Outer sphere, entropy reactions

A model has been considered for Sn2 reactions, based on two interacting states. Relevant bond energies, standard electrode potentials, solvent contribntions (nonequi-librinm polarization), and steric effects are included. Applications of the theory are made to the cross-relation between rate constants of cross- and identity reactions, experimental entropies and energies of activation, the relative rates of Sn2 and ET reactions, and the possible expediting of an outer sphere ET reaction by an incipient SN2-type interaction (Marcus, 1997). 

Reductions of various Co(ni) complexes by Fe(II) have been studied under high pressures . The motivation for performing such experiments resides in the possibility that the volume of activation (AF ), like the entropy of activation, might be a criterion for distinguishing between inner- and outer-sphere reactions. For reactions of the type... 

There are two other mechanistic possibilities, halogen atom abstraction (HAA) and halonium ion abstraction (EL), represented in Schemes 4.4 and 4.5, respectively, so as to display the stereochemistry of the reaction. Both reactions are expected to be faster than outer-sphere electron transfer, owing to stabilizing interactions in the transition state. They are also anticipated to both exhibit antiperiplanar preference, owing to partial delocalization over the C—C—Br framework of the unpaired electron in the HAA case or the electron pair in the EL case. Both mechanisms are compatible with the fact that the activation entropies are about the same as with outer-sphere electron donors (here, aromatic anion radicals). The bromine atom indeed bears three electron pairs located in two orthogonal 4p orbitals, perpendicular to the C—Br bond and in one s orbital. Bonded interactions in the transition... 

The extent to which the radicals react according to Eqs. 6 or 7 depends on the nature of Ri, Ra, and R3. If Ri = Rj = H and R3 = H through NO2, the ratio (6) (7) > 20. The addition reactions observed with these systems are characterized by strongly negative activation entropies, which can be rationalized in terms of immobilization of water molecules by the positive charge at C in the transition state [15]. That the transition state for addition has pronounced electron-transfer character concluded from the fact [15] that the rate constants for addition depend on the reduction potential of the nitrobenzene in a way describable by the Marcus relation for outer-sphere electron transfer. 

Relaxation of complicated ligands may occur as a step in both pathways. Diebler and Eigen 461 indicated the ways in which such mechanisms could be analysed using fast reaction methods. Several studies of Ln(III) complex formation and of the formation of Ln(III) mixed complexes have been analysed. Generally the dissociative mechanism is considered to dominate and we are then concerned with the water exchange rate. Several studies have shown that the rate decreases from La(III) to Lu(III) but there seems to be a minimum rate around Tm(III). This is also seen in the rate of rotation of ligands on the surface of the ions, Fig. 7. There may be a small crystal field term, or another contribution to a tetrad -like effect from the 4f electron core. However in the hydrate the precise relationship between the inner and outer sphere water may also be important as we saw when we discussed the heat and entropy of complex ion formation. 

The AAH (a-a) value is — 11.8 kJ mol 1 for [Co(alamp)(py)]+ and —5.6 kJ mol 1 for [Co((R,R)-promp)(H20)]+. These values are largely compensated by the AASJ(a-a) value. Interestingly, the AH value linearly depends on the AS value. This result shows that the enthalpy-entropy compensation certainly occurs in the reaction. The compensation is discussed, as follows Since this reaction involves outer-sphere-type electron transfer, the activation enthalpy is necessary to bring the reactants close enough together to allow electron transfer and to break up the hydration shell of the reactants. The entropy term contains the contribution due to rearrangement of the solvent molecules. As a result, the enthalpy-entropy compensation occurs in the reaction. 

Some general observations on the energies and entropies of activation of redox reactions which proceed by bridged activated complexes are in order. These quantities, even for the few systems for which they have been determined, cover the range 4 to 14 kcal and —20 to —45 e.u. respectively. The ranges overlap with those for the outer-sphere activated complexes and, except possibly in extreme cases, it is not safe to use the magnitude of these quantities as diagnostic of mechanism. The comparison of AS for the process... 

J/m/K. The agreement between the nmr estimates and those from equation (1) add weight to the estimates in Table III. In Figure 2 the variation of log i and log 0 as functions of pKa reflect the vital role of ligand basicity in the inner-outer sphere competition. These curves indicate that the cross-over from predominantly outer sphere to predominantly inner sphere occurs near pKa values of 2. However, since the enthalpy and entropy changes for inner sphere complexation are larger than for outer sphere formation, both AH and AS would still be endothermic (characteristic of inner sphere reaction). 

