Inner-sphere complex formation

As we shall see (Chapter 4), the kinetics of surface complex formation is often related to the rate of H20 loss from the aquo cation. This is another (indirect) evidence for inner-sphere complex formation. 

The most direct evidence for surface precursor complex formation prior to electron transfer comes from a study of photoreduc-tive dissolution of iron oxide particles by citrate (37). Citrate adsorbs to iron oxide surface sites under dark conditions, but reduces surface sites at an appreciable rate only under illumination. Thus, citrate surface coverage can be measured in the dark, then correlated with rates of reductive dissolution under illumination. Results show that initial dissolution rates are directly related to the amount of surface bound citrate (37). Adsorption of calcium and phosphate has been found to inhibit reductive dissolution of manganese oxide by hydroquinone (33). The most likely explanation is that adsorbed calcium or phosphate molecules block inner-sphere complex formation between metal oxide surface sites and hydroquinone. 

Figure 11.1. Schematic views of various ways in which an organic chemical, i, may sorb to natural inorganic solids (a) adsorption from air to surfaces with limited water presence, (b) partitioning from aqueous solutions to the layer of vicinal water adjacent to surfaces that serves as an absorbent liquid, (c) adsorption from aqueous solution to specific surface sites due to electron donor-acceptor interactions, (d) adsorption of charged molecules from aqueous solution to complementarily charged surfaces due to electrostatic attractions, and (e) chemisorption due to surface bonding or inner sphere complex formation.

For perchlorate solutions of different compositions the results show no significant dependence on the concentration of the metal ion (34, 35). Values for the coordination number, Er—H20 bond lengths and their rms variations do not differ significantly between a 1 M and a 3 M solution (Fig. 15), and are independent of the perchlorate concentration. No inner-sphere complex formation is indicated. 

For the reactions in Eq. 1.50, it is known5 that the first reaction comes to equilibrium much more quickly than the second and that in the second reaction the forward rate is much larger than the backward rate. As in the C02 hydration reaction, the concentration of water is effectively constant (species E in Eq. 1.52). Thus the rate of inner-sphere complex formation from the outer-sphere complex intermediate species limits the overall rate of the reaction in Eq. 1.8. The impact of these experimental facts on the coupled rate laws in Eq. 1.53a and 1.54c is to reduce them to a single equation ... 

A reaction rate law for the Eigen-Wilkins-Werner mechanism is developed in Section 1.5 (Eqs. 1.50, 1.52, 1.54a, 1.54c). If inner-sphere complex formation is rate limiting and the concentration of water remains constant, the rate of inner-sphere complex formation is (cf. Eq. 1,57)... 

Equation 4.26, as noted above, has two terms—a chemical complexation term, [-SM(m 1)[H+]/[-SHj[Mm+], and an electrical potential term, exp[(m-l)A /// T]. The electrical potential term is directly dependent on pH (see Eq. 4.27b). Therefore, by regulating the magnitude of the physical attraction between a metal and a surface, the electrical potential indirectly affects the magnitude of surface complexes that could form. Recall that before a chemical complex or inner-sphere complex between two reactants is formed, they must physically collide successfully at a given frequency. When a metal-ion (e.g., contaminant) and a surface are oppositely charged, physical collisions maximize, and, thus, inner-sphere complex formation maximizes. When a metal-ion (e.g., contaminant) and a surface are similarly charged, physical collisions minimize, and inner-sphere complex formation also minimizes. 

A good example of outer-sphere complex formation is the adsorption of Co(CN -) ions on y Al203. As can be seen from Fig. 9.3, lowering the pH leads to a concomitant increase in the amount of anion adsorbed, while neutralizing the solution again induces the Co(CN) 3- ions to desorb again. The process is perfectly reversible, which is not usually the case for inner-sphere complex formation. 

Stumm et al. (5) ended their paper with a variety of remarks that, taken as a whole, implied that the adsorbed metal products in equations 5a and 6a are inner-sphere surface complexes. Their suggestion reflected observations of specific metal cation adsorption and comparisons of aqueous metal complexes with the corresponding surface complexes. They cautioned, however, that this kind of interpretation could not be made unequivocally without direct molecular evidence for inner-sphere complex formation. 

