extent to which the distribution of charge in the transition complex resembles that of the reactants (a+O) or the products (a-1). Therefore, to test eqn. (6) we compare (AS+-AS$,) with A S (table 2). Where possible, values of AS were calculated from accepted values of ionic entropies,26 but for several reactants and products it has been necessary to estimate 11 ionic entropies, usually by following established procedures.27 Many quoted values of AS are therefore imprecise and since most values of AS+ are also subject to large errors, we have rounded the values of AS and (AS+-ASto)) to the nearest 10 units.58 SOME OXIDATION-REDUCTION MECHANISMS If eqn.(6) holds we should expect AS, whether of positive or negative sign, to be greater numerically than the corresponding value of ( A P - ASto,) since a cannot exceed unity. Reference to reactions (l), (3), (4), (7), (8) (table 2) shows that corresponding values of these quantities are similar, suggesting that a+l. How- ever, in reactions (54, (6a), (go), (lOa), in which AS is calculated by assuming the oxidation-reduction process is formally a simple electron-transfer, (AS+- ASP,,) is seen to be much greater than AS.In these reactions one of the products is taken to be a vanadium cation less hydrolyzed than the normal form and consequently in a less stable state. We therefore suggest that partial hydrolysis occurs within the corresponding transition complexes and in (56), (6b), (96), (lob) we record values of AS calculated on the assumption that sufficient hydrolysis to give stable vanadium oxy-cations occurs in the overall reactions. We now find AS exceeds (AS+- AS&’). Possibly different values of A S should be used for reactions in which the number of solute species alters,28 but neglect to do so will not affect the evident distinction between these reactions and the others. Reaction (2) is of a type different from the rest and we have assumed that the products are 2V02+ rather than the other extreme, V4+ and V02 ; in the latter case AS would probably be negative.1 2 3 4 5a 5b 6a 6b 7 8 9a 96 1 Oa 1 Ob TABLE 2 reaction C O ~ ++Tl’--> CO~++ TI’+ vo 2* -1- v3 +-+2v02+ Ce4 + + Ag +-> Ce3 + + Ag2+ CO~++ Hg; ++CO~++ Hg++ Hg2+ C03 ++ vo2+-, Co2++ v03+ C03++ VO2++ H~O+CO~++VO; + 2H+ CU2++V3++Cu++V4+ CU~++ V3++ H2O-t CU + + V02++ 2H + PUO$ ++ Pu3 ++PuO,+ + Pu4+ TP++Fe2++TlZ++Fe3+ C03 + + v3 +->co2 + + v4 + C03 + + V3+ + H20->C02+ + VO2+ + 2H + Fe3 + + V3 +-+Fez + + V4+ Fe3++ V3+ + HzO+Fe2++ VO2+ -1- 2H 4- AS cal mole- Ideg.-* -1- 30 + 10 + 20 4- 40 + 10 + 60 - 10 4- 50 - 40 -I- 10 -1- 10 + 70 0 4- GO (AS” - AS:’) cal mole-1 dcg.-l + 30 + 20 + 30 + 30 +a + 40 + 30 + 30 - 20 + 20 Q= -m 4=+30 + 20 + 20 We do not consider that the data in table 2 provide a clear-cut demonstration of our hypothesis and we acknowledge that specific factors other than the entropy of reaction may contribute to the entropy of activation.However, this com- parison does suggest that bond-breaking and making may occur together with electron transfer, even in cases where the formation of bridged transition com- plexes 29 seems improbable. 1 Rosseinsky and Higginson, J. Chem. Sac., 1960, 31. 2 Sutclfle and Weber, Trans. Faraday SOC., 1956,52, 1225. 3 Sykes, Thesis (Manchester University, 1958). 4 Kenttamaa, Suomen Kem. By 1958,31,273. 5 Harkness and Halpern, J.Amer. Chem. Sac., 1959,81, 3526. 6 Ardon and Plane, J. Amer. Chem. Soc., 1959,81,3197. 7 Westheimer, Chem. Rev., 1949, 45,419. 8 Armstrong and Halpern, Can. J. Chem., 1957, 35, 1020. 9 Ashurst and Higginson, J. Chem. Sac., 1953, 3044. 10 Stead, Thesis (Manchester University, 1959).53 HIGGINSON, ROSSEINSKY, STEAD AND SYKES 11 Kosseinsky, Thesis (Manchester University, 1958). Ila Baker, Newton and Kahn, J. Physic. Chem., 1960, 64, 109. 12Betts, Can. J. Chem., 1955, 33, 1780. 13 Higginson and Marshall, J. Chem. SOC., 1957, 447. 14 Kolthoff and Meehan, J. Polymer Sci., 1952, 9, 327. 15 Halpern, Can. J. Chem., 1959,37, 148. 16Sillkn, Quart. Rev., 1959, 13, 146. l7 Gorin, J. Amer. Chem. SOC., 1936,58, 1787. 18 Mulay and Selwood, J. Amer. Chem. SOC., 1955, 77, 2693. l9 Glasstone, Laidler and Eyring, The Theory of Rate Processes (McGraw-Hill, New 20 Frost and Pearson, Kinetics and Mechanism (Wiley, New York, 1953), pp. 131-3. 21 Ashurst and Higginson, J. Chem. Soc., 1956, 343. 22 Newton and Rabideau, J. Physic. Chem., 1959,63, 365. 23 Bell, Acid-Base Catalysis (Oxford, 1941), chap. 8. 24 ref. (20), pp. 214-18. z5 Warhurst, Quart. Rev., 1951, 5, 51. 2G Latimer, Oxidation Potentials (Prentice-Hall, New York, 2nd ed., 1952). 27see, e.g., Powell and Latimer, J. Chem. Physics, 1951, 19, 1139. Cobble, J. Chem. Connick and Powell, J. Chem. Physics, 1953, 21, 2206. York, 1st ed., 1941), pp. 433-5. Physics, 1953, 21, 1443. Powell, J. Physic. Chem., 1954, 58, 528. 28 King, J. Physic. Chem., 1959, 63, 1070. 29Taube, Can. J. Chem., 1959, 37, 129. 30 Sheppard and Wahl, J. Amer. Chem. SOC., 1957,79, 1020. 31 Prestwood and Wahl, J. Amer. Chem. Soc., 1949,71, 3137. 32 Silverman and Dodson, J. Physic. Chem., 1952, 56, 846. 33 Krishnamurty and Wahl, J. Amer. Chem. SOC., 1958, 80, 5921. 34 Wahl, quoted by Basolo and Pearson, Mechanisms of hor.panic Reactions (Wiley, 35 this paper. 36 Johnson, J. Amer. Chem. SOC., 1952, 74, 959. 37 Biedermann, Arkiv Kemi, 1953,5,441. New York, 1958), p. 318.