Micellar Efllecls on Inorganic Reactions.—Electron transfer between ferric ion and phenothiazine is inhibited by cationic micelles and accelerated by up to 10 -fold in anionic micelles of sodium lauryl sulphate. " In both cases the rate-surfactant concentration profile can be simulated accurately. Anionic micelles only cause a small effect on the reactivity of ruthenium(iii) tris(bipyridyl) with molybdenum(iv) octacyanide but accelerate the reaction between ferrous ion and tris(tetramethylphenanthroline)iron(ra). In the latter case a plot of surfactant concentration is linear with the reciprocal of the observed rate constant. Fast outer-sphere electron-transfer reactions may decrease in rate constant by up to four orders of magnitude when one of the reactants is solubilized in an anionic micelle. When this partner is neutral the inhibition is reduced somewhat by added salt, but when it is cationic the effect may be attenuated by competitive binding of Na or HsO and exclusion of reactant from the micelle. Oxidation of diethyl sulphide is catalysed by micelles of sodium lauryl sulphate containing carboxylate-ions by the mechanism shown. (Scheme 3). The rate advantage is quantitatively accounted for by the entropy term, and hexanoate is forty-fold more effective than acetate. Electron-transfer between the anionic trans-1,2-diaminocyclohexane... 

Non-aqueous Solvents.—Mention has already been made of the evidence for an associative (/a) mechanism for the exchange of DMSO with the [Cr(DMSO) ] + ion. Both the entropy and volume of activation are large and negative. A recent study of the exchange process by n.m.r. in DMSO-MeNOj mixed solvents (nitro-methane is an inert, non-co-ordinating diluent which is known to have very little rate effect) shows that the exchange rate is approximately constant above 0.2 mole fraction of DMSO, but drops off sharply below this concentration. On the other hand the fraction of DMSO molecules in the solvation shell of the [Cr(DMSO) J + ion decreases immediately with the decrease in the DMSO mole fraction. This difference in concentration effects is postulated to arise from a unique outer-sphere solvation site which preferentially binds DMSO molecules and preferentially participates in the exchange reaction. 

The reduction of ferricytochrome c by hydrated electrons and by several free radicals has been studied by pulse radiolysis. The reduction of oxidized cytochrome c by [Fe(edta)] - follows first-order kinetics for both protein and reductant, with a rate constant of 2.57 x 10 1 mol" s" at pH 7 and activation enthalpy and entropy of 6.0 kcal mol" and —18 cal K" mol", respectively. These values are comparable to those for outer-sphere cytochrome c reductions and redox reactions involving simple iron complexes, and are compatible with outer-sphere attack of [Fe(edta)] " at the exposed haem edge, although the possibility of adjacent attack through the haem pocket is not ruled out. The rate data at pH 9 are consistent with [Fe(edta)] " reduction of two slowly interconverting forms of the protein, native kt = 2.05 X10 1 mol" S" ) and high-pH kt = 2.67 x 10 1 mol" s" ) isomers. A possible route for the transfer of the electron from Cr + to ferricytochrome c has been suggested as a result of the chemical analysis of the chromium(m) product. The reduction by Cr + of the native protein and of ferricytochrome c carboxy-methylated at the haem-linked methionine (residue 80) has been studied kinetically. At pH 6.5 the former process is simple and corresponds to a second-order rate constant of 1.21 x 10 1 mol" s". The latter, however, is complex - two chromium-... 

The activation free energy for an outer-sphere electron transfer process, AG, consists of an internal contribution, AGin, associated with rearrangement of the inner-coordination spheres and an external contribution, AGSut, due to solvent rearrangement [equation (2)]. Reaction entropies, A5rc, for... 

Cobalt(in) oxidizes 2-mercaptoethylamine (HMea) in [Co(en)2(Mea)] to the corresponding co-ordinated disulphide complex by pathways involving Co + and [CoOH] +. An outer-sphere mechanism is suggested by the activation entropy (—3.1 cal K mol ) for reaction with Co and the reaction with [CoOH] + is substitution controlled. Redox proceeds by formation of a co-ordinated radical complex [Co(en)2(Mea)] +,... 

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