# 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 (it is thus one member of a class of methods known as continuum solvation methods).

It was derived by Max Born.

where:

*N*_{A}= Avogadro constant*z*= charge of ion*e*= elementary charge, 1.6022×10^{−19}C*ε*_{0}= permittivity of free space*r*_{0}= effective radius of ion*ε*_{r}= dielectric constant of the solvent

## Derivation

The 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

*ε*

_{r}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 (

*ε*

_{r}=1) to a medium of dielectric constant

*ε*

_{r}is:

Categories: