An expanding argon-hydrogen plasma is investigated by means of simulations. The effect of molecular hydrogen injection at the start of the expansion on the ionization degree and on the electron and the heavy particle temperatures in the expansion is studied. The used simulation model is the non-local thermal equilibrium one-dimensional model SPeX. The SPeX code is used to investigate the causes of deviation from temperature equilibrium and deviation from ionization-recombination equilibrium. SPeX is a hydrodynamic model specific for plasma expansions, solving the conservation balances of mass, momentum and energy. A decrease in ionization degree and deviations from local thermal equilibrium are shown after the injection of molecular hydrogen for the expansion from an inductively coupled plasma source with a separated Laval-nozzle.