Variations of Surface Tension with Body and Surface Concentrations

Mathematical derivatives of surface tension with body concentration and with surface concentration are examined analytically for solutions in which the activity coefficient of the solute is taken as a linear function of solute concentration in the body, and as fixed at unity in the surface. As an approximation, the surface concentration is taken as a uniform value maintained throughout a surface domain extending from the geometrical surface to a fixed depth into the solution, at which the concentration changes as a step function to the body concentration. The writer accepts previous experimental and theoretical conclusions that for an ionic solute the increment of surface tension per surface ion increases with decreasing ionic radius. The Debye-Hückel equation for the activity coefficient of electrolytes predicts that the activity coefficient of an ionic solute increases with increasing ionic radius. Experimentally, this predicted dependence and its reverse are observed about equally often. For those solutes which behave according to the Debye-Hückel prediction it is found that a negative derivative must exist between the derivatives of surface tension with body and with surface concentration at sufficiently high values of the increment of surface tension per surface ion.