Born equation

The Born equation is a means of estimating the Gibbs free energy of solvation of a gaseous 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.

$\Delta G =- \frac{N_A z^2 e^2}{8 \pi \epsilon_0 r_0}\left(1-\frac{1}{\epsilon_r}\right)$

where:

• N_A = Avogadro constant
• z = charge of ion
• e = elementary charge, 1.6022×10⁻¹⁹ C
• ε₀ = permittivity of free space
• r₀ = effective radius of ion
• ε_r = dielectric constant of the solvent