ISSN:0366-9033    

DOI:10.1039/DF9602900049

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

THE REACTION BETWEEN C o o AND Pb(N) ACETATES IN ACETIC ACID BY D. BENSON,* P. J. PROLL, L. H. SUTCLIFFE AND J. WALKLEY Dept. of Inorganic and Physical Chemistry, The University, Liverpool Received 20th January, 1960 While the order of the reaction with respect to plumbic acetate is unity under all con- ditions, the order with respect to cobaltous acetate is non-integral and can be varied by the addition of plumbous acetate. These facts are accounted for by a reaction mechanism which requires the postulation of dimeric Co(I1) and the reactive intermediates Pb(II1) and Co(IV). The influence of water on the reaction is consistent with the presence of an unstable intermediate like Co(rV). Added sodium acetate accelerates the reaction probably because of the formation of reactive ionic species of the reactants.Ion-migration experi- ments show that ionic species of Co(1I) and Pb(1V) are present even in pure acetic acid. A survey of oxidation-reduction reactions between metal acetates in anhydrous acetic acid has shown that several occur at measurable rates.1 The kinetically simplest of these, namely, the oxidation of cerous acetate by plumbic acetate, has been reported in detail? In this reaction, ionic species were shown to be present even in the pure solvent and may take part in the rate-determining steps : in the presence of sodium acetate the reacting species are probably Ce(0Ac); and Pb(0Ac)j or Pb(OAc):-. Furthermore, it seems likely that Pb(II1) takes part in the reaction as an intermediate. The purpose of this paper is to present the more complicated results of the Co(II)+Pb(IV) reaction in acetic acid.EXPERIMENTAL MATERIALS ACETIC ACID.-A.R. acetic acid was purified by refluxing with A.R. finely divided chromium irioxide along with a calculated amount of A.R. acetic anhydride to remove water.3 The amount of anhydride required was estimated from freezing-point measure- ments.4 After distillation the excess water or acetic anhydride was determined both from the freezing-point and by a spectrophotometric method.5 The acetic acid usually pro- duced had a melting point of 16.6"C and was estimated to be 99.98 % pure; the remaining 0.02 % was probably acetic anhydride. PLUMSIC ACETATE.-This was prepared by the method of Dimroth and Schweizer,6 then recrystallized from anhydrous acetic acid, pumped dry and stored under a vacuum.The purity was found to be 100 % by titration with hydroquinone using quinalizarh as indicator.7 COBALTOUS ACETATE.-SohtiOnS of known concentration were prepared by refluxing 99-95 % pure cobalt sponge (Johnson Matthey) with purified anhydrous acetic acid. COBALTIC AcETAn.-The method adopted was basically that described by Sharp and White.8 Cobaltous acetate in acetic acid was oxidized electrolytically to cobaltic acetate giving a maximum conversion of about 50 %. The resulting solution was diluted to about 2 x 10-3 M and passed four times through a column 30 cm long and 1.5 cm &am. filled with Amberlite resin IR--120H. This procedure enabled the ratio [Co(III)l/[Co(II)] to be increased to 4911. The concentration of Coon) in the final solution remained con- stant to & 1 % for 24 h.Other reagents were of A.R. quality but before use they were dissolved in anhydrous acetic acid and then dried under a vacuum for 10 h. The procedure was repeated at least once. * present address : Department of Chemistry, College of Further Education, Widnes. 60BENSON, PROLL, SUTCLIFFE A N D WALKLEY 61 ION-MIGRATION EXPERIMENTS The migration cell consisted of a W-shaped vessel having three compartments isolated from one another by two sintered-glass discs. The solution under investigation was placed in the central compartment and the solvent was placed in the outer compartments. A potential of 500 V d.c. was applied to platinum foil electrodes situated in the two outer limbs of the cell.Current was passed for 20 h then the polarity was reversed and the current passed for a further 20 h. SPECTROPHOTOMETRY All measurements were made by means of a Unicam SP 500 spectrophotometer fitted with a thermostatted cell compartment which enabled solutions to be maintained to within &0-02"C. KINETIC MEASUREMENTS Since both plumbous and plumbic acetates dissolved in acetic acid do not absorb appreciably in the visible region 9 and the absorption of cobaltous acetate is a good deal less intense than that of cobaltic acetate (see fig. 1) in this region, the wavelength of 400 mp is a convenient one for measuring the rate of appearance of Co(II1). Final optical density readings DK,, corresponding to complete reaction, were obtained after leaving reaction mixtures to stand overnight.wavelength FIG. 1.-The absorption spectra of cobaltous (A) and cobaltic (B) acetates in anhydrous acetic acid at 25OC. RESULTS REACTANT AND PRODUCT SPECIES IN ACETIC ACID LEAD Successive complexes up to Pb(0Ac); formed by plumbous perchlorate with acetate ions in water have been detected and their formation constants determined.16 The ion-migration experiments showed that both negatively and positively charged62 THE CO(I1) f P b(1V) REACTION species of Pb(l1) are present in pure acetic acid : the likely species are PbOAc+, Pb(0Ac)z and Pb(OAc),. The addition of 10 % v/v water increased the amount of migration to the cathode thus indicating increased dissociation in favour of PbOAc+ with a possibility of Pb2+ being formed, When the solvent used was anhydrous acetic containing 1 M sodium acetate, the greatest transference was to the cathode which means that dissociation is then in favour of Pb(0Ac); and possibly higher complexes. Ion-migration results for plumbic acetate under the above conditions and kinetic studies on its decomposition9 and on its reaction with tert.-butyl hydro- peroxide 10 led to the conclusion that dissociation is very small and that the most reactive species is Pb(OAc)t-.COBALT Cobaltic acetate appears to dissociate fairly readily in acetic acid, there being considerable migration in the approximate ratio 3/1 for the anode : cathode compartments. The addition of 10 % v/v water or 1 M sodium acetate reduced migration to the cathode almost to zero while that to the anode remained sub- stantial.It seems that cobaltic acetate occurs in acetic acid as Co(OAc)$, Co(0Ac) and Co(0Ac)Z with the concentration of the latter being increased by the addition of water or sodium acetate. Sharp 11 has estimated the dissociation constant of cobaltic acetate in acetic acid to be 4 . 4 ~ 10-8 at 25°C. Cobaltous acetate behaves like plumbous acetate when subjected to electrolysis, there being four likely species, namely, CoOAc+, Co(OAc),, Co(OAc), and Co(OAc)i-. The first is favoured by the addition of 10 % v/v water and the last two by 1 M sodium acetate. Cobaltous acetate is different from the acetates of Co(III), Pb(1V) and Pb(I1) considered above, in that its absorption spectrum is affected markedly by the medium changes described thus permitting a detailed spectrophotometric investigation to be made, as described elsewhere.12 The effect of water on the spectrum can be interpreted as a dielectric effect on the equilibrium, Co( OAc), + CoOAc' + OAc- .The addition of sodium acetate promotes the formation of Co(0Ac);- via the equilibria, Ki KZ Co( OAc), + OAc- + Co( OAc), , Co( OAc); + OAc- + Co(OAc)i-. The type of relationship obtaining between the observed extinction coefficient and the sodium acetate concentration indicates that Co(0Ac)Z- predominates over Co(0Ac)J. K3 STOICHIOMETRY The stoichiometry was determined under various conditions by measuring the optical density at 400 mp of the cobaltic acetate produced from known approxim- ately equivalent amounts of plumbic and cobaltous acetates. The concentrations of the reactants were varied in the range 10-3 to 10-2 M.ANHYDROUS SOLVENT An average of six determinations gave a value of 2-01 f0-01 at 23°C for Co(III)/Pb(IV) which corresponds to the overall reaction, Pb(1V) + 2Co(IT)+Pb(TI) + 2Co(liII).63 BENSON, PROLL, su*rcLIi;pE AND WALKLEY 10 % v/v ACETIC ANHYDRIDE Co(III)/Pb(IV) = 2-02 0.02 at 23°C. Co(III)/Pb(IV) = 2.01 3-0.02 at 23°C. Co(IIl)/Pb(lV) = 2.02 & 0.02 at 23°C. Co(III)/Pb(lV) = 1-96 & 0-02 at 23°C. Co(III)/Pb(IV) = 1.39 & 0.01 and 1.06 & 043 at 23°C respectively. 10 % V/V BENZENE 1 M SODIUM ACETATE 0.25 M PLUMBOUS ACETATE 10 % V/V ETHANOL OR 10 % V/V METHANOL WATER The addition of water reduced the stoichiometry as shown in fig. 2 ; temperature Corrections were made for the dependence of the has little effect on the values.molar extinction coefficient of Co(II1) on the water concentration. 2.0 40 w 2 0 1 FIG. 2.-The effect of water on the stoichiometry of the Co(II)+Pb(IV) reaction at temperatures of 23°C (denoted by circles) and 37°C (denoted by crosses). The only additives which affected the stoichiometry are methanol, ethanol and water: the other additives listed clearly do not prevent the reaction from going to completion. However, methanol, ethanol and water do not bring about the decomposition of plumbic acetate 10 or of cobaltic acetate 8 under the conditions used here, therefore these additives must be reacting with a transient intermediate and thus cause the final concentration of Co(II1) to be decreased.64 THE Co(II)+ Pb(1V) KEACTION KINETICS THE REACTION IN ANHYDROUS ACETIC ACID Rate data were obtained using concentrations of cobaltous acetate in the range 2-3 x 10-3 M to 2.5 x 10-2 M and concentrations of plumbic acetate in the range 2 .0 ~ 10-4 M to 4.0~ 10-4 M. From fig. 3 it can be seen that the reaction time (min) FIG. 3.-The first-order dependence of the rate on the plumbic acetate concentration at 20.90"C. Cobaltous acetate concentrations : A = 0 . 3 1 2 ~ 10-2 My B = 0.625 x 10-2 My C = 1 . 2 5 ~ 10-2 My D = 1 . 8 7 ~ 10-2 M and E = 2 . 5 0 ~ 10-2 M. is accurately first order with respect to plumbic acetate. The slopes of the lines in fig. 3 were multiplied by 2.303/60 and designated kobs.. From plots of log kobs. against log [CoOI)] the cobaltous dependence was established to be to the power 1.50 f0.05.Fig. 4 illustrates this dependence at four temperatures ; the slopes of the lines give the specific rate constant k. The reaction was also studied at 2540°C with plumbic acetate in excess having concentrations in the range 4 . 3 ~ 10-3 M to 1 . 7 ~ 10-2 M and cobaltous acetate concentrations of about 1 . 5 ~ 10-3 M. The rate law and rate constants obtained were in good agreement with those given already for excess cobaltous acetate. From the Arrhenius relationship the apparent activation energy and entropy of activation at 25°C were calculated to be 17.5 f l . 0 kcal mole-1 (table 1) and - 8 f4 cal mole-1 deg.-l respectively. Reaction products were added to the system in order to detect reversible steps in the reaction mechanism. Concentrations up to 1 .5 ~ 10-3 M cobaltic acetate did not affect the reaction rate but, however, the addition of plumbous acetate in the range 0.05 M to 0.5 M caused a marked retardation. It has already been remarked in the section on stoichiometry that the reaction virtually proceeds to completion when excess plumbous acetate is present. Furthermore, no reaction can be detected when cobaltic acetate is mixed with excess plumbous acetate. The addition of Pb@) also increases the dependence on cobaltous acetate from the power 1.5 f0.05 to 2-3 f0-1 as shown in fig. 5. There is a linear dependence of the reciprocal of kobs. on the plumbous acetate concentration (for high concentra- tions) as may be seen from table 2. Similar measurements were made at other temperatures and from them (see table 1) the energy and entropy of activationBENSON, PROLL, SUTCLIFFE AND WALKLEY 65 at 25°C were found to be l O f l kcal mole-1 and -35 f 4 cal mole-1 deg.-l respec- tively.The first-order dependence on Pb(IV) was marred at the higher [Co(II)] * -5 FIG. 4.-The dependence of kobs. on [Co(II)]1*5 at temperatures : A = 36*52"C, B= 30*92"C, C = 2540°C and D = 20.90"C. [Co(II)12-3 FIG. 5.-The effect of plumbous acetate on the reaction between cobaltous and plumbic acetates in anhydrous acetic acid at 25.00"C. Plumbous acetate concentrations : A = 0.050 M, B = 0.125 M, C = 0-250 M, D = 0-330 M and E = 0.500 M. temperature, there being a departure from linearity of the first-order plots after 70 % reaction. CTHE Co(I1) + Pb(1V) REACTION TABLE 1 .