In this paper, a non-equilibrium mathematical model for an argon-oxygen inductively coupled plasma (ICP) torch with a supersonic nozzle is developed without making chemical equilibrium assumptions. Reaction rates of dissociation and recombination of diatomic gas and ionization are taken into account. Higher-order approximations of the Chapman-Enskog method are used to obtain better accuracy for transport properties, taking advantage of the most recent sets of collision integrals available in the literature. In order to validate the developed model, results are compared qualitatively and quantitatively with existing experimental data. The calculated results for the axial temperature profile for pure argon less than 10 mm above the substrate are in good agreement with spectroscopic measurements.