Reactive spheres diffusion-controlled rate

The effect of OH and O 2 on the reactivity of complexes deserves special mention. It was found that some hydroxy complexes—e.g., Al(OH)4 and Zn(OH)4 2, are extremely inert to attack by e aq (11). Since no orbitals are involved in these cases, it must be concluded that OH is an extremely poor bridge for electrons. Hydroxy complexes which still contain water in their inner sphere, like cuprate (II), chromate (III), or plumbate(II) do not differ as much from their corresponding aquo complexes. The inhibitory effect of O-2 on the reactivity of the central atom is not sufficient to suppress the reactivity of the metal ions in their higher states of oxidation. Thus we find that Mn04 or Cr207 2 react at diffusion-controlled rates (122). 

Two Spheres. The steady state diffusion controlled rate constant for two uniformly reactive spheres interacting via a centrosymmetric potential of mean force can be solved numerically and in special cases analytically as given by Eq. 2. For a potential of mean force of zero and no hydrodynamic interaction (NHI), Eq. 2 reduces to the Smoluchowski result (1)... 

The hydrolysed iron(ra) species is considered to react by an inner-sphere mechanism, being more reactive than Fe(H20) + by a factor of 5 x 10 probably due to the bridging nature of the hydroxy-group. The corresponding reaction involving the CuOH+ species is discounted since the rate constant calculated exceeds that for the diffusion-controlled value in water at 25 °C. 

---