-TEMPERATURE DATA FOR VARIOUS CONDITIONS apparent activa- apparent entropy of kcal mole-1 cal mole-1 deg.-1 additive temp., "C k, M-1.5 sec-1 tion energy. activation at 25"C, none 20.90 1 *20 17-5 f 1.0 -8f4 25.00 1 *70 30.92 3.00 36.52 5-38 NaOAc 25.00 2.37 30.74 4.20 35.23 6.6 1 5.15 x 10-2 M 21.02 1.81 17.0f 1.0 -954 3.70 M H2O 20.42 0.44 17-0 f 1.0 -11&4 25-00 0.68 3049 1.1 3 36.08 1.90 k[Pb(II)] M-~*~;scc-~ Pb(0Ac)z 20.90 7.14 lO&l 25.00 9.09 30-92 12.5 -35f4 TABLE 2.-THE LINEAR DEPENDENCE OF kit)s.ON [Pb(II)] AT 2540°C PW>l M 0.500 0.333 0.250 0-125 0.050 0.500 0.333 0.250 0.125 0.050 0.500 0.333 0250 0.1 25 0.050 0.455 0341 0.227 0.1 13 0.500 0.333 0.250 0.125 0.050 0.500 0.250 0.125 0.050 -1 kobs, 479 384 248 174 164 787 582 483 290 238 1450 1090 935 543 3 84 1470 1150 863 581 2180 1590 1300 725 62 1 4000 2220 1 200 1000 A k k .A[Pb(II)] sec M-* 570 920 820 700 - - 1210 1230 1320 1220 - 2150 2060 2420 2370 - 2800 2660 2600 I 3530 3 520 3880 3470 - 7100 7500 6700BENSON, PROLL, SUTCLIFPE AND WALKLEY 67 THE EFFECT OF SODIUM PERCHLORATE In a previous investigation,z sodium perchlorate has been shown to have a retarding influence on the Cc(III)+Pb(IV) reaction in acetic acid. It was pointed out that a combined primary and secondary salt effect, as would be expected, cannot in principle give rise to an observed ncgative total salt effect. A similar retarding effect was encountered when sodium perchlorate was added to the Co(II)+Pb(IV) reaction up to concentrations of 0.125 M at 2540°C (see table 3).TABLE 3.-THE EFFECT OF SODIUM PERCHLORATE AT 25.00"C [Co(II)] = 1.98 x 10-2 M [NaC1041 M [NaClO.Jt Ma kobs. sec-l log /Cobs. A log kobs./d[NaC104]f 0.125 0.59 1 2-87 x 10-3 3.458 - 0.0938 0-553 3.10 8,491 -0.87 0.0625 0.500 3.22 3.508 - 0.56 0.03 13 0.42 1 3.61 8.558 -0.59 0.023 5 0.392 3.84 3.584 - 0.68 0.01 56 0.354 4.1 5 3-618 - 0.68 0~0000 0000 4.53 3.656 - 0.34 - - The linear dependencc of log kobs. on [NaCIO& (a function of ionic strcngth) gives a value of -0-6 for the apparent charge product ZAZB of the reactants. 1.0 [NaOAc] acetate concentrations : A = 9-80 X 10-3 M and B = 6.55 x 10-3 M. FIG. &-The variation of kobs. with sodium acetate concentration at 2500'C. Cobaltous THE EFFECT OF SODIUM ACETATE The fact that sodium acetate accelerates the reaction, in contrast jvith sodium Fig.6 perchlorate, is indicative of a spccik cffect rather than an incrt salt cflect.68 THE Co(II)+ Pb(IV) REACTION shows the variation of /Cobs. with sodium acetate concentrations up to 0.25 M at two concentrations of cobaltous acetate. The shape of the line resembles that obtained for the reaction between cerous and plumbic acetates 2 under similar conditions. The order with respect to cobaltous acetate was found to be unchanged at 1.5 when determined at several temperatures in the presence of 5.15 x 10-2 M sodium acetate (see fig. 7). From these data was obtained an apparent activation I I 1 1 [CO(II)]'*5 FIG. 7.-The 1 +order dependence on the cobaltous acetate concentration in the presence C = 2540°C and D = 21.02"C.of 5.15 x 10-2 M sodium acetate. Temperatures : A = 35*23"C, B = 30*74"C, energy of 17.0fl.0 kcal mole-1 and an entropy of activation of -9 rt4 cal mole-1 deg.-1 at 25°C (see table 1). Sodium perchlorate caused acceleration when added to reaction mixtures con- taining 4 . 1 2 ~ 10-2 M sodium acetate. THE EFFECT OF ACETIC ANHYDRIDE Normally the solvent used in this investigation contained about 0.02 % V/A acetic anhydride therefore its effect was tested by adding 1 % v/v to reaction mixtures when it was found not to affect the observed rate constant. THE EFFECT OF BENZENE The addition of benzene had an accelerating influence on the reaction up to the limit of 25 % v/v which was attempted. The experimental data could be interpreted in terms of a dielectric effect, there being a linear dependence of log kobs.on D-1 (table 4). In the calculations, a value of 2-28 for the dielectric constant D TABLE 'I.-THE EFFECT OF BENZENE AT 2540°C [Co(II)] M benzene, % v/v D-1 1 . 9 6 ~ 10-2 25.00 0.192 21.83 0.1 88 18.75 0.184 15.63 0.180 12.50 0.176 6.25 0.1 69 0.00 0.162BENSON, PROLL, SUTCLIFFE AND WALKLEY TABLE 4.--continued 69 1-21 x 10-2 25.00 0. I92 5.60 x 10-3 3-748 - 18.75 0.1 84 4-40 3.644 12.2 12.50 0.176 3.48 3.542 12.6 6.25 0.169 2.96 3.471 11.4 0.00 0.162 2.60 3.415 11.0 of benzene at 25°C was used.13 The dielectric effect gives a negative sign to the apparent value of ZAZB, in agreement with the findings from the neutral salt effect. THE EFFECT OF ETHANOL Ethanol was shown to form a reactive complex with plumbic acetate in the Ce(III)+ Pb(1V) and the Pb(IV)+ t-butyl hydroperoxide reactions 2, 10 hence a similar occurrence was expected for the reaction under discussion.Unfortunately, complicated kinetics were obtained which prevented any conclusion from being drawn about the Pb(IV)+ethanol complex. The overall effect of ethanol addition was to increase the rate of reaction. THE EFFECT OF WATER Since the stoichiometry of the reaction was affected by water the final optical density of Co(II1) was calculated and then used to compute the values of kobs.. TABLE 5.-THE 1'543RDER DEPENDENCE ON COBALTOUS ACETATE IN THE PRESENCE OF 2.78 M WATER AT 25.00"C kObs.9 SW-' [CO(II)]~-~, M k o b s . / [ c o ~ I ) ] l * ~ , M-1.5 s a - 1 6.87 x 10-3 7-42 x 10-3 0.93 4.53 4.8 1 0-94 2.61 2.76 0.94 1.80 1.76 1-02 0.96 0.97 0.99 TABLE THE DEPENDENCE OF kobs.ON THE WATER CONCENTRATION temp. = 25-00"C. [Co(II)] = 1 . 9 6 ~ 10-2 M k0bs.s SCC-l [HzOI. M log kobs. D-1 A log kobs.lAD-l 4.53 x 10-3 4.35 4.10 3.70 3.50 2.61 2.09 1 *42 0-96 0000 0-348 0.695 1.39 1.75 2.78 3.70 4.1 7 5-56 3.655 3.638 3.612 3.568 3.543 3.416 3.320 3.151 4-98 1 0.162 0.151 0.148 0.122 0.108 0.102 0.094 0.086 0.075 - 1.6 3.1 2.2 2.1 4.0 4.7 6.6 7.7 As may be seen from table 5, the addition of water to the system did not change the order of the reaction with respect to Co(I1). Table 6 illustrates the variation of kobs. with water concentration. From rate measurements at four temperatures and a ccqstant water concentra- tion of 3.70 M (table 1) the apparent energy and entropy of activation were found to be 17.0 f 1.0 kcal mole-1 and - 1 1 f4 cal mole-1 deg-1 respectively.70 THE Co(II)+ Pb(IV) REACTION D I § CUS SI ON THE REACTION IN PURE SOLVENT The important features of the reaction in pure solvent are (i) the non-integral order with respect to Co(l1) and (ii) the retardation caused by plumbous acetate.These are the main differences between the Co(II)+Pb(IV) reaction and the simplcr Ce(llI)+ Pb(1V) reaction.2 The following reaction scheme provides an explanation for most of the experimental observations : K Co(I1) + Co(I1) + [CO(II)],, Pb(IV)+[Co(II)],~'-,Pb(Il)+2Co(III), Pb(1V) + [Co(II)],~~Pb(lII) + Co(lI1) + Co(II), Pb(1V) + [Co(I1)I2~+Pb(II) + Co(1V) + Co(II), k4 Pb(1V) + Co(I1) + Pb(I1) + Co(IV), k ; Pb(1V) + Co(IIp+Pb(III) + Co(III), Co(1V) + Co(IIp+2Co(III), Pb(II1) + Co(IIF%Pb(II) + Co(II1).By assuming that the concentrations of Pb(II1) and Co(IV) are stationary and that the cobaltous acetate is mainly in the monomeric form then the following rate law is obtained : kobs. = (k, + k2)K[Co(II)l2 + k5[Co(II)] + 2k6[Co(II)] The tetravalent state of cobalt has had to be introduced in order to account for the retardation brought about on the addition of excess plumbous acetate. The alternative reaction Pb(1V) + Pb(11)+2Pb(III) could not be included because the exchange of radio lead between plumbous and plumbic acetates in acetic acid has not been detected.14 The postulation of a reactive dimer of cobaltous acetate is necessary to the rate law and there may well be higher polymers present in the solutions.We have obtained some evidence for the existence of polymeric species in acetic acid solutions of cobaltous acetate.12 Dimers are well known for solutions of copper alkanoates in solvents of low di- electric constant .15 From the measurement of the lowest concentration of plumbous acetate which gave a linear dependence of k&s. with respect to [Pb(II)]-l a value of about 2 x 10-3 at 25°C was obtained for k;/k6. THE EFFECT OF SODIUM ACETATE An important aspect of the effect of sodium acetate is that the order with respect to cobaltous acetate remains at 1.5 but it should be pointed out that the rate increase is not very large. One may draw the tentative conclusion that bothBENSON, PROLL, SUTCLIFFE AND WALKLEY 71 the monomeric and dimeric forms are affected similarly by the addition of sodium acetate.The following empirical relationship represents the influence of the salt on kobs. : kobs.= A+B[N~OAC]~+C[N~OAC], where A , B and C are constants. The expression is identical with that found for the reaction between cerous and plumbic acetates.2 If, for simplicity, only reaction path 5 is considered then the following detailed reaction mechanism will yield an equation of the same type as the empirical one: Pb(OAc),+Co(OAc), 5 Pb(OAc),+Co(OAc);% Pb(OAc),+Co(OAc)',-~ Pb(0Ac); + CoOAc' 5 Pb( OAc); + Co(OAc), 5 Pb( OAc), + Co( OAc), % Pb( 0Ac):- + CoOAcs k Pb( 0Ac):- + Co( OAc), 5 In setting up this scheme use has been made of the species of Pb(1V) and Co(I1) indicated by the ion-migration and spectrophotometric experiments.Using the cobaltous acetate equilibria mentioned earlier and the equilibria K4 Pb( OAc), + OAc- + Pb( 0Ac)J , Pb( OAc), + OAc- + Pb( OAc);-, Ks KA NaOAc + Na' + OAc- , then k5 = k, + k,K, K4 + (I<&, + k,K, + k,K1K,K5)K~[NaOAc]* On account of the very small dissociation occurring in acetic acid it has been as- sumed in deriving this expression that the total concentrations of Co(1I) and Pb(1V) correspond to Co(0Ac)z and Pb(OAc)4. The above reaction scheme cannot be simplified since there is no means of distinguishing between the various reaction paths. It is clear, however, that ionic species play an important part in the reaction. +(k,K,K, + k&&+ k,,K,K,)K,[NaOAc]. THE EFFECT OF WATER From the experimental data the addition of water was seen to affect the reaction in the following ways : (i) there is probably a primary dielectric effect on the reacting species; (ii) there is a secondary dielectric effect on the ionic equilibria involving the (iii) there is direct reaction of water with a reactive intermediate.reactants and on the Co(I1) dimer equilibrium ;72 THE Co(I1) + Pb(IV) REACTIONS If it is assumed that the following rapid reaction occurs, Co(1V) + H20+ Co(I1) + 2H+ + 3 0 2 , thereby eliminating step 6 in the main reaction scheme then the stoichiometry of the reaction should be 1.2 : from fig. 2 it may be seen that the limiting value is about 1.6. The rate law becomes hence the order with respect to Co(I1) will remain at approximately 1.5 and there will be a reduction in the rate of the reaction upon the addition of excess water. A further reduction in rate occurs due to the increase of dielectric constant of the solvent (see table 6). The interpretation in terms of a dielectric effect is supported by the negligible change in the apparent activation energy (table 1) which results from the addition of water. Both the benzene and water dielectric effects are indicative of the participation of ionic species in the reaction even in the pure solvent. Alcohols probably have an effect similar to that of water but the lower values obtained for the stoichiometric ratio [Co(III)]/[Pb(IV)] may be due to their reaction with Pb(II1). 1 SutclXFe and Walkley, Nature, 1956, 178, 999. 2 Benson and Sutcliffe, Trans. Farday SOC., 1960, 56, 246. 3 Orton and Bradfield, J. Chem. SOC., 1927, 983. 4 de Visser, Rec. trav. chim., 1893, 12, 101. 5 Bruckenstein, Anal. Chem., 1956, 28, 1921. 6 Dimroth and Schweizer, Ber., 1923, 56, 1375. 7 Tomidk and Valcha, Czech. Chem. Comm., 1951-2, 16-17, 133. 8 Sharp and White, J. Chem. SOC., 1952, 110. 9 Benson, Sutcliffe and Walkley, J. Amer. Chem. SOC., 1959, 81,4488. 10 Benson and Sutcliffe, Trans. Faraday SOC., 1959,55, 2107. 11 Sharp, J. Chem. SOC., 1957, 2030. 12 Proll, Sutcliffe and Walkley, to be published. 13 Smith and Rogers, J. Amer. Chem. SOC., 1930, 52, 1824. 14 Evans, Huston and Norris, J. Amer. Chern. SOC., 1952,74,4985. 15 Martin and Whitley, J. Chem. SOC., 1958, 1394. 16 Burns and Hume, J-TAmer. Chem. SOC., 1956, 78, 3958.

