The energy U stored in an electrostatic field distribution is: U = 1 2 ε ε 0 ε ε r ∫ ∫ | E | 2 d V Knowing the magnitude of the electric field of an ion in a medium of dielectric constant ε r is | E | = z e 4 π π ε ε 0 ε ε r r 2 and the volume element d V can be expressed as d V = 4 π π r 2 d r , the energy U can be written as: U = 1 2 ε ε 0 ε ε r ∫ ∫ r 0 ∞ ∞ ( z e 4 π π ε ε 0 ε ε r r 2 ) 2 4 π π r 2 d r = z 2 e 2 8 π π ε ε 0 ε ε r r 0 Thus, the energy of solvation of the ion from gas phase (ε r =1) to a medium of dielectric constant ε r is: Δ Δ G N A = U ( ε ε r ) − − U ( ε ε r = 1 ) = − − z 2 e 2 8 π π ε ε 0 r 0 ( 1 − − 1 ε ε r )