A two-dimensional (2D) fluid-analytical transformation coupled to the plasma reactor model was developed using the COMSOL capacitively coupling finite element simulation tool with a plasma source included in the model as well as a capacitive bias for the wafer electrode. The bulk fluid plasma model solves the time-dependent plasma fluid equations for the continuity of H+, H2+, H3+, Ar+ and ArH + ions, and electron density. In this work, the ion-molecule kinetics of cold Ar/H2 plasmas are studied in capacitively coupled discharges mainly focuses on the modalization of an 80% H2/20% Ar mixture to illustrate the production rates of ne, H+, H2+, H3+, Ar+ and ArH+ and mainly the dominant ions H3+, Ar+ and ArH+, for this, we have presented the set of cross-sections of Hydrogen and Argon which enter into the calculation of the transport coefficients of the mixture for a certain percentage of each gas, the results will be compared to the measurement data using the lxcat code and we end our work with a presentation of the 1D results for a variation in the mixture from zero up to 100% Ar where the evolution of H+, H2+, H3+, Ar+ , ArH+ and Ar* ions are illustrated.