A steady state global (volume averaged) model is developed for a low pressure (1-100mTorr) high density hydrogen discharge that is diluted with argon. The electron density increases, the dissociation fraction of hydrogen increases and the electron temperature decreases with increased argon dilution. We find that H3+ is the dominant positive ion up to roughly 30% argon dilution at 10mTorr, at which point Ar+ becomes the dominant positive ion. The reaction rates for the creation and destruction of various species are explored versus the discharge pressure. In particular we explore the role of the vibrationally excited levels of the hydrogen molecule in the creation of the negative ion H- through dissociative attachment. The role of the ArH+ ion in the discharge chemistry is discussed and we find that ArH+ plays a significant role in the destruction of the H- ion. Furthermore, the creation and destruction of H 3+ and ArH+ ions are explored. The electronegativity increases with increasing H2 content and reaches a value of approximately unity in a pure H2 discharge at 100mTorr. The model is compared with measurements found in the literature and is found to be in agreement with measurements although certain discrepancies are pointed out and discussed.