ISSN:0366-9033    

DOI:10.1039/DF9602900060

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

MECHANISMS OF SOME ELECTRON EXCHANGE REACTIONS BY D. R. STRANKS" School of Chemistry, The University, k d s 2 Received 3rd February, 1960 Electron exchange between ferrocene and the ferricinium cation proceeds with half- times of a few milliseconds between -65" and -75°C. The second-order rate constants are best reproduced by calculations based on the Marcus tunnelling theory. Electron exchange between a series of aqua-ammines of CoII and Con' proceeds through bridged transition states. The energy of activation remains constant in this series but the entropy of activation becomes less negative as ammine ligands are replaced by hydroxo-ligands. Bridging mechanisms may operatc in other systems in which substantial reorganization of the primary co-ordination sphere is involved. 1.INTRODUCTION The rate at which the mutual oxidation and reduction of two valence states of an element proceeds : is largely determined by the two electronic configurations of M, the sizes of the two species MX,, and the character of both the ligands X and the solvent. Since the standard free energy of these reactions is zero, the importance of such factors can be asscssed directly in systematic studies of these so-called " electron exchange reactions 77. This paper aims to summarize the results of recent kinetic investiga- tions of some selected electron-exchange reactions (the details of which are being submitted for publication independently) and to compare the observed rates with those predicted by the electron-tunnelling models proposed by Marcus 1 and by Laidler.;! Conclusions are then drawn as to the detailed mechanism of the actual electron-transfer steps.2. THE FERROCENE+ FERRICINIUM SYSTEM Little accurate information is available on the rates of electron exchange be- tween a neutral and a charged species. In the absence of Coulombic interactions, the theory of Marcus ascribes the free energy of activation solely to the need for reorganization of solvent molecules to form a non-equilibrium transition state. Since the Laidler model includes solvent rearrangement in Coulombic terms, the rate of such an electron-exchange reaction would be attributed to the rate of a diffusion-controlled reaction with no charge barrier. Both models ignore any possible polarization of the reactants by each other. The bis-cyclopentadienyl complexes of iron (11) and iron (111)-usually desig- nated as " ferrocene " and " ferricinium " (cation) respectively-are relatively inert to substitution and do not interact markedly with hydroxylic solvents such as methanol.This exchange system therefore seemed to be a suitable one for the comparison of measured rates with those calculated from the alternative theoretical * present address : Chemistry Department, University of Melbourne, Melbourne, Australia. 7374 ELECTRON EXCHANGE REACTIONS models. The '' sandwich '' structure of ferrocene is shown in fig. 1, which has been constructed on the basis of the following molecular dimensions : FeTr-C= 2.045 A, C-H = 1-09 A, half-thickness of the cyclopentadkne ring = 1.70 A, van der Waals' radius of the hydrogen atom = 1-2& and covalent radius of Fen = 1.23 A.Excepting the central void of the ferrocene molecule, the maximum distance from the centre to the periphery is 4.10A and the minimum distance is 3.54 A. It is anticipated that the dimensions of the ferricinium cation will closely resemble those of ferrocene and for the subsequent calculations the average mini- mum and maximum " radii " (a) of the ferrocene and ferricinium species will be taken to be 334A and 4-10A respectively. TheZencounter diameter 0 required for calculations based on Laidler's theory will be&taken as either 7-08 or 8.2081. FIG. 1 .-Scale diagram of the ferrocene molecule (side view). In an earlier publication 3 we reported that 10-4 M methanolic solutions of ferrocene and ferricinium nitrate or perchlorate underwent complete isotopic exchange in 50 msec at 0°C.The flow apparatus has now been modified to achieve contact times as low as 3 msec. The exchanging solution is led into a second jet- mixing chamber into which flows a much larger volume of petroleum ether (in which ferricinium salts are insoluble) and from a third jet, a carrier ferricinium solution enters. The separations are then conducted at - 80°C. In this manner, I have been able to obtain definite estimates of the rates of this electron exchange in 10-4-10-5 M methanolic solutions between - 75" and - 65°C. Exchange half- times are some milliseconds even at these temperatures and cannot be measured at higher temperatures. Mean half-times values are quoted in table 1.These rates appear to be the fastest yet reported for an electron-exchange reaction studied by means of isotopic tracers. At -75", a second-order rate law has been estab- lished within the limits of experimental error. Ferricinium nitrate or perchlorate exhibit the same rate behaviour but with the chloride salt, the rate becomes im- measurably fast at -75". The addition of " inert " electrolytes at concentrations exceeding 10-3 M also causes the rate to be immeasurably fast at -75". (These observations demonstrate that anion catalysis is possible even for redox reactions involving two substitution-inert species.) Worthwhile estimates of the activation energy cannot be made ; values ranging from 4-4 to 15.6 kcal mole-1 are covered by the upper and lower limits of the rate constants.Table 1 compares the experi- mentally-determined values with those calculated from the theories of Marcus and of Laidler.D . R . STRANKS 75 TABLE 1 .-RATES OF ELECTRON EXCHANGE BETWEEN FERROCENE AND FERRICINIUM calc. rates expt. rates Laidler theory a Marcus Theory k k k k k b teyz. G = 7.08 A G = 8-20 A a = 4-10 A a = 3-54 A 'g- M-1 sec-1 M-1 sec-1 M-1 sec-1 M-1 sec-1 msec M-1 sec-1 25 9.1 x 108 l * O X 109 1.6X 109 3.1 x 108 <0*5 >7 x 106 0 4.9 x 108 5.6 X 108 4.5 X 10s 9.2 X 107 <0.5 >7x 106 -65 5.1 X 107 5.9X 107 1-4X 107 1 . 6 ~ 106 1*0fO*S 3.5f1.8x 106 -70 4.0X 107 47X 107 9*4X 106 1.2X 106 2-0f0.5 1*7&0*4X 106 -75 3 . o ~ 107 3 . 5 ~ 107 6 . 5 ~ 106 7 . 5 ~ 105 4 . o ~ . o s.7f2-2~ 105 a Assuming D (ferrocene) = 3 x 10-5 cm2 sec-1, B (ferricinium) = 1.2 x 10-5 cm2 sec-1 b both reactant concentrations = 1.0 x 10-4 M.at 25"C, and Eact (diffusion) = 4 0 kcal mole-1. The apparent agreement between the experimentally-determined rate constants and those calculated from Marcus' theory, assuming a = 3.54 fn, is extraordinarily close considering the probable shortcomings of both theory and experiment. The experimental rates are significantly less than those calculated on the basis of simple diffusive encounters ; the latter are considered to be the minimum values permitted by the Laidler theory. Whilst a preference can therefore be expressed in favour of the Marcus theory, the differences in rates are not sufficiently large to justify the rejection of the diffusion model entirely nor could one infer that the exchanging reactants approach end-on (a = 354& rather than side-on (a = 4.10fn).It is considered that the isotopic studies need verification by means of n.m.r. and e.s.r. techniques before any completely reliable deduction can be made. Most of the " covalent " cyclopentadienyl complexes have dimensions which do not differ by more than 0.3 fn (e.g. Fe, Coy Ni, Rh, Ru) and one would anticipate that similar exchange rates, within a factor of five, would exist in all such cases. Resonance studies should be performed below 0" since at higher temperatures, the exchange process is probably diffusion-controlled (see table 1). Around - 70", the Marcus theory suggests an activation energy of either 6-83 kcal mole-1 (a = 3.54&, or 5.96 kcal mole-1 (a = 4.10 fn), whereas that for diffusion probably does not exceed 4.0 kcal mole-1.On the Marcus model, the entropy of activation is only - 1 cal (mole deg.)-1 in both cases since the entropy changes on solvent reorganization around the two reactants almost cancel. Should it be possible to perform more extensive measurements of the exchange rates in analogous systems, a distinction between the two models might be drawn with more certainty. 3. ELECTRON EXCHANGE BETWEEN COBALTAMMINES OF Con AND Corn The Marcus theory has had reasonable success in calculating rates of electron exchange between pairs of complex ions which are inert to substitution and whose molecular dimensions are essentially the same in the two valence states. How- ever, with pairs of aquated cations, such as F e ~ ~ + F e ~ ~ , the calculated rates are lo5 times greater than the observed rates.This discrepancy has been attributed 1 to the need for reorganization of the primary hydration spheres in addition to the normal solvent reorganization process, Laidler's model yields a calculated rate which only exceeds by a factor of about ten the rate observed for the Fei;+ Fe: exchange. Nevertheless, this calculated rate includes a major contribution from electron-tunnelling at distances of separation (3.5 to 6.0fn) which are less than the minimum separation of the two aquated cations (-6-88A). The latter value is the tunnelling distance assumed in the Marcus model. At such close distances of approach, significant interactions between the reactants might well occur.Ac- cordingly alternative redox mechanisms, involving the bridging or transfer of76 ELECTRON EXCHANGE REACTIONS groups, have been proposed especially for labile species.4 The " hydrogen-atom transfer " mechanism proposed as a general mechanism for aquated cations is an unfortunate description.5 The need to transfer a hydrogen atom does not really arise in these systems and indeed the observation of a DzO-solvent isotope effect (often presented as substantiating evidence) merely indicates considerable stretching of 0-H bonds in the hydration spheres of the two reacting ions. Thus when bridging anions such as the halides are absent, it is suggested that the transfer of an electron occurs between two aquated cations via a hydrogen bridge temporarily formed between the waters of hydration of the two ions.This hydration bridge would serve to couple the two reactants in the activated state and so reduce any energy differences between the two orbitals principally involved in the electron transfer step.6 (This case of " significant orbital overlap " is not treated by the Marcus theory.) It is further postulated that, even if substantial energy differences do remain after the formation of this bridge, electron transfer will proceed by a quantum-mechanical-tunnelling mechanism whose probability is temperature-inde- pendent and little influenced by the energy barrier. The distinction between this mechanism and the models already proposed for electron tunnelling is that the former involves a more specific participation of the solvent with weak orbital overlap of the two reactants.The measurement of the rates of electron exchange between pairs of cobalt- ammines was undertaken for these two main reasons. (i) Exchange between Co(NH&+ and Co(NH&+ has been often cited as a system in which reorganization of primary co-ordination spheres is necessary as a prelude to electron transfer. The Corn-N distance in CO(NH~):+ is 2-05A whereas the CoXr--N distance is reported as about 2.5 &7 although we have suggested that 2.39 A might be a more realistic value.8 If preliminary rearrangement is necessary to equalize the Co-N bond distances before electron transfer can occur, then it may be shown 8 that this would require an expenditure of some 30 kcal mole-1. A detailed kinetic investigation of the Co(NH&++ Co(NH3);f exchange system therefore seemed appropriate to assess the mechanistic importance of this large energy barrier.(ii) In electron exchanges involving aquated cations, water performs the duaI function of solvent and ligand and due to the rapid exchange between primary and outer hydration spheres, it is difficult to devise unambiguous tests of these functions. Consequently we have studied the variation in the rates of electron exchange in aqueous solution between a series of redox pairs of the formula, Co(NH&_,(H20): ,+, where n varies from 0 to 6. At least for the higher members (n>3), the aqua-ligand is reasonably inert to exchange with solvent water. It has transpired that the eventual displacement of six ammine ligands by six aqua ligands in this series accelerates the rate of electron exchange by a factor of lo5.TABLE 2.-RATES OF ELECTRON EXCHANGE BETWEEN AQUA-AMMINES OF COX' AND cOIT' reactants k EX& AS* (64.5'C. p = 1.0) 1. mole-1 min-1 kcal/mole cal/mole deg. Co(NH,)Z ++CO(NH~)~+ < 10-8 - - Co(NH,)$.+CI-+ Co(NH,)g + (44-tO.7) X 10-2 - - cis-Co(NH3),(OH)2+Co(NH),2+ (15f2.4) x 10-1 t t Co(NH,)$. +OH-+ Co(NH,)z + (3.3 f0.2) X 10-1 12.9 & 1.6 - (35 15) Co(NH,), OH2 ++ Co(NH,)$' (5.4f0.3) X 10-2 13.4rt0.4 -(33.1 fl.4) trans-Co(NH,),(OH)~+Co(NH,), + (2-5ikO.2) x 10-1 13*8&0.9 -(29.0k2.0) t This system is currently under study. Table 2 summarizes the kinetic data obtained so far. We have found that great care is required to avoid catalysis of these exchanges by dissolved oxygen and by an insoluble hydroxo-species of Co" which tends to precipitate under certainD.R. STRANKS 77 conditions. The rate constant for direct electron exchange between Co(NH,);+ and Co(NH3)g+ is less than M-' min-' at 64.5". Calculations based on the Marcus model show that if reorganization of the arnmine co-ordination spheres is unnecessary, then the rate constant for the direct exchange should be 2x lo8 M-1 min-1 at 64.5". The Laidler model would yield a value of approximately lo5 M-1 min-1. If the reorganization energy barrier is included, then the rate constant on the Marcus model would be 10-12 M-1 min-1 with an extraordinarily high activ- ation energy of 38 kcal mole-1. Instead of this direct exchange reaction, an alter- native pH-dependent mechanism operates : Co(NH&+ + H20+Co(NH&.+OH- + H+, K1 Co(NH,);.+OH- + 6oCo(NH3)~+-+Co(NH3)~+ + 60Co(NH3),"+ + OH-.(3.2) (Our analytical scheme detects only the net conversion of 6OCo to the CoIX1 state rather than the formation of 60Co(NH3);+ alone.) We exclude the alternative amide entity Co(NH,),NH$+ since the value of K1 derived from the kinetic analysis (Kl = 4x 10-12 at 64.5") is in satisfactory agreement with an extrapolated value derived by independent workers. Nevertheless, the value of K1 is uncertain by a factor of at least three so that the energy and entropy of activation for (3.2) are subject to a larger error than the normal experimental error. The most striking result is that the energy of activation for reaction (3.2) is quite low considering the magnitude of the energy barrier to direct exchange.The entropy of activation on the other hand has a rather large negative value. More- over the exchange is also catalyzed by chloride ion but after due allowance is made for the degree of ion association, the rate constant is eight times less than that for the hydroxide-catalyzed path. Finally, we find that Co(NH3)2+ exchanges at equal rates with the cobaltous ammines from n = 3 to n = 6. As required by reaction (3.2), isotope dilution analysis has established that the 6OCo isotope is distributed among the various ColIr ammines and a net conversion of cobaltic hexammine to lower hydroxo-ammines is observed spectrophotometrically. (This conclusion is quite general for all members of the aqua-ammines studied so far.This inter- pretation is contrary to that of Taube and co-workers9 for the exchange of CO(NH,)~OH~+ with cobaltous-ammines although our measured rates do agree within the experimental error.) Two possible transition states might be proposed for reaction (3.2). The first involves a hydroxo-bridge formed by prior expulsion of one ligand from the COT' species : e 4 f I* 4- - 0- - CO"(NH,),(OH),-~ I H + One might expect that as a consequence of the eIectron-transfer process, the hydroxide ion would be completely transferred to the newly-created Con1 species. After exchange has proceeded to equilibrium, the Co(NH&+ ion should be entirely converted to lower hydroxo-ammines. The second transition state would involve a hydrogen bridge without net substitution on the newly created Co"1 centre, although motion of OH- during electron transfer may well occur : H H H H Our tracer studies reveal that hydroxide-ion transfer and substitution occur in 50 % of all transfers.Either the first mechanism operates alone (with only 50 % (NH3)SCo ''I-N-H - - 0 - - H-N-CO Ir(NH3),- I ( OH), -n.78 ELECTRON EXCHANGE REACTIONS OW- substitution) or equal contributions are made by the two mechanisms (the first involving 100 % OH- substitution). The first mechanism might be preferred since it involves greater overlap of the two reactants. Since clilorammines of ColI1 are rapidly hydrolyzed in basic solution, net transfer of C1- cannot be demonstrated although one would anticipate transition states analogous to those suggested for the OH--catalyzed path.The superior hydrogen-bonding tendency of OH- as compared to C1- seems related to the higher electron transfer rate for the OH--catalyzed path. Electron transfer between spin-paired CoI'I and spin-free Corr complexes may be represented in the general equation : Orgel 6 predicted that the spin-multiplicity restriction and the d,-d, energy separ- ation should lead to a high activation energy whereas the observed value is quite low. The discrepancy seems to be due to the nature of the bridged transition state. It is postulated that the vital part of the mechanism is the formation of a bridge of sufficient strength to facilitate electron transfer by tunnelling. The activation energy required for electron transfer is largely devoted to the formation of a bridge between the two exchanging species. Once this bridge is established, then an electron will tunncl across the bridge despite the energy differences between the two critical dr orbitals.The probability of tunnelling will be small, tem- perature-independent and soniewhat influenced by the height of the energy barrier, i.e. the separation between the dE and d, orbitals. Since all the CoII complexes are highly labiIe, the initial expulsion of one ligand to form a penta-co-ordinatcd intermediate requircd for the main mechanism is not difficult and all complexes can exchange with equal ease despite differences in the ligand field strengths of -OH and -NH3. The other results summarized in table 2 suggest that this mcchanism is also operative for the two lower hydroxo-ammines of ColIr.The activation energy for electron transfer remains constant within experimental error at a value of 1 3 3 kcal mole-1, whilst the entropy of activation becomes steadily more positive. As -NH3 ligands are replaced by -OH ligands of weaker field strength, the d,-d, orbital separation in the ColIr species will be reduced. In addition, the lability of ligands-and presumably the ease of stretching to form a bridge with Coll-will be increased and thus lead to a more positivc AS* value. It is especially note- worthy that cis-Co(NEI,),(OH)~ exchanges six times faster than does trans- Co(NH,),(OH)$. If thc d,-d, orbital separation were the critical Factor deter- mining the electron transfer rate between ColI and ColI1, then the reverse would be expccted.6 On the other hand, it is well cstablished that cis-Colll complexes are more labile than the trans-isomers.It is also noteworthy that the Co(en),"++ Co(en)i+ electron cxchange exhibits in chloride ion media an activation energy of 13.7 kcal mole-1 whilst AS* = - 39 cal (mole deg.)-l.lO Here a chloride bridge may be operating although bridged paths have been hitherto ignored for substitu- tion-inert species like Co(en)g-+. Finally, ii is tempting to suggest from our limited results, that each successive introduction of an -OH group in the aqua-ammine series would increase AS* by 3-4 cal (mole deg.)-l. For the Co,?,'+Co:i- ex- change one might then expect Eact = 13.5 kcal mole-1, AS* ;= - 13 cal (mole deg.)-1 yielding AF* = 17-4 kcal mole-1. The experimental value 11 is AF* = 16.4 kcal mole-1 although the energy and entropy of activation are as yet undeter- mined.The apparent agreement may well be fortuitous and there is a necd for an experimental detcrmination of this rate over wider conditions. Elcctron exchange bctwecii CrIJ and CrrJ1 species also involves transfer of a dy elcctron but without thc additional rearrangement of othcr d electrons as with Co[I and Co"' spccics. Exchange bctwecri CrF2 1 and Cr2-I- procccds via a bridgcd path and exhibits thc rate piirametcr's : Ei,ct - 13.7 and ASQ -= -20 cal (molcD . R. STRANKS 7 deg.)-1 12 whilst our recent studies of the exchange of urea-14V with Cr(urea)ii reveal that the catalysis by added Cr2+ may be attributed to electron exchange be- tween Cr(urea)z+ and Cr(urea);+ for which Eact = 13.0 kcal mole-1 and AS* = - 4( cal (mole deg.)-1.Once again when there is a significant reorganization energj barrier, a bridged mechanism as already described may operate. With Feu+ Fe1] exchanges, it is difficult to decide on the constancy or otherwise of the activatior energy for electron transfer. As always, further experimental work is needed. I am indebted to Miss Emma Movsessian, Dr. N. S. Biradar, Dr. D. J. Simysor (on sabbatical leave from the University of the Witwatersrand) and Dr. M. S Vaidya for their enthusiastic co-operation in undertaking aspects of the problem5 described here. I am also indebted to Prof. F. S. Dainton, F.R.S., for his constani encouragement and interest. The studies described in this paper were supported by grants from the Royal Society and the Chemical Society to whom gratefu: acknowledgement is made. 1 Marcus, J. Chem. Physics, 1956, 24, 966 ; 1957,26, 867. 2 Laidler, Can. J. Chem., 1959, 37, 138. 3 Dainton, Laurence, Sclineider, Stranks and Vaidya, Radioisotopes in Scient$c 4 Taube, J. Chem. SOC. Special Publ. no. 13, 1959, 57. 5 See, for example, Stranks in Modern Co-ordination Chemistry, ed. Lewis and Wilkins 6 Orgel, Report 10th Solvay ConJ, 1956, p. 289. 7 Biltz, 2. anorg. Chem., 1927, 164, 246. 8 Biradar, Stranks and Vaidya, submitted for publication. 9 Appelman, Anbar and Taube, J. Physic. Chem., 1959,63, 126. 10 Lewis, Coryell and Irvine, J. Chem. SOC., 1949, S386. 11 Bonner and Hunt, J. Amer. Clzem. Soc., 1952, 74, 1886. 12 Ball and King, J. Anzer. Chem. SOC., 1958, 80, 1091. Research (Proc. 1st UNESCO Int. Conf.), vol. 11, p. 305. (Interscience Hnc., New York, 1st ed., 1960), chap. 2.

