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.^[1]^[2]

$\Delta G=-{\frac {N_{A}z^{2}e^{2}}{8\pi \varepsilon _{0}r_{0}}}\left(1-{\frac {1}{\varepsilon _{r}}}\right)$ 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

^ Born, M. (1920-02-01). "Volumen und Hydratationswärme der Ionen". Zeitschrift für Physik (in German). 1 (1): 45–48. Bibcode:1920ZPhy....1...45B. doi:10.1007/BF01881023. ISSN 0044-3328. S2CID 92547891.
^ Atkins; De Paula (2006). Physical Chemistry (8th ed.). Oxford university press. p. 102. ISBN 0-7167-8759-8.

[1] Born, M. (1920-02-01). "Volumen und Hydratationswärme der Ionen". Zeitschrift für Physik (in German). 1 (1): 45–48. Bibcode:1920ZPhy....1...45B. doi:10.1007/BF01881023. ISSN 0044-3328. S2CID 92547891.

[2] Atkins; De Paula (2006). Physical Chemistry (8th ed.). Oxford university press. p. 102. ISBN 0-7167-8759-8.

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