Inner-sphere complexes, without water

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... 

When metal cations are placed in aqueous solutions two kinds of spheres normally appear (a) a sphere of water molecules that binds directly to the metal, called inner coordination sphere (or simply, inner sphere), and (b) a more loosely bound group of water molecules (not directly bound to the metal), called outer coordination sphere (or simply, outer sphere). In this way, a cationic complex can have an outer sphere interaction with an ionic ligand or a solvent molecule without displacing the inner ligands directly bonded to the metal. At higher anion concentrations, the outer sphere complex [M(H20)6]n+An is more prevalent than its corresponding inner sphere complex, [M(H20)5A], Interestingly, the number of inner-... 

Adsorption defines the accumulation of a substance, or material, at tlie interface between a solid surface and a bathing solution (Sparks, 2002). Within the adsorption framework, the individual components are referred to as the adsorbate, the accumulating material at the interface, and the adsorbent, or solid surface (Sparks, 2002). If adsorption occurs and results in the formation of a stable molecular phase at the interface, this entity can be described as a surface complex. Two general surface complexes exist and are described by the configuration geometry of the adsorbate at the adsorbent surface. These are the iiuier-and outer-sphere surface complexes, defined by the presence, or absence, of the hydration sphere of the adsorbate molecule upon interaction. When at least one water molecule of the hydration sphere is retained upon adsorption, the surface complex is referred to as an outer-sphere complex (Sposito, 1984) when an ion or molecule is bound directly to the adsorbent without the presence of the hydration sphere, an inner-sphere complex is formed. 

As an example of behavior of a typical Gd-complex and Gd-macromolecule we discuss here the NMRD profiles of a derivative of Gd-DTPA with a built-in sulfonamide (SA) and the profile of its adduct with carbonic anhydrase (see Fig. 37) 100). Other systems are described in Chapter 4. The profile of Gd-DTPA-SA contains one dispersion only, centered at about 10 MHz, and can be easily fit as the sum of the relaxation contributions from two inner-sphere water protons and from diffusing water molecules. Both the reorientational time and the field dependent electron relaxation time contribute to the proton correlation time. The fit performed with the SBM theory, without... 

Given that the concentration deviation for species E, H20, will be negligible, the second term on the right side of Eq. 4.32b will reduce to -k bAcD, making the corresponding term in Eq. 4.34b equal to - (k b + k f)AcD, and a equal to (k b + k f) in Eq. 4.36e. From Eq. 4.39 it then follows that the second term on the right in Eq. 4.41b will be simply k b, without the equilibrium concentrations of species D and E, in this case. Thus, if outer-sphere surface complexation is much faster than inner-sphere surface complexation and if the effect of any perturbation of the reactions in Eq. 4.40 on the concentration of water is negligible, the linear relationships... 

---