Numerical simulation has been used to study the fluid dynamics and chemical kinetics in a supersonic nozzle situated downstream of a plasma reactor. To assist in system scale-up and optimization, effective nozzle design can help in maximizing the transport of chemically active species to the substrate. This paper examines the chemical non-equilibrium of the flow, the effect of different flow parameters, and the effect of different nozzle geometries. A three species hydrogen-argon gas mixture was modeled with finite dissociation and recombination. Non-equilibrium transport and thermodynamic mixture properties based on species pair collision cross sections were implemented. Running a plasma torch off design power can significantly alter power losses through the nozzle wall and subsequently change the species distribution at the nozzle exit. Decreasing the effective nozzle throat diameter can notably decrease atomic concentrations. Small changes in upstream or downstream pressures have a negligible effect on supersonic species transport through the nozzle. Flow separation can be avoided by correctly designing the divergent portion of the nozzle.