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).
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 (εr =1) to a medium of dielectric constant εr is:
Referencesedit
^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. ISBN0-7167-8759-8.
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born, equation, used, estimating, electrostatic, component, gibbs, free, energy, solvation, electrostatic, model, that, treats, solvent, continuous, dielectric, medium, thus, member, class, methods, known, continuum, solvation, methods, derived, born, displays. 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 D G N A z 2 e 2 8 p e 0 r 0 1 1 e r displaystyle Delta G frac N A z 2 e 2 8 pi varepsilon 0 r 0 left 1 frac 1 varepsilon r right where NA Avogadro constant z charge of ion e elementary charge 1 6022 10 19 C e0 permittivity of free space r0 effective radius of ion er dielectric constant of the solventDerivation editThe energy U stored in an electrostatic field distribution is U 1 2 e 0 e r E 2 d V displaystyle U frac 1 2 varepsilon 0 varepsilon r int bf E 2 dV nbsp Knowing the magnitude of the electric field of an ion in a medium of dielectric constant er is E z e 4 p e 0 e r r 2 displaystyle bf E frac ze 4 pi varepsilon 0 varepsilon r r 2 nbsp and the volume element d V displaystyle dV nbsp can be expressed as d V 4 p r 2 d r displaystyle dV 4 pi r 2 dr nbsp the energy U displaystyle U nbsp can be written as U 1 2 e 0 e r r 0 z e 4 p e 0 e r r 2 2 4 p r 2 d r z 2 e 2 8 p e 0 e r r 0 displaystyle U frac 1 2 varepsilon 0 varepsilon r int r 0 infty left frac ze 4 pi varepsilon 0 varepsilon r r 2 right 2 4 pi r 2 dr frac z 2 e 2 8 pi varepsilon 0 varepsilon r r 0 nbsp Thus the energy of solvation of the ion from gas phase er 1 to a medium of dielectric constant er is D G N A U e r U e r 1 z 2 e 2 8 p e 0 r 0 1 1 e r displaystyle frac Delta G N A U varepsilon r U varepsilon r 1 frac z 2 e 2 8 pi varepsilon 0 r 0 left 1 frac 1 varepsilon r right nbsp References edit Born M 1920 02 01 Volumen und Hydratationswarme der Ionen Zeitschrift fur 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 External links editaspects about this equation nbsp This physical chemistry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Born equation amp oldid 1083767607, wikipedia, wiki, book, books, library,
