## Abstract

Films of neutral substances adsorbed at the oil/water interface obey the equation of state and the adsorption isotherm which are derived assuming complete mobility of the molecules in the interface. The equations are obeyed down to areas of $\sim $ 30 angstrom $^{2}$ per molecule; deviations which occur below this value result from interactions between the adsorbed molecules. Adsorbed films of completely ionized sodium alkyl sulphates and quaternary ammonium compounds also obey these equations when allowance is made for the electrical contribution to the adsorption energy and for electrical interaction between the ions in the aqueous bulk phase. The activity coefficients cannot be neglected in these systems at concentrations exceeding 0$\cdot $001 M. In the range 0$\cdot $001 to 0$\cdot $09 M the 'complete' Debye-Huckel equation is used to calculate these coefficients; at the higher concentrations (for sodium decyl and octyl sulphates) the activity coefficients thus calculated are suspect. The electrical energy is given exactly by a modified Gouy equation, when allowance is made for the film ions being situated a finite equilibrium distance from the interface and for the fact that counter-ions will be present above the head groups. This modified equation yields linear plots for the isotherm and leads to consistent values for the free energy of adsorption of the molecules. It also (a) demonstrates that the electrical potential at the phase boundary ($\psi _{d}$) differs from that in the plane for the film ions ($\psi _{0}$) and that the true $\psi _{0}$ is lower than that calculated from the simple Gouy equation; from the measured surface potentials ($\Delta $V) interpreted by the equation of Schulman & Hughes (1932), it is shown that the calculated $\psi _{d}$ is experimentally confirmed; (b) predicts much more accurately than the simple equation the relation between the observed surface pressure (II) and area per molecule (equation of state). Deviations from the equations occur for short-chain compounds (C$_{8}$ and C$_{10}$) in water at high concentrations, and for all surface-active agents in high electrolyte concentrations (> M/100), especially where A < 70 angstrom $^{2}$. It is concluded that these deviations result mainly from a neglect of ionic size in the theoretical treatment. There is no evidence in any of the systems for any specific interaction between counter ions and adsorbed film ions. The experimental results are inconsistent with the view that appreciable energy changes associated with dehydration of the surface-active ions occur as they approach the oil/water interface.