Born equation
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The Born equation can be used for estimating the electrostatic component of
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and ...
of
solvation Solvation (or dissolution) describes the interaction of a solvent with dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence many properties of the ...
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. \Delta G =- \frac\left(1-\frac\right) where: *''N''A =
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining c ...
*''z'' = charge of ion *''e'' =
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
, 1.6022 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:U=\frac \varepsilon_0 \varepsilon_r \int , , ^2 dVKnowing the magnitude of the electric field of an ion in a medium of dielectric constant ''ε''r is , , =\frac and the volume element dV can be expressed as dV=4\pi r^2 dr , the energy U can be written as: U=\frac \varepsilon_0 \varepsilon_r \int_^\infty \left(\frac\right)^2 4\pi r^2 dr=\fracThus, the energy of solvation of the ion from gas phase (''ε''r =1) to a medium of dielectric constant ''ε''r is:\frac = U(\varepsilon_r )- U(\varepsilon_r=1)=- \frac\left(1-\frac\right)


References


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aspects about this equation
Enthalpy Max Born {{Physical-chemistry-stub