Outer-sphere complex Formation constant

The dashed line in the complex in (4.21) and (4.22) indicates an outer-sphere (o.s.) surface complex, Kos stands for the outer-sphere complex formation constant and kads [M 1 s 1] refers to the intrinsic adsorption rate constant at zero surface charge (Wehrli et al., 1990). Kos can be calculated with the help of a relation from Gouy Chapman theory (Appendix Chapter 3). 

We can now calculate the outer-sphere complex formation constant according to Eq. (4.24) ... 

A proper D mechanism requires that kx be identical to the rate constant for the exchange of solvent (due account being taken of any statistical correction when more than one solvent molecule is present) and the value of k2 (in reality the term fc2/fc i[S] is used because the constants cannot be separated) should be sensitive to the chemical nature of L rather than its size and charge (factors that control Kos in an interchange mechanism). The most convincing demonstration of a D mechanism would be found in cases where k2/k-1[S] is much larger than any value expected for an outer-sphere complex formation constant, but this is not a necessary requirement for the mechanism. 

The dashed line in the complex in 5 and 6 indicates an outer-sphere (OS) surface complex ATqs stands for the outer-sphere complex formation constant... 

The overall rate const kf is measured by the relaxation methods. Assuming that the outer-sphere complex formation is faster than the water substitution by ligand L, the interchange rate constant k can be calculated using the equation... 

The insensitivity of the formation rate constants to the nature of the ligand is ubiquitous for non-transition and transition metal ions alike. This phenomenon is believed to be the result of either an SnI mechanism [Eq. (2, 3)], or a two-step, SNl-like mechanism [Eq. (4, 5)] involving first outer sphere complex formation followed by SnI loss of water from the aquo ion (7, 2). 

Kq3 is the equilibrium constant for outer-sphere complex formation, k is the first order rate constant for water loss from the nickel aquo-ion and k is the first-order rate constant for the decomposition of the complex. 

Since the equilibrium constant for the outer-sphere complex formation K g l/[Ni2+], ... 

Zinc chloride and (under some conditions) zinc nitrate solutions in aqueous DMSO, on the other hand, yield " two ultrasonic absorption maxima with the chloride this is taken as evidence for an octahedral-tetrahedral coordination change accompanying the addition of the third bound Cr, while with the nitrate the high-frequency relaxation (observable only at low-water-mole fractions) is attributed to outer-sphere complex formation. The rate constants (25 C) for solvent loss with the nitrate (Xh20 = 0.59) and the chloride (Xhjo = 0.039 and 0.904) are, respectively, 2.2 X 10 , 4.1 X 10 , and 3.3 x lO s. ... 

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. 

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... 

The separation of the two stages is easier to discern when the rates of the two processes are so different, but it can also be seen in the ultrasonic spectra of metal-sulfate systems (Sec. 3.4.4). Ultrasonic absorption peaks can be attributed to formation of outer-sphere complexes (at higher frequency, shorter t) and collapse of outer-sphere to inner-sphere complexes (at lower frequency). In addition to uv spectral and ultrasonic detection, polarimetry and nmr methods have also been used to monitor and measure the strength of the interaction. There are difficulties in assessing the value of ATq, the outer-sphere formation constant. The assemblage that registers as an ion pair by conductivity measurements may show a blank spectroscopically. The value of Aq at T" K may be estimated using theoretically deduced expres-... 

The equilibria considered up to now have all involved inner sphere complexes. There is the possibility that an inner sphere complex may react with free ligands in solution this includes the solvent itself, to give an outer sphere complex where the ligand enters the secondary solvation shell of the inner sphere complex. If the two species involved in this type of interaction are of opposite sign, which is the situation where this type of complex formation is expected to be most effective, the outer sphere complex is called an ion pair. Fuoss65 has derived an expression (equation 38) for the ion pair formation constant, XIP, from electrostatic arguments ... 

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 ... 

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