ISSN:0366-9033    

DOI:10.1039/DF9602900073

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

BRIDGED MECHANISM FOR THE FLATINUM(IH) CATALYSIS OF CEILBWE EXCHANGE IN CHLOROAMMINE PLATIIWJM(I[V) COMPLEXES 1 BY FRED BASOLO, MELVIN L. MORRIS AND RALPH G. PEARSON Dept. of Chemistry, Northwestern University, Illinois Received 1 1 th January, 1960 A kinetic study was made of tho platinum(I1)-catalyzed chloride-ion exchange of various chloroamineplatinum(1V) complexes). The exchange was observed to follow the rate law R = k[Pt(IV)][Pt(II)][CI-] and to be essentially the same as the rate of platinum exchange. The rate of chloride exchange with trans-Pt(NH,),Cli + is about 2000 times faster than with the cis isomer and about 10,000 times faster than with Pt(NH3)5CP+. There is no chloride exchange in the system trans-Pt (tetrameen),Cli ++ Pt(tetrarneen)$++*Cl-. All of these observations are explained on the basis of a two- clectron-change redox reaction involving a bridged activated complex.The mechanisms of redox reactions have been recently reviewed by Taube.2 In general, these reactions are found to occur either by way of (i) an outer-sphere activated complex or (ii) a bridged activated complex.* The classification as a reaction proceeding by an outer-sphere activated complex is given to systems where there is no evidence for the formation of a bridged intermediate and where it appears that, because of the nature of the species involved, such an intermediate might not be formed, e.g., Fe(CN)%-+ Fe(CN)z-, Cobhen):+ + Co(yhen)?+. In some of the cases that have been studied there is direct evidence that a bridged activated complex is involved.For example, it was shown 3 that the reduction of Co(NH3)5X2+ by Cr(H20)2+ proceeds via the activated complex 3 (NH3)5CO- - X- - Cr(H20)<+ and that the exchange of chromium in the system Cr(H2O)sX2++ *Cr(H20);+ involves the bridged complex 4 (H20)sCr- -X- -*Cr(H20);+. Most of the studies that support a bridged activated complex for the redox reaction have been made on systems such as those mentioned above and which involve a one-electron change. However, some two-electron-change processes are also known to proceed by such a reaction path. For instance, oxygen-18 experi- ments indicate 5 that the oxidation of SO$- by Cloy occurs through the intermediate 02S--O--Cl02. Similarly, the exchange of chloride and of platinum in the system trans-Pt(en)ZCl:+ +Pt(en)$+ +Cl-, also an example of a two-electron change, is believed to involve the bridged intermediate Cl(en)#t- -C1- -Pt(en)2C13+.Making use of this mechanism as a guide, it was possible to prepare several com- pounds 6 of the type trans-[Pt(en)zX2]X2 starting with trans-[Pt(en)2C12]Cl2. In order to test further the generality of this bridged mechanism, the platinum(I1) catalysis of chloride exchange with various chloroammineplatinum(IV) cations has been investigated and is reported here. EXPERIMENTAL PREPARATION OF COMPOUNDS Except for [Pt(tetrameen)2]Cl~ . 2H20 and trans-[Pt(tetrameen)2Cl&l2 . Ha0 the compounds used in this investigation are known compounds and they were prepared by * Tn the earlier literature on this subject, category (i) was referred to as electron transfer and (ii) was designated as atom transfer.Since experiments and theory to date do not permit such a detailed assignment of mechanism, the classification into outer-sphere or bridged activated complexes as suggested by Taube is preferable. 80F . BASOLO, M. L. MORRIS AND R . G . PEARSON 81 methods described in the literature.8 These compounds were purified by recrystallization and characterized by means of analyses (table 1). The tetramethylethylenediamine complexes were prepared as follows. A reaction mixture containing 5 ml of 1.6 M tetrameen, 3-3 g of K2PtCb. and 25 ml of water was heated on a steam bath until the solution became a pale yellow and no more solid appeared to separate. At this point the mixture was cooled in an ice bath after which the crystalline Pt(tetrameen)C12 was collected on a suction filter and washed with a small amount of water.This complex was then suspended in 100 ml of water and 6 ml of 1-6 M tetrameen was added. The mixture was then refluxed until complete solution had taken place, concentrated until crystals began to separate, and cooled in an ice+salt bath; crystals were collected on a suction filter and finally washed with ethanol and ether. Further crops of the white crystals were obtained from the mother liquors. The product was air-dried at room temperature and found to weigh 4.0 g (95 "/o yield) and have an analysis corresponding to [Pt(tetrameen)2]C12,2H20 (table 1). Chlorine was slowly bubbled through a solution containing 0.5 g of IPt(tetrameen)2]- C12.2H20 in 30 ml of water for a period of 5 min.During this time the solution turned yellow, then a deep brownish yellow. A vigo- rous stream of air was then passed through the solution to remove the excess chlorine. The mixture which was slightly cloudy was passed through a filter and the clear filtrate was concen- trated to the point of crystallization on the steam bath. After cooling in an ice+salt bath the straw-yellow crystals that separated were col- lected on a filter and washed with acetone. Additional product was obtained by further concentration of the mother liquor. The pro- duct was air-dried at room temperature and found to weigh 0.5 g (91 % yield) and have an analysis corresponding to [Pt(tetrameen)2Cla] C12. H20 (table 1). CHLORIDE EXCHANGE All of the experiments were carried out in 10 ml volumetric flasks which were covered with aluminium foil to exclude any light. The re- action solutions were prepared either by adding known volumes of freshly prepared stock solutions of the platinum complexes or weighed amounts of the solid to the flask.This solu- tion was then allowed to reach equilibrium temperature in a constant (f0.1 "C) temperature bath and a known amount of radioactive chloride ion was added in the form of a stock solution of H36Cl. At various times 0-2 ml of the sample was withdrawn and added to a small centrifuge tube containing 0.1 ml of a solution of in 0.2 N KN03. The amount of AgN03 was always approximately 40 % in excess of the chloride ion. This mixture was then centrifuged82 BRIDGED MECHANlSM OF CHLORIDE EXCHANtiE for 15 min after which time 0.2 ml of the clear solution was carefully removed with a 200 A pipette and placed on a piece of filter paper contained on an aluminium planchet. One drop of concentrated NH40H was added and the sample was dried by means of an infra-red lamp.The radiocounting was done with a Nuclear Chicago model 181A scaler. Each sample was counted for a period of 1 h and the reproducibility of successive sample counts was within 2 %. The rate expression used to calculate the rate of exchange of n-chlorides where there was no net chemical change was Rt = ii[Pt(IV)][CI-]/n[Pt(IV)] -f- [Cl-] x 2-303 log [(CW - C,)/(C, - C,)], (1) where CW is the count at infinite time, CO is the count at zero time and Ct the count at any time t .The velocity constant k was calculated from the expression R = ic[Pt(IV)][Pt(II)][CI- J. (2) In soiiie cases the chloride exchange is accompanied by a net chemical change, e.g., Pt(NH,),C13+ + Pt(NH,)i' +H+ + C1-+Pt(NHJ)z' + trans-Pt(NH,),Cl;' + NH;. (3) In this case the measured radioactivity was converted into concentrations and the apparent rate constant kapp. was calculated using the equation (a-b)kapp.t = 2.303 log [b(a-x)/a(b-x)], (4) where (a-x) is the concentration of the reactant C1- and (b-x) is the concentration of the original Pt(IV) complex at any time t. The true velocity constant k was then obtained from the relationship, k = kapp./[Pt(II)I* ( 5 ) The experimental iiifinity counts always agreed with the calculated infinity Colin t to within 5%.PLATINUM EXCHANGE The platinum exchange was examined in the ethylenediamine system only, These exchange studies were done in three different ways and in three different laboratories. Polarimetric studies using laevo-propylenediamine complexes were made by Dr. R. G. Wilkins in this laboratory. The optical rotation of trans-Pt(1-pn),C$ + is approximately three times that of Pt(l-pn);+ ; the propylenediamine and ethylenediamine complexes are of comparable stabilities and all of the complexes are substitution inert. Therefore it was possible to determine the rate of platinum exchange polarimetrically by taking ad- vantage of the equilibrium c1- Pt(en)i++ trans-Pt(l-pn),CIi+ + trans-Pt(en),CI;+ + Pt(1-pn) :+. (6) In a typical experiment a solution was prepared which was 6.0 x 10-3 M in [Pt(en)2](C104)2 and in trans-[Pt(l-pn)2Clil(N03)2 and had an optical rotation of 1-25" at the sodium-D line.The optical rotation of this solution changed only very slowly but upon the addition of sufficient solid KCl to give a concentration of 3-4 x 10-3 M KC1 there is a rapid measur- able equilibration to an optical rotation of 0.75". The rate of equilibration of (6) was followed polarimettcially at room temperature (approx. 25°C) in a dark room with the reaction solution being exposed only to the light source of the sodium vapour lamp. Essentially the same experiment was done starting with trans-[Pt(en)2C12]C104 and [Pt(l-pn)2](ClO& and the results by these two methods were in good agreement. Making use of carbon-14 labelled ethylenediamine, Dr.R, G. Wilkins at Sheffield University has followed the rate of platinum exchange in the reaction c1- Pt(en*)z + + trans-Pt(en),CIj4 + + trans-Pt(en*),Cl; I- -I- Pt(en)2, + . ('7)F . BASOLO, M. L. MORRIS AND R. G . PEARSON 83 A reaction mixture which was 1.44 x 10-3 M [Pt(en*)2]Cl2, 2.72 x 10-3 M trans- [Pt(en)2C12](C104)2 and 9.43 x 10-3 M HC1 was placed in a volumetric flask covered with aluminium foil and thermostatted (rtO.l°C) at 25°C.. Aliquots were removed at various times and added to a centrifuge tube containing an excess of aqueous K2PtC14 to pre- cipitate [Pt(en)2] [PtC14]. This precipitate, after quick centrifuging, was washed, dried and counted as the solid. Using platinum-195 as a tracer, the exchange of platinum in the system trans- Ft(en),Cli +-I-Pt(en)z ++ C1- was investigated by Prof.D. S. Martin 9 at Iowa State College. Details of these studies are to be published later by Martin. CHLORIDE CONSUMPTION The rate of decrease of chloride ion concentration in the reaction mixture of Pt(NH3)&13++Pt(NH3)$++ 61- according to eqn. (3) was followed by means of titrations at various time intervals using the Volhard method. The calculated and experimental value of the chloride ion con- centration at zero time agreed to within 3 %. These solutions were prepared and handled in the same way as described above for the chloride exchange studies. The product of this reaction (3) was isolated and shown by analysis and infra-red spectrum to be trans- [Pt(NH&CIz]C12. A similar observation had been reported earlier.10 The chloride ion concentration was also observed to decrease in the system ci~-Pt(NH3)&1$++Pt(NH3):++ C1-.However, since in this case it is likely that several products are formed, no quantitative study of the rate of disappearance of chloride ion was made. For the same reason, the fact that chemical reaction was occurring was ignored in calculating the rate of exchange by radiochemical methods. The reaction was slow and was followed to no more than 25 % of completion with a fair excess of chloride ion present. Since linear first-order plots were obtained, changes in composition were not great enough to affect the rates. Initially there was a very fast exchange corresponding to essentially a 6-7 % zero time exchange when plotted on a time scale convenient for the remainder of the reaction.It was assumed that this was due to some 6-7 % of the trans isomer contaminating the cis. HYDROLYSIS Conductivity measurements and chloride ion determination on solutions of the chloro- ammineplatinuni(1V) complexes studied showed that there was no appreciable hydrolysis for any of these during the time and experimental conditions for chloride exchange. How- ever, this was not true for cis- and trans-Pt(NH&C14. Solutions of both of these com- pounds gave evidence of hydrolysis even when kept in the dark. Because of the com- plications due to hydrolysis no attempt was made to investigate the exchange of chloride in these systems. RESULTS The uncatalyzed exchange of radiochloride ion with the chloroammineplatinum- (IV) complexes studied at these experimental conditions was extremely slow.In all cases the exchange was catalyzed by platinum(I1) and kinetic studies show a first-order dependence on each of the three reactants so that the rate law is given by eqn. (2). Linear plots of the kinetic data, log[(C, - Co)/(C, - C,)] against t, were obtained. Results of experiments on the system trans-Pt(en)2ClZ++ Pt(eii)$++*Cl- are given in table 2. The activation energy for exchange is ap- proximately 11.5 kcal. Addition of hydroquinone or of barium diphenylamine sulphonate does not detectably alter the rate of exchange, whilst the presence of aniline only slightly decreases the exchange ratc. Qualitative observations on the rates of platinum exchange using complexes of laevo-propylenediamine are summarized in table 3.Quantitative data using carbon-14 and platinum-195 also are given. The first of these gives excellent agreement and the second moderate agreement with the rates of chloride exchange. In the case of carbon-14, it was assumed that Pt(en)2 exchanged as a unit.84 BRIDGED MECHANISM OF CHLORIDE EXCHANGE TABLE 2.-&TE OF CHLORIDE EXCHANGE IN THE SYSTEM trans-Pt(en),Cl; ++€%(en); ++ *C1- AT 25°C IN THE DARK k, 1.2 mole-2 min-1 run [trans-~t(en)2~122+1 [~t(en),+l [HCU 1 2 30 4b 5 6 7c 8 9d 1 Od 1 Id 12d 0.001 M 0.001 0.001 00005 0.001 0.002 0.002 0.001 0.001 0.001 0.001 0.002 0-00005 M 0~00010 0~00020 0*00020 0-00020 0.00023 0*00023 040025 0~00012 0.00025 0*00012 - 0.01 M 0.01 0.01 0.01 0.02 0.015 0.01 5 0.01 0.01 5 0.01 5 04085 0.017 9.2 x 102 9.2 x 102 9.2 X 102 8.8 X 102 8-8 X 102 9-2X 102 7.4x 102 no exchange in 2 days 2 3 x 102 2.4 x 102 1.6 x 102 1 .6 ~ 102 (a) Making the reaction mixture 0002 M in hydroquinone after one half-life did not nieasurably alter the exchange rate. This same reaction at 37.5"C has a value of k = 2.0 x 103 1.2 mole-2 min-1 allowing an estimate of EA = 11.5 kcal/mole. (6) Making soIution 0.001 M in barium diphenylamine sulphonate after one half-life did not measurably alter the exchange rate. (c) Reaction mixture was 0004 M in aniline. ( d ) For runs 9-12 the Pt(I1) catalyst is Pt(NH,)i+. 10 20 30 4 0 5 0 time, h FIG. l.-The rate of exchange of chloride ion in the system trans-Pt(NH3),C14, +Pt(NH,)$+ +*c1- at 25°C in the dark. Calculated on the basis of two exchangeable chlorides, 0 ; The experimental observations on all other systems are tabulated in table 4.me rate data reported for trans-Pt(NH3)3CI$ are based on the assumption of two replaceable chlorides only. When on the basis of three exchangeable chlorides, A. The justification for this is shown in fig. 1.TABLE 3.-POLARIMETRIC STUDIES OF PLATINUM EXCHANGE IN trans-Pt(AA),Xz ++Pt(AA)g ++x- SYSTEMS b run 13 14 16 17 18d 19e 20 21 22 1 9 concentration Pt(1V) Pt(IV) WII) 0.006 M 0.006 0.006 0.012 0.01 3 0.010 0.004 0.006 0.006 0.005 Pt(I1) 0006 M 0.006 0.006 0.01 3 0.01 3 0-012 0-004 0,006 0.004 0.005 optical rotation initial 040" 038 1.26 0.37 1.26 0.40 0.80 0.45 0.78 0.37 final 0.40" 0.75 1-14 0.76 0.76 0.82 0.80 0.86 0.47 0.37 remarks F no change in 15 min.Add 0.015 h.I KCI td and get equilibrium value of 0.75 in 20 min 0 r after 1 h, 0.49" ; complete overnight after 1 h, add 0.0034 M KCI and t4-20 min ,O equilibrium reached in 20 min, &,-0-85 % same as 16 above equilibrium reached in 30 min r % no change in 24 h 0 equilibrium reached in 10 min, KEq.-'1 TI same as 20 above M no change in 24 h ; no effect of added KCl 9 Z U (a) Reaction mixtures were at room temperature (approx. 