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. 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