Two Theorems Concerning Electrolytes

(1) Fluctuations in the average total electrostatic energy E of the free ions of an electrolytic solution as calculated by the theory of Debye and Huckel are negligibly small in accessible concentration ranges. If delta E = {(E-2) over bar((E) over bar)(2)}(1/2), then delta E/(E) over bar=(-kT/2 (E) over bar)(1/2); i.e., the ratio of the fluctuation in energy to the total energy is of the order of the square root of the ratio of the kinetic energy per degree of freedom of a single molecule to the total electrostatic energy of the system. (2) A general relationship connecting free energy F and average electrostatic energy. (E) over bar is derived; for the case where the average potential around an ion is given by the Debye-Huckel formula, F = 2 (E) over bar /3.