Inner-sphere reactions rate laws

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)... 

Quantitative rate data for reactions discussed in this section are given in Tables 3 and 4. The use of the ion [Ru(NH3)6] + as an outer-sphere reductant is much in evidence. The effect of sodium polystyrene sulphonate and sodium polyethylene on the rate of reduction of the series of complexes [Co(en)2(Cl)A] + (A = py, HjO, or NH3), [Co(en)2Cla]+, and [(NH3)6CoBrp+ has been investigated, for comparison with known effects in inner-sphere reactions. Though acceleration factors were found for both mechanisms, activation parameters reveal that for outer-sphere a lowering of Aff and for inner-sphere a more favourable AS are responsible. With [Ru(NH3)b] + in large excess, the consumption of horse heart ferricytochrome c obeys the rate law... 

The observed rate law for inner-sphere, as for outer-sphere, reactions is commonly first order in each reactant but this does not indicate which step is ratc-dcteriiiining. Again, details should be obtained from more extensive accounts." ... 

An [H + ] term in the rate law for reactions involving an aqua redox partner strongly suggests the participation of an hydroxo species and the operation of an inner-sphere redox reaction (Sec. 5.5(a)). Methods (a) and (b) are direct ones for characterizing inner-sphere processes, analyzing for products or intermediates which are kinetically-controlled. Method (c) is indirect. Other methods of distinguishing between the two basic mechanisms are also necessarily indirect. They are based on patterns of reactivity, often constructed from data for authentic inner-sphere and outer-sphere processes. They will be discussed in a later section. 

Organonickel(II) species are believed to be formed during the reaction between [Ni(TMC)] and primary alkyl halides, and subsequently undergo hydrolysis with cleavage of the Ni—C bond. Kinetic data measured in the presence of excess alkyl halide indicate a rate law -dlNi1 (TMC)+]/cft = MNi (TMCr][RX]. The rate constants increase for R and X in the order methyl < primary < secondary < allyl < benzyl halides and Cl < Br < I (133, 140). This suggests that the rate-determining step is electron transfer from the Ni(I) complex to R—X via an inner-sphere atom-transfer mechanism (143). 

It is often difficult to distinguish between outer and inner sphere mechanisms. The rate law is of little help since both kinds of electron transfer reactions usually are second order (first order with respect to each reactant) 9... 

The kinetics of chromium(l 11 )-catalyscd oxidation of fonnic acid by Ce(TV) in aqueous H2SO4 can be rationalized in terms of initial formation of an outer-sphere complex involving oxidant, catalyst, and substrate (S), Ce(TV)(S)Cr(III), followed by an inner-sphere complex Ce(III)(S)Cr(IV). It is proposed that electron transfer occurs within this complex from substrate to Cr(TV) (with elimination of H+) followed by fast reaction to give CO2 (again with elimination of H+).54 In contrast, there was no kinetic evidence for the accumulation of a corresponding inner-sphere intermediate in the osmium(VIII)-catalysed Ce(TV) oxidation of DMSO to dimethyl sulfone here, the observed rate law was rationalized in terms of rate-determining bimolecular electron transfer from DMSO to Os(VHI) in an outer-sphere step.55 The kinetics of oxidation of 2-hydroxy-l-naphthalidene anil by cerium(IV) in aqueous sulfuric acid have been... 

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 ... 

Equation 4.35 shows that the concentration deviations based on a linearization analysis of the rate laws in Eqs. 1.54a and 1.54c will decay to zero exponentially ( relax ) as governed by the two time constants, r, and r2. These two parameters, in turn, are related to the rate coefficients for the coupled reactions whose kinetics the rate laws describe (Eqs. 4.36c-4.36e and 4.38). If the rate coefficients are known to fall into widely different time scales for each of the coupled reactions, their relation to the time constants can be simplified mathematically (Eq. 4.39 and Table 4.3). Thus an experimental determination of the time constants leads to a calculation of the rate coefficients.20 In the example of the metal complexation reaction in Eq. 1.50, with the assumptions that the outer-sphere complexation step is much faster than the inner-sphere complexation step and that dissociation of the inner-sphere complex is negligible (k b = 0 in Eq. 1.54c), the results for tx and r2 in the first row of Table 4.3 can be applied. The expression for tx indicates that measurements of this parameter as a function of differing equilibrium concentrations of the complexing metal and ligand will produce a straight line whose slope is kf and whose y-intercept is kb. The measured values of l/r2 at these same two equilibrium concentrations then lead to a calculation of kf. 

Prior coordination of Cl to a variety of Pt(II) substrates has also been observed to precede various oxidations that proceed by inner-sphere electron transfer or atom transfer) 193). Nucleophilic solvents might be expected to mimic the role of the anions in some systems, and examples are known. Thus Mel addition to the rho-dium(I) complex of Scheme 20 is in competition with a second reaction that is dependent on solvent addition 194). Rate law (25) was observed, As being the solvent dependent part. 

---