25°C) and in only the light path of the sodium vapour lamp. w (b) Using 1"-en, platinum exchange in the dark at 25°C for the reaction mixture 0.00144 M [TPt(en*)2]C12, 0.00272 M trans-[Pt(en)2C12l(ClO& p and 0.0094 M HC1 has a value of k = 9.7 x 102 1.2 mole-2 min-1. Preliminary experiments with 195Pt give a value of k = 6*6+ 1 x 102 1.2 mole-2 cd min-1.In both of these studies the rate law (2) was confirmed. M P (c) Chloride exchange at these conditions has t+ = 17 min. (d) The P t O complex is supposedly the cis isomer, a sample of which was obtained from G. Johnson. (e) In more concentrated solutions of trans-Pt(en),Cl$ ++ Pt(NM,)$ f+ Cl- precipitation with PtCl$- gave no indication of the formation of Pt(en);+. It would seem that K E ~ . for this reaction is small.TABLE 4.-&TE OF PLATINUMQI) CATALYZED CHLORIDE EXCHANGE OF CJ3LOROAMMINEPLATINUM@v) COMPLEXES AT 25°C IN THE DARK run 23 24 25 26 27 28 29a 30b 3 1 C 32 33 34a 35 3 6d 37e 38a 39f 40a 41b 42 43 44g 45 platinum complexes W V ) WlI) t rans-Pt (NH 3)4C1: + Pt(NH 3 >t + 3) Y Y ¶ Y YY Y Y - $9 [O-OOS h4 Ce(IV)] Y Y ]Pt(en)$ + cis-Pt(NH,),CI$ * Pt@?H,)i+ Y Y Pt(NH3) Ibl3 * Y Y - Pt(NH,): + Y, Y f Y Y Y Y Y Y - trans-Pt(NH,), Cll Pt(NH3 ): + - Y Y Y Y [0.004 M C e O ] Y Y Pt(NH,),CI+ trans-Pt(tetrameen),Cl: * Pt(tetrameen)z + Y Y Y, WIV) 0.0010 M 0*0010 00010 o*m91 0.00091 0.00036 0.0010 Q*OOlO 0.0008 1 0-0184 0.0258 0.0279 0.01 15 0.0101 00125 0.0122 00010 0~0010 0.0010 0.0010 0.00069 0-00178 0.001 87 Pt(1I) 0.00025 M 000025 000012 0.00025 0.00025 0.00025 I - 0*00012 0.01 64 0.0336 0.0152 0.01 52 0.0037 0*00025 - - - - 0*00014 0*00009 0.0022 0*0001 concentration k, 12.mole-2 min-1 HCl 0.0085 M 3-8 X 102 3.8 X 102 0.01 5 4.8 X 102 0.015 0.01 5 3.3 x 102 0.0088 4-3 x 102 0.014 3.7 x 102 0.01 5 t4-44 h 0.015 no exchange in 2 days 0.010 initial rate very fast 0.050 1.7 >( 10-1 0064 1.4 X 10-1 0.896 0.047 3.9 x 10-2 0.043 3.2 X 10-1 0.050 4.0 0.049 0.014 tg-66 h 0.014 0-014 0.0084 04184 0.0122 no exchange in 14 days no exchange in 14 days 0.014 1.3 x 103 1.8 x 103 no exchange in 3 days no exchange in 14 days no exchange in 2 days no exchange in 1 day (a) In these runs no Pt(1I) was added.However, this does not exclude the possibility of catalytic amounts of Pt(I1) being present because in (b) The solutions of Pt(1V) complex containing Ce(IV) were allowed to stand overnight in the dark at room temperature prior to the addition (c) This exchange is complicated by the accompanying chemical reaction yielding Pt(NH,);+ and trans-Pt(en),CI$ + (see run 19, table 3). ( d ) Reaction temperature was 50°C. Under the same conditions the rate of consumption of chloride ion due to the formation of trans- (e) Reaction temperature was 81°C.The activation energy EA is 16.7 kcal/mole. (f) The value of k is calculated on the basis of two exchangeable chlorides (see fig. 2). (g Reaction temperature 50°C. most cases the Pt(IV) complex is prepared by the chlorination of a Pt(1I) compound. of HCP. Pt(NH3)4Cl$+ (see eqn. (3)) has a value of k = 2 8 x 10-1.F. BASOLO, M. L . MORRIS AND R. G . PEARSON 87 the data are plotted for three exchangeable chlorides, a linear plot is not obtained. However, theuse of a calculated C, based on only two exchangeable chlorides gives reasonable linearity. The experimental C, slowly approaches that for three replaceable groups. The activation energy for the chloride exchange in Pt(NH3)&13++ Pt(NH3):'f *Cl- is found to be 16.7 kcd.This reaction mixture yields the products shown in eqn. (3) and the rate of loss of chloride ion concentration is equal to the rate of chloride exchange if it is assumed that the product trans-Pt(NH3)&1$+ contains two completely exchanged chlorides. DISCUSSION The direct exchange of chloride with the chloroammineplatinum(1V) complexes investigated is either extremely slow or does not occur under the conditions of these experiments (see runs 8, 29, 34, 38 and 40). Runs 30 and 41 show that even the very slow exchange is almost completely inhibited by prior treatment of the platinum(1V) complex with cerium(1V). I t is believed that this is due to the oxidation of catalytic amounts of platinum(I1) in the platinum(1V) complexes which were prepared by the chlorination of the platinum(I1) compound.The kinetic data in tables 2 and 4 show that the rate law for exchange is given by eqn. (2). The mechanism proposed 1 to explain these results is illustrated by the following equations : fast €%(en)$ + + C1- + Pt(en),CI+ (8) en en slow en en slow en en en en ci--Pt-c12 + + pt-ci + + cl--Pt - - - c i - - - lpt-ci3 + + en + en en en Cl-Pt 3. CL-Pt-C12 + (9) There is now considerable evidence 11 in support of the addition of other groups to square planar complexes as suggested in (8). Similarly the bridged inter- mediate in (9) with the structure shown in fig. 2is analogous toIcomplexes originally CI 6' I FIG. 2.-Bridged intermediate proposed to explain the two electron change redox reaction in certain platinum(1V)-platinum(I1) systems.believed to contain platinum(II1) but later shown to be platinum(I1)-platinum(IV) bridged compounds.12 There is also some evidence for the existence of this particular bridged complex, [Pt2(en)&13]C13 in the solid state. It was observed that upon evaporation of a colourless aqueous solution containing equivalent amounts of trans-[Pt(en)2C12]C12 and [Pt(en)2]C12 an orange solid is obtained. The individual complexes are white. Thus the orange colour of the resulting solid88 BRIDGED MECHANISM OF CHLORIDE EXCHANGE is indicative of a platinum(I1)-platinum(1V) bridged complex, since such systems are known usually to be highly coloured. No spectral evidence for this species in solution could be found. This bridged mechanism for chloride exchange requires that platinum exchanges at the same rate by means of a two-electron-change process.The data in table 3 show that there is an exchange of platinum in these systems. Footnotes (b) and (c) of this table give quantitative data on the rates of platinum exchange which are in agreement with the rate of chloride exchange. It should also be noted that chloride ion is required for rapid platinum exchange. Perchlorate and nitrate ions are not nearly so effective as is shown by runs 13, 14 and 15. Cl Rapld c hlori dc and Pt platinum cxc hanqe similar c 1- equations Pt + NH 3 NH4 FIG. 3.-Mechanism for the chloride exchange and reaction of Pt(NH3)Qt in aqueous hydrochloric acid solution containing Pt(NH,)$+.The only chloroammineplatinum(IV) complex investigated that does not exchange chloride ion in the presence of platinum(I1) is trans-Pt(tetrameen),Cl:+. This is a significant observation as it is exactly what the bridged mechanism would predict. Because of the bulkiness of the C-methyl groups on the chelate rings, the Pt(tetrameen)$+ cannot get close enough to form a bridged complex through the chloro group. Therefore the bridged mechanism is not available to this system and no chloride exchange is expected. Similarly the less bulky Pt(en)f+ does not catalyze chloride exchange in Pt(tetrarneen),Clf-'- presumably because there is still steric resistance to the formation of the bridged complex (see runs 43, 44 and 45). A comparison of runs 23-28 and 32 and 33 show that the rate of chloride ex- change of trans-Pt(NH&ClZf is approximately 2000 times faster than that for the cis isomer.This is believed to be a direct consequence of the stronger Pt-N bond compared to the Pt-CI bond, for the trans isomer reduction of the plat- inum(1V) complex to platinum (11) by the bridged mechanism requires the rupture of the Pt-C1 bond opposite the chloro bridge as represented in fig. 2. However, in the cis isomer ammonia is opposite the chloro bridge and reduction necessitates cleavage of a Pt-N bond as shown in fig. 3. This difference in the rate of chloride exchange for the geometric isomers of platinuw(1V) complexes is in agreement with the observations that in such systems the cis isomer is more difficult to reduce than is the trans form.10 This observation is also consistent with Orgel's 13 suggestion that the bridge axis be designated as the z axis and then the electrons enter the dZ2 orbital.Since ammonia has a stronger crystal field than does chloride ion, the dZ2 orbital will be at a higher energy value for the cis isomer where ammonia is opposite the bridging group and consequently the transfer of electrons would require more energy than for the trans isomer. However, the fact that trans-Pt(en),(OH)$+ does not exchange with Pt(l-pn)$f even in the presence of chloride ion (table 3, run 22) indicates that the strength of the bond to be broken, Pt-OH, is more important than crystal field effects. Hydroxide ion and chloride ion are close to each other in the crystal field series.F.BASOLO, M. L . MORRIS AND R. G . PEARSON 89 The rate of chloride exchange with Pt(NH3),C13f (run 35) is approximately 10,00Q times slower than it is for tran~-Pt(NH~)~Cl;+. The activation energy for exchange in Pt(NH3)5C13+ is 16-7 kcal compared to 11.5 kcal for trans-Pt(en),Cl$f. Presumably this slower rate and higher energy of activation is again due to the stronger Pt-N bond opposite the chloro bridge as explained above and as shown in fig. 3. Since the Pt-Cl bond is weaker than Pt-N, it follows that step (1) is rapid compared to step (2). However, (1) results in no change, neither chloride exchange nor chemical reaction. For exchange of chloride step (2) is required which also necessitates a net chemical reaction. The tran~-Pt(NH~)~Cl$+ product then undergoes relatively rapid exchange by step (3) in the usual manner without further chemical change.Two observations were made on this system that afford excellent support to the reaction scheme shown in fig. 3. One is that the rate of decrease of chloride ion concentration is approximately the same as the rate of chloride-ion exchange (see footnote ( d ) in table 4) calculated on the basis of two chlorides exchanged per chloride ion removed from the solution. The other is that trans-[Pt(NH3)&12]C12 was isolated from the reaction mixture. This con- firms and explains the interesting observation of Rubinstein 10 that catalytic mounts of Pt(NH3);-+ will convert Pt(NH3)5C13+ in high yield to trans- Pt(NH3)4C1$f. Only catalytic amounts are required because Pt(NW3)2+ is re- generated as in (3).el I ' / I \ ' CI I F' @ I 1 68 "4, QAO (Q 1 FIG. 4.-Bridged intermediates proposed for the Pt(NH3)3Clf catalyzed chloride exchange of trans-Pt(NH&Cl;. Kinetic data collected on the exchange of chloride with trans-Pt(NH3)3C1$ show that two chlorides exchange much more rapidly than does the third (fig. 1). This can be explained by comparing structures (A) and (B) of fig. 4. The rate of exchange of the two chloro groups trans to each other via (A) requires the cleavage of a Pt-C1 bond and is fast, whereas the exchange of the chloro group trans to ammonia via (B) involves a Pt-N bond rupture and is slow. On the basis of the results mentioned above a difference of at least 103 in the two rates is expected. It is of some interest to note the effect of the charge of the platinum(1V) complex on the rate of chloride exchange.A comparison of the exchange rates show that trans-Pt(NH,),CI$ >tran~-Pt(N€€~)~Cl;+ (runs 23 and 39) and c~s-P~(NH~)~CI;+ >Pt(NH3)5C13+ (runs 32 and 35) by factors of approximately three and four re- spectively. This might be the result of a smaller tendency to form the bridged complex because of the greater repulsive interaction of the more highly charged cations. The charge on the platinum(I1) complex appears to have only a slight effect on the rate of chloride exchange. Runs 39 and 42 show that Pt(NH3)3ClC90 BRIDGED MECHANISM OF CHLORIDE EXCHANGE is only a slightly better catalyst than is Pt(NH,)z+. This may be due to corn- pensating opposing effects ; the smaller the cationic charge, the greater the tendency to form the bridged complex but the smaller the tendency to form the “five- co-ordinated ’’ species (see eqn.(8)). It should also be pointed out that the rate of exchange of tran~-Pt(en)~Cl;+ is about three times that of tran~-Pt(NH~)~Cl$+. One possible explanation for this difference is that the ammonia complex is more highly solvated and thus offers greater resistance to the formation of the bridged complex. The polarimetric studies reported in table 3 indicate that the efficiency of the bridging groups in facilitating electron transfer between platinum(1V) and plat- inum(I1) is Br->CI->OH- (compare runs 16, 20 and 22). This same order was observed for the system chromium(III)+ chromium(II).4 For platinrrm(IV)+ platinum(I1) the non-bridging group is also of considerable importance. Runs 14, 15 and 16 serve to show that the chloride ion is much more efficient than is either nitrate or perchlorate ion.This work was recently extended to show that in the system tran~-Pt(en)~@l$+Pt(en)~ +Xu, when X- is Br-, C1-, C N , CNS-, CNO- and NO; there is rapid exchange of platinum whilst when X- is OH-, SO;-, ClS:, NO,, C2M30; and F- the exchange is very slow.6 Catalysis of chloride exchange in PtC1;- by PtC1;- has been observed by Rich and Taube 14 and explained on the basis of a chain mechanism involving plat- inum(II1). Such a mechanism is probably not operating in the cases reported here because of the rate law and because the reaction is not affected by the in- hibitors which Rich and Taube found effective.Similarly, the suggestion 15 that the mechanism may involve the equilibrium trans-Pt(en),Clg + +Pt(en)i + + Clz accompanied by rapid exchange between C12 and *Cl-, seems unlikely because run 7 shows that aniline, an efficient chlorine trap, has little effect on the rate of exchange. Also Pt(tetrameen)z+ and Pt(tetrameen)2Clz+, which do not exchange, are relatively easy to halogenate and dehalogenate respectively. One observation which does not fit into the general scheme outlined above for the bridged mechanism of exchange is that ci~-Pt(en)~Clzf seems to exchange at a rate similar to that of the trans isomer (run 18, table 3). This is quite unexpected in terms of the bridge mechanism which predicts a very slow rate of exchange as found for cis-Pt(NH,),Clz+ and Pt(NH3)5C13f.A detailed study 16 is being made of the Pt(en)g+ catalyzed chloride exchange of cis-Pt(en),Cl;+. The authors wish particularly to thank Dr. R. G. Wilkins for doing the polari- metric and 04-ethylenediamine experiments and for his very helpful suggestions during the early stages of this investigation. We also thank Dr. M. J. G. Williams who did the tetrameen experiments and Prof. D. S. Martin, Jr., for making available to us his Pt195 results prior to publication. This investigation was supported by a grant from the U.S. Atomic Energy Commission under contract AT(11-1)-89, project no. 2 and in part by a grant from the U.S. Air Force Office of Scientific Research under Contract No. AF 49(638)-3 15. f for a previous communication see Basolo, Wilks, Pearson and Wilkins, J. Inovg. 2 Taube, Advances on Inorganic Chemistry and Radiochemistry, Emeleus and Sharpe 3 Taube, J. Amer. Chem. Soc., 1955,77, 4481. 4 Ball and King, J. Amer. Chem. SOC., 1958, 80, 1091. 5 Halperin and Taube, J. Amer. Chem. SOC., 1952, 74, 375. For a general discussion 6 Johnson and Basolo, J. Inorg. Nucl. Chem., in press. Nucl. Chem., 1958, 6, 161. (editors) (Academic Press Inc., New York, 1959), vol. I, pp. 1-53. see Edwards, Chem. Rev., 1952, 50,455.F. BASOLO, M . L. MORRIS AND R . G . PEARSON 91 7 Symbols used are en = NH2CH2CH2WH2, tetrameen = NH2G(CH3)2-C(CH3)2NH2 8 Gmdin’s Handbuclz der Anovganischen Chemie B, 1930, 58. 9 D. S. Martin, private communication. 10 Rubinstein, U.R.S.S. Compt. rend., 1940, 28, 55/58 ; Izvest. Plat., 1947, 20, 53/83 ; 11 Tschugaeff, Compt. rend., 1915, 161, 563. Harris and Stephenson, Chem. and 12 for references and discussion of apparent platinum(ZI1) compounds, see Watt and 13 Qrgel, Rept. Xe Conseil Inst. Int. Chim. Solvay, 1956, p. 289. 14 Rich and Taube, J. Amer. Chem. Soc., 1954,76,2608. 15 J. Halpern, private communication. 26 J. C . Bailar and G. Johnson, private communication. and pn = NH2CH(CH3)CH2NH2. 1947, 56. Ind., 1957, 14, 426. Harris, Livingstone and Reece, J. Chem. Soc., 1959, 1505. McCarley, J. Amer. Chem. Soc., 1957, 79, 4585.

