The Margules equation is used for interpreting excess Gibbs energy of several ternary systems. An expression for the activity coefficient of a dilute solute, 2(oxygen), in a binary solvent 1--3 is derived. It is used to calculate the logarithmic activity coefficient of oxygen in Pb-O-Cu, Pb-O-Bi, Ag-O-Sn, Pb-O-Sn and Ag-O-Pb metallic systems. Self interaction parameter of the solute is derived from the partial Gibbs energy of solute using constant compositional path. The derived equation is used successfully to deduce the self-interaction parameter of oxygen in Pb-O-Cu and Pb-O-Bi metallic systems. The predicted thermodynamic parameter data i.e. activity coefficient and self-interaction parameters are in an excellent agreement with the experimental data and also the predictions are far more accurate than the predictions made by other models.