Difference between revisions of "Eigen-Wilkins Mechanism"

Latest revision as of 19:18, 21 September 2010

The Eigen-Wilkins mechanism, named after the German chemist Manfred Eigen and R. G. Wilkins,^[1] is a mechanism and rate law in coordination chemistry governing the associative substitution reactions of octahedral complexes. It was discovered for substitution by ammonia of a chromium-(III) hexaaqua complex.^[2][3] The key feature of the mechanism is an initial rate-determining pre-equilibrium to form an encounter complex ML₆-Y from reactant ML₆ and incoming ligand Y. This equilibrium is represented by the constant K_E while the subsequent dissociation to form product P is governed by a rate constant k:

ML₆ + Y 15px ML₆ → P

Derivation

A simple derivation of the Eigen-Wilkins rate law follows:^[4]

[ML₆-Y] = K_E[ML₆][Y]

[ML₆-Y] = [M]_tot - [ML₆]

rate = k[ML₆-Y]

rate = kK_E[Y][ML₆]

Leading to the final form of the rate law,

rate = kK_E[Y][M]_tot / (1 + K_E[Y])

Eigen-Fuoss Equation

A further insight into the pre-equilibrium step and its equilibrium constant K_E comes from the Fuoss-Eigen equation proposed independently by Eigen and R. M. Fuoss:

K_E = (4πa³/3) x N_Aexp(-V/RT)

Where a represents the minimum distance of approach between complex and ligand in solution, N_A is the Avogadro constant, R is the gas constant and T is the reaction temperature. V is the Coulombic potential energy of the ions at that distance:

V = z₁z₂e²/4πaε

Where z is the charge number of each species and ε is the vacuum permittivity.

A typical value for K_E is 20.2 dm³mol^-1 for neutral particles at a distance of 200 pm.^[5]

Results

The result of the rate law is that at high concentrations of Y, the rate approximates k[M]_tot while at low concentrations the result is kK_E[M]_tot[Y].

The Eigen-Fuoss equation shows that higher values of K_E (and thus a faster pre-equilibrium) are obtained for large, oppositely-charged ions in solution.

References

1. ↑ M. Eigen, R. G. Wilkins: Mechanisms of Inorganic Reactions. In: Advances in Chemistry Series. Nr. 49, 1965, S. 55. American Chemical Society, Washington, D. C.
2. ↑ Basolo, F.; Pearson, R. G. "Mechanisms of Inorganic Reactions." John Wiley and Son: New York: 1967. ISBN 047105545X
3. ↑ R. G. Wilkins "Kinetics and Mechanism of Reactions of Transition Metal Complexes," 2nd Edition, VCH, Weinheim, 1991. ISBN 1-56081-125-0
4. ↑ G. L. Miessler and D. A. Tarr “Inorganic Chemistry” 3rd Ed, Pearson/Prentice Hall publisher, ISBN 0-13-035471-6.
5. ↑ Atkins, P. W. (2006). Shriver & Atkins inorganic chemistry. 4th ed. Oxford: Oxford University Press