ISSN:0366-9033    

DOI:10.1039/DF9602900080

出版商:RSC    

年代:1960

数据来源: RSC

摘要:

THALLOUS-TWLLPC EXCHANGE IN SYSTEMS CONTAIN- ING BROMIDE, AND THE OXIDATION OF TE3ULOUS ION BY ]BROMIPJE* BY I,. G. CARPENTER,? M. H. FORD-SMITH, R. P. BELL,$ AND R. W. DODSON Chemistry Dept., Brookhaven National Laboratory, Upton, Long Island, New York Received 26th January, 1960 The rate of the thallous-thallic exchange reaction has been measured over a range of bromide concentrations in solutions 0.5 M in acid and ionic strength 0.5 at 30°C. The results conform to the rate law R = ko[Tl+][T13+]+/~2[TlBrf2]+k3[TlBr3]+ k4[TI-k][TIBri] +kg[T1~r~][T1BrZ]. The first-order terms are thought to arise from the reversible oxida- tion of Br- by TlW Their apparent activation energy is 30 kcal/mole. The rate of oxidation of TlI by Br2 has been measured directly. The main features of the two electron exchange between thallous and thallic ions in aqueous perchlorate media have been established at a variety of temperatures and ionic strengths.1-3 The rate is first order in the concentration of each oxidation state, is acid-dependent, and can be written R = k[Tl+]~l3+]+ k'[T1+][TlOH2+]. When anions other than perchlorate are present other terms appear in the rate law and may predominate.Nitrate appreciably catalyzes the reaction.1 Chloride,2, 4 ~ 5 cyanide 6 and sulphate 79 8 have large effects on the rate. These effects have been interpreted as reflecting different kinetic properties (with respect to oxidation- reduction) of the various complex species present. Like chloride and cyanide, bromide forms quite stable complexes with trivalent thallium. The present work9 was undertaken to determine the kinetic effects of bromide in the thallous-thallic electron exchange system and to assign, if possible, kinetic parameters to various possible pairs of reaction partners.Features of interest found which are similar to those previously observed are inhibition of the exchange rate at ligand concentrations smaller than the TllI1 concentration, and marked catalysis at high concentrations. In these regions the rate is first-order in the total concentration of each oxidation state. When bromide is present in about twice the concentration of trivalent thallium there is a pronounced maximum in the exchange rate ; and the reaction order changes, the rate becoming independent of the concentration of TlI. The mechanism responsible for this effect appears to be the reversible oxidation of bromide by trivalent thallium.On this view, the ex- change rate data together with pertinent equilibrium information lead to a prediction of the rate of oxidation of thallous ion by bromine in aqueous solution. The latter was directly measured, and the results are compared with the exchange data. EXPERIMENTAL For experiments at low thallous concentrations the concentrated hydrobromic acid was re- distilled to remove traces of bromine and other oxidizing agents. Thallous perchlorate * Research performed under the auspices of the US. Atomic Energy Commission. t Part of this work is taken from the Ph.D. Thesis of L. G. Carpenter, Columbia $ Visitor from Balliol College, Oxford University, England.Apart from special preparations, the chemicals used were C.P. or reagent grade. University, 1956. 92CARPENTER, FORD-SMITH, BELL AND DODSON 93 was prepared by dissolving thallium metal in nitric acid and fuming off the nitrate with excess perchloric acid. The solid was recrystallized several times from ordinary distilled water and ultimately from triply-distilled water. Thallic perchlorate solutions in per- chloric acid were prepared by anodic oxidation of a solution of thallous perchlorate, as described by Biedermann.10 Diethyl ether was distilled under nitrogen and further purified by passing it through an alumina column. Ordinary reagent-grade ether also proved satisfactory for thallic chloride extractions. Methyl isobutyl ketone (" hexone ") was similarly purified by distillation and chromatography.The stock solutions of the re- agents, usually made up with triply distilled water, were repeatedly analyzed during the course of the experiments. The isotopes used as tracers were 204Tl and 202T1. The 204Tl was obtained as thallous nitrate from Oak Ridge. The 202T1 was prepared by bombarding a mercuric oxide target with deuterons from the Brookhaven 60-in. cyclotron and purified by ether extraction. Steps were taken to ensure and confirm the radiochemical purity of the tracers. The tracers were used in the form of dilute solutions of thallous perchlorate. Exchange reactions were run in vessels immersed in water baths at temperatures con- stant within about 10.05"C. The reaction vessels were variously : polyethylene bottles ; glass stoppered volumetric flasks or mixing cylinders, usually 100 ml in volume ; 100 ml hypodermic syringes.Light was excluded. The vessels were cleaned with sulphuric acid+ dichromate cleaning solution, were thoroughly rinsed with tap water, and then with distilled water (at least ten rinses with the latter). Reaction mixtures were prepared by mixing appropriate volumes of water and the stock solutions. The mixtures were equilibrated in the thermostat for periods of 1 h to about 12 h. Then tracer was added in the thallous form, typically as 1 ml of a 10-4 M Tlc104 solution. At intervals, 5-ml aliquots were removed with a pipette (or sometimes by expulsion through a delivery tube). The TP and TPII were chemically separated, and the amount of tracer in one or both of the fractions was determined.The beta rays from 204Tl were counted with an end-window proportional counter. The gamma and X- radiations from 202T1 decay were counted with a sodium iodide scintillator. Two methods were used to separate the TlI and TlIII fractions : chromate precipitation and solvent extraction. After addition of thallous carrier, thallous chromate was pre- cipitated from an alkaline cyanide medium as earlier described.2 With 202T1 tracer, the TlIII was extracted from chloride media with an equal volume of organic solvent : diethyl ether, from 2.2 M HC1, or hexone, from 0.15 M HCl. Both aqueous and organic phases were counted, in test tubes calibrated with 202T1. Corrections for phase volume change were applied with diethyl ether; none were necessary with hexone.It was found that the aqueous and organic phases had counting efficiencies so nearly the same that correc- tions for differing self-absorption were unnecessary. In consequence, the extent of reaction (x/xo3 in the McKay formulation 11) was given by [(a+b)/a]H/(A+H), where a and bare the concentrations in the reaction mixture of TlIII and TP respectively, and H and A are the counting rates of equal volumes of hexone and aqueous phases. The rate of the exchange reaction was determined graphically from semilogarithmic plots of 1 -x/xco against time according to the McKay expression X The plots were excellent straight lines when the bromide concentration was 2 ca. 3 x (TFII) or > 0.1 M. In many of the runs the thallous concentration was determined during or after the reaction. A 5-ml aliquot of the reaction mixture was added to 5 ml of 6 M HCI, allowed to stand in the dark for several hours, and the TlIII was extracted with two successive portions of hexone.Under these conditions the exchange is catalyzed to completion by chloride, and the counting rates of the aqueous and first hexone samples are proportional to the thallous and thallic concentrations, respectively. The oxidation of thallous ion by bromine was followed by the method of Bell and Ramsden,l2 which had been previously applied to fast bromination reactions of organic compounds involving bromine concentrations in the range 10-5-10-8 M. The potential of a platinum redox electrode against a glass electrode was followed with a Beckman pH meter as a function of time.Measurements were made at room temperature (25fl"C) with 50 ml of vigorously stirred reaction mixture.94 THALLOUS-THALLIC EXCHANGE An excess of thallous perchlorate was added to a dilute solution of bromine contain- ing thallic bromide and potassium bromide. The concentration of free bromide ions was between 10-4 and 4 x 10-3 M, and [TlIII] was at least 20 times [TII]. Under these conditions the measured potential is determined essentially by the more mobile bromine- bromide system and the potential-time curves can be interpreted simply. The instan- taneous drop of potential produced by adding thallous perchlorate was less than 5mV (except in the experiment with IFpr-] = 4 x 10-3 M, where it was 12 mV). The total fall of potential during an experiment was 30-90 mV, corresponding to a decrease of bromine concentration by a factor of 10-1000.The final readings were steady for several hours, and were consistent with the standard redox potentials of the bromine and thallium systems and the complexity constants given by Benoit.13 In almost all experiments the concentrations of Tl(IP1) and Br- did not change significantly during the course of the reaction, and the concentration of thallous ion (-10-6 M) was at least ten times the initial concentration of bromine, so that the reaction should be kinetically of the first order in both directions. If the potentials at times 0, f and 00 are VO, V and Yoo and we write y = 2FV/RT, etc., then if the potential is determined entirely by the brominefbromide system the bromine concentrations are given by [Br2l0: [Br2] : [Br,], = eyo: ey: eyw.If k is the sum of the forward and reverse first-order velocity constants, in practice almost equal to the forward constant, we find k can therefore be obtained from a plot of In [exp (y-ym)- 11 against t. These plots were in fact linear within experimental error, though the point for t = 0 was usually a little high. exP ( - k 0 = Cexp (Y - Y 00) - 1 3 i b P (Y 0 - v w > - 11 * (1) 0 0 . 2 0.4 0.6 0 . 8 a1 against a1 = [TIBr2+11[Tl~II] at 20°C, I = 0.5 and [Hf] = 0.50 M. RESULTS Between 0 and 0.5 h4 bromide the exchange rate varies over about three orders of magnitude, showing an initial decline fo'ollowed by a steep rise to a maxi- mum, a second decline to a minimum, then a continued rise.The experimental data are given in table 1 and fig. 1 and 2. The simplest interpretation of these FIG. 1.-Inhibition of rate of exchange at low bromide concentrations. Plot of rateCARPENTER, FORD-SMITH, BELL AND DODSON 95 effects is that thallous and thallic ions form various bromide complexes which differ greatly in their exchange properties, and that the overall rate is determined by the specific properties of the individual species and by their concentration in the system. We are thus led to consider the bromide complexes of thallous and thallic thallium. [halide], M FIG. 2.Variation of exchange rate with total bromide or chloride concentration. Plot of rate against halide concentration at 30"C, [H+] = 0.50 M, I = 0.50, [TP] = 2-74 x 10-5 M, [TI1111 = 3.08 x 10-3 M.RO = rate in the absence of halide. bromide curve, - - - - - - chloride curve. I_ Thallous bromide, like thallous chloride, is known to be a weak electrolyte. Higher complexes, up to TlBr2- have been reported 14 on the basis of solubility measurements in concentrated solutions. From similar measurements in the present work the thermodynamic equilibrium constants for the reactions T1++ Br- = TlBr, and T1Br-t-Br- = TlBr, were estimated 9 as 7.5 and 1.0, respectively, at 30°C. The first agrees well with other work ; 15 the second can be regarded as only a rough estimate. With an approximate activity coefficient correction the values become 2-9 and 1.0. These are used in the present discussion. There is some disagreement 139 16 as to the existence in aqueous solution of thallic bromide complexes containing more than four bromides.The present discussion is based on the work of Benoit,l3 who reported species up to TlBr; and determined their formation constants at 18°C. We have approximately corrected his values to ionic strength 0.5, using activity coefficients of EaBr3, IBa[ClQ&, and RbN03. It was not possible to correct for the 12" temperature difference. The values adopted for the stepwise formation equilibrium constants of TlBr"+, TlRrt,96 THALLOUS-THALLIC EXCHANGE TlBr,, and TlBr; under the conditions of the exchange measurements are respectively, 4x 108, 2 . 5 ~ 106, 1 x 184, and 5x 102. TABLE 1 .