Page 270 - MODERN ELECTROCHEMISTRY

206 CHAPTER 2

taken as the basis for a change of energy upon the transfer from vacuum to solution,
one has
Energy of charging in vacuum:

Energy of charging in solution:
where is the dielectric constant of the solution.
Hence, the work of charging in solution, minus the work of charging
the solution, is argued to be a contribution to the solution energy. Therefore,
the corresponding energy change or the so-called Born term is

This equation is used in most theories of solvation (Section 2.15.10) as though it
represented, not the difference in the energy of charging up a conducting sphere in
vacuo and then in solution, but the energy of interaction of an ion with a solvent.
There are a number of fundamental difficulties with the Born equation, which is
still presented in this text because of the prominent part it plays in most theories (it
accounts for around one-third of the hydration energy calculated for simple ions).
1. Behind the idea of the work of charging is an assumption that the charging
occurs slowly, so that all parts of the system concerned are arranged in their equilib-
rium configuration. This is arguable. Any real change of charge on an ion in solution
occurs in a time of about s, so fast, indeed, that atomic motions in molecules
(e.g., vibrations) are taken to be stationary in comparison (Franck–Condon principle).
2. The thinking behind the deduction of Born’s equation is pre-quantal. In reality,
atoms do not charge up by the aggregation of a series of infinitesimally small amounts
of charge. They become charged by means of the sudden transfer of one electron. The
energy of charging an atom to a positive ion is called the ionization energy and is a
known quantity. The energy of charging an atom to be a negative ion is called the
electron affinity and is also known. Both these energies differ significantly from the
Born energy of charging.
3. Although the Born charging energy differs from either the ionization energy
or the electron affinity, its values for simple ions are not unreasonable. However, when
one comes to apply Born’s concepts to protons and electrons, irrational energies result.
For example, the Born energy of a proton in the gas phase is 1000 times the normal
range of chemical energies. The corresponding self-energy for an electron alone is
greater than
So, Born’s equation remains a controversial part of the theory of solvation
although there have been many recent attempts striving to justify it. The difficulty
resides in the avoidance of molecular-level arguments and in applying continuum
electrostatics, which clearly involves fundamental limitations when it comes to atomic