The only study of the complex formation between selenate and trivalent lanthanides found is an X-ray diffraction investigation of some lanthanide selenate solutions by Johansson, Niinisto, and Wakita [85JOH/NI1], The radial distribution function was interpreted to show that inner-sphere complexes were formed. For Er an average of 0.4 SeO per Er was estimated for a solution containing 0.78 M Er and 1.55 M SeOj. The conditional equilibrium constant for the inner-sphere complex formation ... 

It is difficult to evidence pure cases of inner sphere complex formation between surface groups and transition metal ions (also called "grafting") since other phenomena are usually occurring in parallel. The clearest instances are observed when "spectator" ligands are inert to substitution, either because of chelate effects (ds- [Ni(en)2(H20)2p on various supports ) or because of high crystal field activation energies ([Co(NH3)5(RO)] + on TiAl2C)3 RO= OH, H2O or alcohol). 

The triple layer model attempts to take into account inner sphere complex formation and electrostatic adsorption simultaneously by considering "specifically adsorbed" ions which are supposed to be maintained very close to the surface, whether it be through the formation of covalent bonds with some surface groups, or of some outer sphere complex. No specific interpretation of the bonding is required, provided one can define a plane of specific adsorption, located a few A from the surface and containing those ions this is called the Stem layer. The theory distinguishes then between three successive parallel layers the surface plane proper, the Stem layer, and the diffuse layer. 

The constant capacitance model has been applied successfully to describe the adsorption of both inorganic and organic anions by hydrous oxides.Both adsorption isotherms and adsorption envelopes like those illustrated in Fig. 4.8 are accounted for quantitatively, except in the case of sulfate adsorption. It is possible, however, that this anion adsorbs through outer-sphere instead of inner-sphere complex formation, as discussed in Sec. 4.4. Aside from sulfate, anion adsorption envelopes are predicted in the constant capacitance model on the basis of an increase in [OH ], which causes the concentrations of the surface complexes in Eq. 5.53 to decrease, and a decrease in o-p. 

Figure 7. A schematic representation of the inner sphere complex formation at the surface of a metal (hydr)oxide.

In this chapter the reactions between metal ions in a high oxidation state and inorganic and organic substrates are discussed in detail. Many mechanistic data have been derived from these investigations, and it is now clear that many of these reactions take place via an inner-sphere mechanism with, in some cases, evidence for the formation of well-characterised transient intermediates. Inner-sphere complex formation is more likely to take place where neutral or negatively charged substrates are involved rather than with cationic reductants, and three cases of the mechanism ... 

These examples (by no means exhaustive) illustrate the general aspects of cation adsorption onto oxide minerals inner-sphere complex formation, preferentially edge or corner binding as opposed to basal plane binding, eventually forming small polynuclear complexes or surface polymers but more rarely surface precipitates. All that is true of transition metal and p-block representative cations alkaline metals normally bind only electrostatically, and alkali earth metals most often do the same. 

Comparatively little work has been done on the kinetics of complex formation between the alkali metal ions and simple ligands in view of the high rate constants and low stability constants involved. Atkinson has recently studied the ultrasonic absorption of the five alkali metal sulfates in water in the frequency range 25-250 MHz, where he found only one relaxation for each salt. The results are analyzed in terms of the normal two-step mechanism (the fast formation of an outer-sphere complex followed by rapid conversion to the inner-sphere complex) in which the rates of the two steps approach each other as the concentration of the solution decreases. (The concentrations were in the range 0.3-1.0 mol dm". ) As expected, the reactions are nearly diffusion controlled the rate constants for inner-sphere complex formation at 0.5 mol dm and 25°C are 1.0 x 10 s for Li, Na, Rb, and Cs sulfates but 2.0 x 10 s for the potassium salt. 

The distribution of ions H+, IVT"" ", and A" between the surface layer and the bulk solution is governed by the electrostatic field, and Eqs (iii) and (iv) can be applied by substituting the surface potential, i/ q, in aU cases, if CCM and DEM models are applied, because only inner-sphere complex formation is assumed and all of the ions are assigned near the surface whereas the potential is substituted in Eq. (iii) for the distribution of ions and A when the TLM model is chosen, because protolytic processes are assigned to the surface and complexation of other ions, which form outer-sphere complexes, to the plane in the TLM model. 

The inner-sphere complex formation is in fact accompanied by the displacement of solvent molecules from the coordination sphere of the metal ion and should be described by the following more general equation ... 

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