Supercritical water oxidation (SCWO) is an effective technique to treat wet organic wastes. Its modeling requires an accurate calculation of thermodynamic properties. In this work an equation of state (EOS) is proposed which accurately predicts the thermodynamic state of mixtures of water, oxygen, nitrogen, and carbon dioxide for a wide range of compositions, temperatures, and pressures including supercritical conditions. The EOS includes a volume translation, an evolved alpha-function and non-quadratic mixing rules. The introduced parameters are regressed to experimental data. From the pressure-explicit EOS, enthalpy, specific heats at constant volume and constant pressure, and fugacity coefficients are derived and calculated. The binary mixtures H2O/O2, H2O/N2, H2O/CO2, N2/CO2 as well as the ternary mixture H2O/O2/N2 are well predicted by the proposed EOS with relative errors below 10% and 15%, respectively. The region of low temperature and high pressure is most difficult to predict with relative errors up to 20%.