We develop a model for the Helmholtz free energy of fluid hydrogen at high density and high temperature. This model aims at describing both pressure and temperature dissociation and ionization and bears directly on equations of state of partially ionized plasmas, as encountered in astrophysical situations and high-pressure experiments. This paper focuses on a mixture of hydrogen atoms and molecules and is devoted to the study of the phenomenon of pressure dissociation at finite temperatures. In the present model, the strong interactions are described with realistic potentials and are computed with a modified Weeks-Chandler-Andersen fluid perturbation theory that reproduces Monte Carlo simulations to better than 3%%u~. Perturbations of the internal partition functions of H and H2 arising in the nonideal fluid are treated self-consistently with a recently developed occupation probability formalism. Theoretical Hugoniot curves derived from our model are in excellent agreement with experimental data. Pressure dissociation occurs over a narrow density range above 0.5 g/cm' and is remarkably temperature insensitive. Molecules remain the dominant species even at high densities. PACS number(s): 52.25.Jm, 64.30.+t, 05.70.Ce, 65.50.+ m j.INTRODUCTION The past decade has seen tremendous progress in our understanding of dense matter physics, on both the experimental and theoretical fronts. Dynamic compression experiments have revealed exciting new phenomena, such as pressure dissociation in (N2) [1,2], an increase of conductivity upon compression in an initially insulating material (Oz) [3], and they have probed intermolecular potentials down to separations as small as 1.5 A. In particular, experiments on hydrogen and deuterium have determined the H2-Hz interaction potential at high densities [4]Cryogenic samples of solid molecular hydrogen have been compressed to pressures of about 2.5X10 atm, revealing a phase transition in the molecular solid and evidence for reduction of the band gap at the highest pressure reached [5 -7]. This last phenomenon holds the promise of observing the much sought after metallic state of hydrogen in the near future.On the other hand, the recent discovery of global oscillations in Jupiter [8] as well as the achievements of helioand astero-seismology [9,10] give us new information on the interior structure of stars and giant planets, and consequently on the properties of matter under extreme thermodynamic conditions. They offer a unique chance to probe the accuracy of the theoretical models and stress the need for improved equations of state (EOS), particularly in the regime of partial ionization. Indeed, pressure ionization, as well as molecular dissociation, represents a thorny problem in modeling the properties of dense matter. Important advances in statistical physics over the last decade offer the opportunity for significant improvements in our comprehension of this poorly understood phenomenon.Most of the extensive theoretical work on hydrogen has focused on the zero-temperature isotherm whe...