-RATE OF EXCHANGE AT VARIOUS BROMIDE ION CONCENTRATIONS 30°C ; I = 0.50; [Hi-] = 050 [HBrl, M 1.844~ 18-3 1.844 X 10-3 2.767 x 10-3 1.811 x 10-2 1.811 x 10-2 2.767 x 10-3 7-71 ~ 1 0 - 3 7.71 ~ 1 0 - 3 5.57 ~ 1 0 - 3 5-57 ~ 1 0 - 3 5-57 x 10-3 1.219 x 1W2 1.219 x 10-2 1.752 x 10-2 1.752 x 10-2 2.00 x 10-2 2.00 x 10-2 2.25 XlO-2 2.25 ~ 1 0 - 2 3.00 X10-2 3-00 x10-2 3.00 X10-2 340 x10-2 6430 X 10-2 6.00 X10-2 1.00 x 10-1 1.00 x10-1 2.07 X 10-1 2.07 X 10-1 3.07 x 10-1 3-07 X10-1 4.00 x 10-1 4.00 X 10-1 5-04) X10-1 5.00 X10-1 free tBr-I, M 3.2 X 10-8 3.2 X 10-8 4.0 x 10-7 4.0 x 10-7 6.0 x 10-6 6.0 X 10-6 8-5 ~ 1 0 - 5 8.5 ~ 1 0 - 5 2.9 x 10-4 2 9 x 10-4 2.9 x 10-4 1.7 x 10-3 1.7 x 10-3 6-0 x 10-3 6.0 x 10-3 8.35 x 10-3 8.35 x 10-3 1.06 x 10-2 1*06X 10-2 1.80 x 10-2 1.80 X 10-2 1.80 x 10-2 1-80 x 10-2 4.77 x 10-2 4.77 x 10-2 8.77 x 10--2 8-77 X 10-2 1.95 x 10-1 1.95 x 10-1 2.95 X 10-1 2.95 X 10-1 3.88 X 10-1 3-88 X 10-1 488 x 10-1 4.88 X 10-1 1-00 1.846 1.00 1.846 1.50 1.846 1.50 1.846 2.00 9.07 200 9.07 250 3.08 2-50 3.08 3.02 1.846 3.02 1-846 3.02 1.846 3.96 3.08 3.96 3.08 5-68 3-08 5.68 3.08 6-50 3.08 6-50 3.08 7.31 3-08 7-31 3.08 9.74 3.08 9-74 3.08 9.74 3.08 9-74 3-08 19.5 3.08 19.5 3.08 32.5 3.08 32.5 3.08 67.3 3.08 67.3 3.08 99.7 3.08 99.7 3.08 130 3.08 130 3.08 162 3.08 162 3.08 3-01 13.76 3.03 13.62 11.1 410 3.04 13.57 2.16 18.48 2.80 13.1 5 2-80 13.4 2.85 13.1 8 2.92 13.6 2.83 2-86 13.13 13.5 271 13.3 2.75 13.1 2.90 12.78 2.73 12.74 2.85 1274 2.81 2-74 184.8 20.0 86.5 11.6 32.5 2.42 1.21 1.05 4.35 1 -72 11.8 65.0 2-30 10.2 5.6 21.8 7.8 20.8 8-2 23.7 9.0 10.6 17.3 23-7 9.30 13-16 5.00 5.38 1.39 1.43 0.687 0619 0.440 0.387 0.305 0.304 1.03 x 10-6 1.03 X 10-6 7.52 x 10-6 7-63 X 10-6 6.26 x 10-5 6-03 x 10-5 1-99 x 10-5 2.05 x 10-5 8.61 x 10-6 9.86 X 10-6 9-86 X 10-6 8-37 X 10-6 8-56 X 10-6 3.44 x 10-6 4.24 X 10-6 2.50 X 10-6 424 x 10-6 2.40 x 10-6 3.94 x 10-6 2.16 X 10-6 1.85 X 10-6 5.05 X 10-6 3.91 X 10-6 2.02 x 10-6 6.73 X 10-6 3-77 x 10-6 1-62 x 10-5 1.44~ 10-5 5-97 x 10-5 273 x 10-5 1.37 x 10-4 4.45 x 10-5 2-19 x 10-4 6.40 x 10-5 6-27 x 10-5 Rcalc., 1.02 x 10-6 1.02 x 10-6 7.39 x 10-6 7.39 x 10-6 6.66 X 10-5 6.66 X 10-5 M h-1 1-92 x 10-5 1.92 x 10-5 8.97 X 10-6 9.10 x 10-6 10.48 x 10-6 8.37 x 10-6 9.02 x 10-6 3.87 x 10-6 5.01 x 10-6 3.24 X 10-6 4-35 x 10-6 2-49 x 10-6 3-92 X 10-6 1.79 x 10-6 1-79 X 10-6 3-32 X 10-6 3.32 X 10-6 1.96 x 10-6 7.49 x 10-6 408 x 10-6 1.94 x 10-5 1.40 x 10-5 6.15 x 10-5 2.36 x 10-5 1.10 x 10-4 3.57 x 10-5 4-57 x 10-5 4.45 x 10-5 1-60 x 10-4 The concentrations of free bromide and of the various thallium species were calculated by successive approximations from the equilibrium and mass-balance relations.Because the equilibrium constants are not well known the error may be considerable, but the general trends are probably correct. In particular, it is pro- bable that the principal species at [Br-]/mllll] ratios of 1, 2, 3, and 4 are TlBr2+, TlBrZ, TlBr,, and TBr;. Fig. 1 shows the decrease in rate when small amounts of bromide are added at 20°C. Assuming the rate to be expressible as R = Ic~[Tl+][Tl3f]3-J~~[Tlf][TlBr2+],CARPENTER, FORD-SMITH, BELL AND DODSON 97 it follows that a plot of rate against the ratio a1 = [TIBr2+]/[T1111] should be linear and extrapolate to a value kl[Tll][TlrrI] at a1 = 1.The extrapolated intercept at a1 = 1 is zero within experimental error, showing that kl is negligible compared to ko, i.e. that TlBr2+ exchanges with TI+ at a rate negligible compared to that of T P . A reasonable upper limit on the ratio kl/ko would be 0.05. Fig. 2 shows the exchange rate at various total bromide concentrations between 3.08 x 10-3 M and 0.5 My for rJ[r1]=2-78 x 10-5 M and [TIIII] = 3-03 x 10-3 M. In some cases the experimental values were determined at different thallium con- centrations ; the values in the graph have been corrected when necessary by use of the measured reaction orders with respect to [TlI] and fr.III1].For comparison, the dependence 4 of exchange rate on chloride is illustrated by the dashed line. The two systems are very similar at low and high halide concentrations ; there is a striking difference in the region of n = 2. temp. O C 40 38 20 10 20 30 50 TABLE 2.-DETERMINATION OF THE REACTION ORDER WITH RESPECT TO THALLOUS AND THALLIC I = 050, w+] = 0.50 M 5.57 x 10-3 5-57 x 10-3 5.57 x 10-3 5-57 x 10-3 5-57 x 10-3 5.57 x 10-3 5-57 x 10-3 5-57 x 10-3 5-57 x 10-3 5-57 x 10-3 5.57 x 10-3 5-57 x 10-3 5.57 x 10-3 5-57 x 10-3 1-85 X 10-2 1-12 x 10-2 2-23 X 10-2 3.09 x 10-1 3.09 X 10-1 7-72 x 10-3 7-72 x 10-3 23.16 x 10-3 1-846 x 10-3 1.846 x 10-3 1-846 x 10-3 1-846 x 10-3 14346 x 10-3 1.846 x 10-3 1.846 X 10-3 1.846 X 10-3 1.846 X 10-3 1.846 X 10-3 1.846 X 10-3 1.846 x 10-3 1.846 X 10-3 1.815 X 10-3 3.692 x 10-3 7.384 X 10-3 6-16 ~ 1 0 - 3 3-05 ~ 1 0 - 3 3-05 ~ 1 0 - 3 3.64 ~ 1 0 - 3 3.64 ~ 1 0 - 3 10.92 X 10-3 2-25 x 10-5 6-40 x 10-5 1-85 x 10-4 1-85 x 10-3 216 x 10-5 1.85 x 10-4 1-85 x 10-3 2.16 x 10-5 1-85 x 10-4 1.85 x 10-3 2-02 x 10-4 2 .1 6 ~ 10-5 1-85 x 10-4 2-61 x 10-4 2.50 x 10-4 2.91 x 10-4 2.15 x 10-5 2-24 x 10-4 4-15 x 10-4 2-49 x 10-3 2-49 x 10-3 1.85 X 10-4 * TlIII order assumed = 1. 3.02 3.02 3-02 3.02 3.02 3 a02 3.02 3.02 3.02 3-02 3.02 3-02 3.02 3.02 3-04 3.02 3.02 LO1 101 2.12 2.12 2.12 0.52 0.96 2-48 12.8 1.72 11.8 ' 65 9.0 67.0 23.3 625 360 385 1890 80.7 46.3 27.0 0.52 2-00 0.89 3.50 x 10-5 4-49 x 10-5 469 x 10-5 5-01 x 10-5 8.61 x 10-6 9.86 x 10-6 9-86 X 10-6 1.46 X 10-6 1.74 x 10-6 1-78 x 10-6 5.82 x 10-6 * 2-36 X 10-7 3.02 x 10-7 3.39 x 10-7 1-96 X 10-6 3.51 X 10-6 0.95 7.21 X 10-6 29 x10-5 3-16 x 10-4 5.00 x 10-4 5-13 x 10-4 1-58 x 10-3 1-02 t T1I order assumed = 0.0.03 002 0.04 007 t t t 1 -02 0.014 When the reaction order was checked in this region, the rate was found to be first order in [TlU1] but closely zero order in [TI1]. Table 2 gives the results of order determinations under various conditions. Measurements were also made at two different T1I concentrations, in ratio ca. 5 : 1, at a number of points in the transition region. From the results, included in table 1, the first- and second-order contributions can readily be evaluated. These are illustrated in fig. 3. It will be seen that the first-order part rises as ulBr$] rises, but drops off less steeply after D98 'r H A LLOU S -T H A LLI C EXCH A NG E the maximum. It then falls approximately with [TIBrJ.The course of the second- order part can be associated with the rise of [TlBr,] and, subsequently that of [TlBr;]. It ultimately rises somewhat faster than the calculated FIBr;}. 0.1 0.01 Id2 Id' I lBr-1, M FIG. 3.-First- and second-order contributions to the rate and the relative populations of complex species. -0-0- net first-order rate constant --a-O- net second-order rate constant multiplied by [TII]. The solid lower curves are, from left to right, the fraction of TlIII present as TI3+, TIBr2+, TlBr,, TlBr, and TlBr,, respectively. The dashed curves refer, correspondingly, to TI+, TIBr, and TIBr;. pi11 = 2 7 4 ~ 10-5 M The temperature dependence of rate was measured at n = 0,2,3, and [Br-] = 0.5.The results are shown in fig. 4. The apparent activation energies are respectively 16.0, 30, 30, and 7.5 kcal/mole. Two sets of measurements pertain to the reactions in the neighbourhood of the maximum, where the mechanism is believed to involve the equilibrium formation of Br2. The first of these comprises experiments with organic additives which react rapidly with Br2. The results are given in table 3. If the organic substrate removes Br2 as it is formed, it would be expected that the exchange would cease and that TITIT would be converted to Tll at the rate with which the exchange proceeds when no organic compound is present. The exchange rate was, in fact, greatly reduced. The last two columns of table 3 confirm the other expectation.In this series of experiments the logarithm of the [TllI1] was plotted against time and good straight lines were obtained initially. As the reaction proceeded the rate decreased ; this deceleration can be attributed to the formation of unreactive TIBr;. The second comprises the results, given in table 4, of direct measurements of the rate at which bromine oxidizes thallous ion. It will be noted that the specific rate is constant over a wide range of conditions, and that it is independent of the free bromide concentration when the latter is varied 40-fold.CARPENTER, FORD-SMITH, BELL A N D I)OL)SON 99 temp. O C 10 20 20 40 40 40 40 40 40 40 50 I I r I 1 3-00 3.10 3.20 3.30 340 3.50 3.60 i/r, KX 103 FIG. 4.-Arrhenius plots.A. [Br-] = 0.50 M C. [Br-] = 9 . 2 4 ~ 10-3 M D. [Br-1 = 0.0 [TI1111 = 3-08X 10-3 M, [TI11 = 2 . 7 4 ~ 10-5 M, [H+] = 0.50 M, 1 = 0.50. B. [Br-] = 7 . 1 6 ~ lO--3 M TABLE 3.-&MPARISON OF BROMINE REMOVAL AND EXCHANGE RESULTS Pr-]/[TlIII] = 3-0 ; I = 0-50; [H+] = 0-50 M additive k, h-1 kr concentration, for decrease of exchange, additive [TIm1] mlq initial initial M [TI"'] h-1 xi03 M x 105 M 3692 3.692 6.16 1 -846 1.846 1.846 3,692 3.692 3.692 3.692 1.846 4.51 4.5 1 0.2 6-60 660 2.55 4.51 451 4.51 4.5 1 2.55 N,N-dimeth yl-aniline phenol N,N-dimethyl-aniline aniline acetanilide ally1 alcohol phenol N,N-dimethyl-aniline aniline 9 9 99 Y, 9 , ,> 9 ) 3.4 x 10--2 3.4 x 10-2 1.8 x 10-1 3.5 x 10-2 1 . 4 ~ 10 1 1.68 x 10--2 6-7 x 10-2 1-18 x 10-1 3-36 x 10-2 1 . 4 ~ 10-1 7.8 x 10-3 1-59 x 10-4 1.06 x 10-3 1.00 x 10-3 2.12x 10-2 267 x 10--2 2-60 x 10-2 2.30 X 10-2 3.94 x 10-2 2.31 x 10-2 2-60 x 10-2 1.10 x 10--1 1-58 x 10-4 9-06 x 10-4 9.06 x 10-4 2.24 X 10-2 2.24 x 10-2 2.24 X 10-2 2-24 X 10-2 2.24 x 10-2 2.24 X 10-2 224 x 10-2 * determined by separate exchange rate studies.100 THALLOUS-THALLIC EXCHANGE TABLE 4.-&TE OF OXIDATION OF THALLOUS ION BY BROMINE room temperature (-25°C) 0.5 1 3.5 1.0 6.6 x 10-4 3.7 x 10-4 0.50" 1.0" 1.0 4.0 x 10-4 1-35 x 10-4 0.50 2-6 1-0 4.0 x 10-3 3-65 x 10-3 0.40 2.9 7.0 3.2 x 10-3 9.5 x 10-4 0.12 1.9 2.0 1-24 x 10-3 6.2 x 10-4 0.04 3.7 1-0 5.4 x 10-4 27 x 10-4 0.02 2.3 1.0 4.0 x 10-4 1-35 x 10-4 mean 248 2.45 2.77 2.4 1 2.8 1 2.74 2.4 1 = 2-59 x 107 M-1 h--I * In this experiment the initial concentrations of bromine and thallous perchlorate were each 1.0 x 10-6 and the results treated by second-order kinetic equations.DISCUSSION The data can be fitted with a simple rate law, in terms of the concentrations of the principal species of TP and TllI1 which are present. Up to [Br-] = 0.2 M a satisfactory expression is R = ko[Tl+][TP+]+ k2[TlBr$] + k3[TlBr3]+ k4[Tl+][TIBr,] +ks[TlBr;][TlBr4]. The values of the specific rate constants at 30°C, I = 0.5 are : ko = 0.69 M-1 h-1; k2= 8 x 10-3 h-1; k3 = 4.5 x 10-3 h-1; 1c4 = 4.6M-1 h-1; k 6 = 2.37~ 103 M-1 h-1. The first term applies to the joint contributions of the unhydrolyzed and hydrolyzed aquo-thallic ions. The fit can be seen by comparing the sixth and seventh columns in table 1. The poorest agreement is at [Br-J = 0.03 My where duplicate runs are discrepant.The system is being further studied in this region of minimum rate, where experimental difficulties were most evident. Above [Br-] = 0.2 M the rates are systematically higher than calculated, which may indicate that activated complexes containing more than six bromines are be- coming significant. On the other hand, the drift would be reduced by a moderate downward revision in the formation constant of TlBr. It appears conclusive that the reaction of TlBr2+ with TI+ is very much slower than that of Tl3+ and TlOH2+. The corresponding situation prevails in the chlo- ride and cyanide systems. One might have supposed that the anion could form a bridge to TI+, by which electron transfer would be facilitated.This is clearly not the case; furthermore, the single anion appears to block whatever electron transfer mechanism operates with the aquated ions. It may be conjectured that the anion alters the orbitals of TIrI1 in such a way that the latter can less readily accept two electrons. Evidence for a strong effect of chloride and bromide on the electron configuration of TllIr has been reported by Figgisy17 who found large chemical shifts in the n.m.r. spectrum of 205Tl when these ions were present. The rapid rise in rate at high bromide concentrations is surely accompanied by a rapid rise in the relative population of species such as TlBry. It is attractive to picture the activated complex as a symmetrically bridged structure such as and to associate the high reactivity with the high symmetry of this arrangement.Such a picture is necessarily speculative at the present time. The main new features of the present work are found in the region where TlBrt and TlBr3 are presumed to predominate and the reaction order becomes zero inCARPENTER, FORD-SMITN, BELL AND DODSON 101 ["I. Weiss 18 has suggested that electron exchanges may proceed through revers- ible redox reactions with a third reactant; the idea is applicable to our results. Consider the reaction TlBr; = Tl++Br,. The equilibrium constant, K = kf/k,, can be estimated from the thallic-thallous and bromine-bromide half-cell potentials 19 to be 2x 18-11 at 25°C and I = 0. Identifying kf with the specific rate k2 of the exchange reaction (interpolated value 3.4 x 10-3 h-1 at 25"), it follows that k, should equal 1 .7 ~ 108 M-1 h-1. The value found (table 4) is 2.7 x lO7M-1 h-1. The agreement is probably within the uncertainties of the equilibrium data. Confirma- tion that the mechanism involves free bromine is given by the results in table 3, which show that when Bra is continually removed from the system the rate of disappearance of TlIIL is closely equal to the thallous-thallic exchange rate when Br2 is not removed. In terms of such a mechanism, the k3r]rlBr3] term in the exchange rate is not compatible, however, with the lack of Br- dependence of the reaction of thallous with bromine. At the concentrations employed the reaction may be written TlBr3 = Tl++Bra+Br-. A calculation similar to the above shows that the observed velocity constant for thallous oxidation (based on TI++ Br2) should in- crease by a factor about 25 when free bromide increases from 10-4 to 4 x 10-3. As table 4 shows, a constant value was found in this range.The discrepancy is not removed by moderate adjustments of the equilibrium constants ; nor, it was found, could it be explained by catalysis on the platinum electrode. Further investigation will be required. Many of our colleagues have aided us in this work. We wish particularly to acknowledge our indebtedness to R. W. Stoenner for chemical analyses and many of the thallium preparations, to J. Hudis for cyclotron bombardments, to D. Christman for purification of the organic solvents, and to J. Galvin and K. T. Brennan for technical assistance. 1 Prestwood and Wahl, J. Amer. Chem. SOC., 1949,71, 3137. 2 Harbottle and Dodson, J. Amer. Chem. Soc., 1951,73,2442. 3 Dodson, J. Amer. Chem. SOC., 1953,75. 1795. 4 E h e r and Dodson, Brookhaven National Laboratory Quarterly Progress Report, 93 5 Brubaker, Groves, Mickel and Knop, J. Amer. Chem. SOC., 1957, 79, 4641. 6 Penna-Franca and Dodson, J. Amer. Chem. SOC., 1955,77,2651. 7 Brubaker and Mickel, J. Inorg. Nuclear Chem., 1957, 4, 55. 8 Wiles, Can. J . Chem., 1958, 36, 167. 9 Carpenter, Thesis (Columbia Univ., 1956, Univ. Microfilms 17044). 10 Biedermann, Arkiv Kemi, 1953, 5, 441. 11 McKay, Nature, 1938,142, 997. 12 Bell and Ramsden, J. Chem. SOC., 1958, 161. 13 Benoit, Bull. SOC. chim., 1949, 518. 14 Nilsson, Arkiv Kerni, 1957, 10, 363. 15 Nair and Nancollas, J. Chem. SOC., 1957, 318. 16 Peschanski and Valladas-Dubois, Compt. rend., 1955, 241, 1046 ; Bull. SOC. chim., 17 Figgis, Trans. Faraday SOC., 1959, 55, 1075. 18 Weiss, J. Chem. Physics, 1951, 19, 1066. 19 Latimer, Oxidation Potentials (Prentice-Hall, Xnc., New York, 2nd ed., 1952), (S-8), 67-69 (March, 1951). 1956, 1170. p. 60 and 135.

ISSN:0366-9033    

DOI:10.1039/DF9602900092

出版商:RSC    

年代:1960

数据来源: RSC