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