In this chapter, the Poisson–Boltzmann equation is solved in spherical polar coordinates using what is known as the Debye–Hückel approximation. The goal is to calculate the ion activity coefficients, whose concentration dependence lies behind the non-ideal behavior of solutions of electrolytes. Formulae for the ion activity coefficients are given in the both the Debye–Hückel limitingDebye – Huckel limiting form, which applies rigorously in the limit of infinitely dilute solution, and also in a practical form which applies in the case of moderately concentrated solutions. The Debye–Hückel theory of activity coefficients is applicable to both equilibrium phenomena and dynamic phenomena. Examples of equilibrium phenomena include the solubility of an ionic solid in water and the analysis of the effect of a strong electrolyte on the ionization of a weak acidWeak acid. In the case of dynamic phenomena, the theory can be used to calculate: (1) the effect of the ion concentration on the rate coefficientRate coefficient for an ionic reaction, and (2) the effect of the ionization of a weak electrolyte on its conductivity.