Born equation

The Born equation can be used for estimating the electrostatic component of <a href="/facts/Gibbs_free_energy/bvenDuzh">Gibbs free energy</a> of <a href="/facts/Solvation/JVM6j8R1">solvation</a> 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 <a href="/facts/Continuum_solvation/hkRw1gMX">continuum solvation</a> methods).
The equation was derived by <a href="/facts/Max_Born/6VnUDWhA">Max Born</a>.

Δ
        G
        =
        −
        
          
            
              
                N
                
                  A
                
              
              
                z
                
                  2
                
              
              
                e
                
                  2
                
              
            
            
              8
              π
              
                ε
                
                  0
                
              
              
                r
                
                  0
                
              
            
          
        
        
          (
          
            1
            −
            
              
                1
                
                  ε
                  
                    r
                  
                
              
            
          
          )
        
      
    
    {\displaystyle \Delta G=-{\frac {N_{\text{A}}z^{2}e^{2}}{8\pi \varepsilon _{0}r_{0}}}\left(1-{\frac {1}{\varepsilon _{\text{r}}}}\right)}

where:

<ul><li>NA = <a href="/facts/Avogadro_constant/SwajCq22">Avogadro constant</a></li>
<li>z = charge of ion</li>
<li>e = <a href="/facts/Elementary_charge/lPcj6CoQ">elementary charge</a>, 1.6022×10−19 <a href="/facts/Coulomb/WNV9ueGr">C</a></li>
<li>ε0 = <a href="/facts/Permittivity_of_free_space/gWRUhPGY">permittivity of free space</a></li>
<li>r0 = effective <a href="/facts/Ionic_radius/C3dwKrrB">radius of ion</a></li>
<li>εr = dielectric constant of the solvent</li></ul>

Born equation open-in-new

Born equation