Eigen-Fuoss Equation
A further insight into the pre-equilibrium step and its equilibrium constant KE comes from the Fuoss-Eigen equation proposed independently by Eigen and R. M. Fuoss:
- KE = (4πa3/3000) x NAexp(-V/RT)
Where a represents the minimum distance of approach between complex and ligand in solution, NA 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 KE is 20.2 dm3mol−1 for neutral particles at a distance of 200 pm. The result of the rate law is that at high concentrations of Y, the rate approximates ktot while at low concentrations the result is kKEtot. The Eigen-Fuoss equation shows that higher values of KE (and thus a faster pre-equilibrium) are obtained for large, oppositely-charged ions in solution.
Read more about this topic: Associative Substitution, Eigen-Wilkins Mechanism
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