Inner-sphere constants

Unfortunately, for ligands of strong acids, this equation may underestimate the stability constant as it calculates values for inner sphere formation only. Eigen (22) has proposed that the formation of complexes proceeds sequentially as follows ... 

In contrast to the situation observed in the trivalent lanthanide and actinide sulfates, the enthalpies and entropies of complexation for the 1 1 complexes are not constant across this series of tetravalent actinide sulfates. In order to compare these results, the thermodynamic parameters for the reaction between the tetravalent actinide ions and HSOIJ were corrected for the ionization of HSOi as was done above in the discussion of the trivalent complexes. The corrected results are tabulated in Table V. The enthalpies are found to vary from +9.8 to+41.7 kj/m and the entropies from +101 to +213 J/m°K. Both the enthalpy and entropy increase from ll1 "1" to Pu1 with the ThSOfj parameters being similar to those of NpS0 +. Complex stability is derived from a very favorable entropy contribution implying (not surprisingly) that these complexes are inner sphere in nature. 

Let us consider the electron transfer between two rigid metal ions located some distance x from each other in the bulk of the solution. It is assumed that the inner-sphere reorganization of the donor D and acceptor A does not take place. The experiments show that the rate constants of these reactions differ by many orders of magnitude and the processes have an activated character even for identical ions D and A. The questions to be answered are Why does the electron exchange between identical ions in the solution require activation What is the reaction coordinate ... 

Fig. 2.7. Characteristic rate constants (s 1) for substitution of inner-sphere H20 of various aqua ions. Note The substitution rates of water in complexes ML(H20)m will also depend on the symmetry of the complex (adapted from Frey, C.M. and Stuehr, J. (1974). Kinetics of metal ion interactions with nucleotides and base free phosphates in H. Sigel (ed.), Metal ions in biological systems (Vol. 1). Marcel Dekker, New York, p. 69).

Where solvent exchange controls the formation kinetics, substitution of a ligand for a solvent molecule in a solvated metal ion has commonly been considered to reflect the two-step process illustrated by [7.1]. A mechanism of this type has been termed a dissociative interchange or 7d process. Initially, complexation involves rapid formation of an outer-sphere complex (of ion-ion or ion-dipole nature) which is characterized by the equilibrium constant Kos. In some cases, the value of Kos may be determined experimentally alternatively, it may be estimated from first principles (Margerum, Cayley, Weatherburn Pagenkopf, 1978). The second step is then the conversion of the outer-sphere complex to an inner-sphere one, the formation of which is controlled by the natural rate of solvent exchange on the metal. Solvent exchange may be defined in terms of its characteristic first-order rate constant, kex, whose value varies widely from one metal to the next. 

The kinetics and the mechanism of superoxide reduction by SORs have been studied by several researchers. It was suggested that SORs react with superoxide via an inner-sphere mechanism, binding superoxide at ferrous center to form a ferric hydroperoxo intermediate [46,48 50]. The rate constant for this reaction is equal to 108 109 1 mol-1 s-1 [46,49], This... 

If in addition one inner-sphere mode of frequency oj, with Tuo 3> kT, is reorganized, the total rate constant can be written as a sum over partial rates ... 

Table 1. Hydrolysis constants3 and exchange rate constants for substitution of inner-sphere water ligandsb...

In the course of our investigations to develop new chiral catalysts and catalytic asymmetric reactions in water, we focused on several elements whose salts are stable and behave as Lewis acids in water. In addition to the findings of the stability and activity of Lewis adds in water related to hydration constants and exchange rate constants for substitution of inner-sphere water ligands of elements (cations) (see above), it was expected that undesired achiral side reactions would be suppressed in aqueous media and that desired enanti-oselective reactions would be accelerated in the presence of water. Moreover, besides metal chelations, other factors such as hydrogen bonds, specific solvation, and hydrophobic interactions are anticipated to increase enantioselectivities in such media. 

S. Kobayashi, S. Nagayama, T. Busujima, Lewis Acid Catalysts Stable in Water. Correlation between Catalytic Activity in Water and Hydrolysis Constants and Exchange Rate Constants for Substitution of Inner-Sphere Water Ligands J. Am. Chern. Soc 1998, 120, 8287-8288. 

We have argued that (inner-sphere) surface complex formation of a metal ion to the oxygen donor atoms of the functional groups of a hydrous oxide is in principle similar to complex formation in homogeneous solution, and we have used the same type of equilibrium constants. How far can we apply similar concepts in kinetics ... 

We can simplify by considering that k.- k.w, and by setting k k-i = Kos. Kos is the equilibrium constant of the outer sphere complex. For the rate of the formation of MeLJ2 n)+ inner-sphere complex (now written without water), we have... 

Pathway (d) in Fig. 9.3 provides a possible explanation for the efficiency of a combination of a reductant and a complex former in promoting fast dissolution of Fe(III) (hydr)oxydes. In this pathway, Fe(II) is the reductant. In the absence of a complex former, however, Fe2+ does not transfer electrons to the surface Fe(III) of a Fe(III) (hydr)oxide to any measurable apparent extent. The electron transfer occurs only in the presence of a suitable bridging ligand (e.g., oxalate). As illustrated in Fig. 9.3d, a ternary surface complex is formed and an electron transfer, presumably inner-sphere, occurs between the adsorbed Fe(II) and the surface Fe(III). This is followed by the rate-limiting detachment of the reduced surface iron. In this pathway, the concentration of Fe(U)aq remains constant while the concentration of dissolved Fe(III) increases thus, Fe(II)aq acts as a catalyst to produce Fe(II)(aq) from the dissolution of Fe(III)(hydr)oxides. 

The Rate of reductive Dissolution of Hematite by H2S as observed between pH 4 and 7 is given in Fig. 9.6 (dos Santos Afonso and Stumm, in preparation). The HS" is oxidized to SO. The experiments were carried out at different pH values (pH-stat) and using constant PH2s- 1.8 - 2.0 H+ ions are consumed per Fe(II) released into solution, as long as the solubility product of FeS is not exceeded, the product of the reaction is Fe2+. The reaction proceeds through the formation of inner-sphere =Fe-S. The dissolution rate, R, is given by... 

Figure 4. Illustration of inner-sphere tunneling in an exchange reaction. The reactants and products are assumed to have the same reduced force constant, and only the energy levels and wave functions for the lowest vibrational states of the reactants and products are shown.

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

Since it has been reported that in the inner-sphere SOD catal5rtic pathway (Scheme 5) the water-exchange process is the rate-limiting one, the inner-sphere catalytic rate constants is were correlated with the water-exchange rate constants on [Mn(H20)6l (22,31). However, it seems that it is not possible to draw a direct correlation between these rate constants. Firstly, is (which is pH independent) according to the observed rate law for dismutation of superoxide (V — —d[02 ]/ d = [Mn][02 ] H[H+]+ ind>, ind 2kis, ku = 2kos/KJ has the unit... 

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