A comprehensive experimental investigation of absolute ion and neutral species densities in an inductively coupled H_2-N_2-Ar plasma was carried out. Additionally, the radical and ion densities were calculated using a zero-dimensional rate equation model. The H_2-N_2-Ar plasma was studied at a pressure of 1.5 Pa and an rf power of 200 W. The N_2 partial pressure fraction was varied between f_N2 = 0 % and 56 % by a simultaneous reduction of the H_2 partial pressure fraction. The Ar partial pressure fraction was held constant at about 1 %. NH_3 was found to be produced almost exclusively on the surfaces of the chamber wall. NH_3 contributes up to 12 % to the background gas. To calculate the radical densities with the rate equation model it is necessary to know the corresponding wall loss times t_wrad of the radicals. t_wrad was determined by the temporal decay of radical densities in the afterglow with ionization threshold mass spectrometry during pulsed operation and based on these experimental data the absolute densities of the radical species were calculated and compared to measurement results. Ion densities were determined using a plasma monitor (mass and energy resolved mass spectrometer). H^+_3 is the dominant ion in the range of 0.0 ≤ f_N2 < 3.4 %. For 3.4 < f_N2 < 40 % NH^+_3 and NH^+_4 are the most abundant ions and agree with each other within the experimental uncertainty. For f_N2 = 56 % N_2H^+ is the dominant ion while NH^+_3 and NH^+_4 have only a slightly lower density. Ion species with densities in the range between 0.5 and 10 % of n_i,tot are H^+_2 , ArH^+, and NH^+_2. Ion species with densities less than 0.5 % of n_i,tot are H^+, Ar^+, N^+, and NH^+. Our model describes the measured ion densities of the H_2-N_2-Ar plasma reasonably well. The ion chemistry, i.e., the production and loss processes of the ions and radicals, are discussed in detail. The main features, i.e., the qualitative abundance of the ion species and the ion density dependence on the N_2 partial pressure fraction, are well reproduced by the model.