In an effort to establish the optimum conditions for depositing high-quality diamond films at high deposition rates using a plasma torch, modelling work has been focused on developing a realistic model for determining temperature, velocity and particle density distributions in the plasma jet. To enhance molecular decomposition, which favourably improves diamond synthesis, high-speed gas is passed through a supersonic anode nozzle. In the subsequent low-pressure chamber, the chemical reactions cannot follow the fast macroscopic translation, resulting in distributions of dissociated precursors that are far from chemical equilibrium. To simulate the finite rate chemistry, a generalized implicit multi-component algorithm is introduced and examined in the context of a two-dimensional computational model of a chemically reacting Ar-H2 supersonic plasma jet. The scheme can be adapted to other plasma flows in which chemical non-equilibrium is encountered.