A zero-dimensional, semi-empirical model is used to describe the plasma chemistry in an argon plasma jet flowing into humid air, mimicking the experimental conditions of a setup from the Eindhoven University of Technology. The model provides species density profiles as a function of the position in the plasma jet device and effluent. A reaction chemistry set for an argon/humid air mixture is developed, which considers 84 different species and 1880 reactions. Additionally, we present a reduced chemistry set, useful for higher level computational models. Calculated species density profiles along the plasma jet are shown and the chemical pathways are explained in detail. It is demonstrated that chemically reactive H, N, O and OH radicals are formed in large quantities after the nozzle exit and H2, O2(1Δg), O3, H2O2, NO2, N2O, HNO2 and HNO3 are predominantly formed as 'long living' species. The simulations show that water clustering of positive ions is very important under these conditions. The influence of vibrational excitation on the calculated electron temperature is studied. Finally, the effect of varying gas temperature, flow speed, power density and air humidity on the chemistry is investigated.