Born equation


The Born equation can be used for estimating the electrostatic component of Gibbs free energy of solvation of an ion. It is an electrostatic model that treats the solvent as a continuous dielectric medium.
The equation was derived by Max Born.
where:NA = Avogadro constantz = charge of ione = elementary charge, 1.6022 Cε0 = permittivity of free spacer0 = effective radius of ionεr = dielectric constant of the solvent

Derivation

The Electric potential energy#Energy stored in an electrostatic [field distribution|energy U stored in an electrostatic field distribution] is:Knowing the magnitude of the electric field of an ion in a medium of dielectric constant εr is and the volume element can be expressed as, the energy can be written as: Thus, the energy of solvation of the ion from gas phase to a medium of dielectric constant εr is: