We have used molecular dynamics and Monte Carlo methods to simulate the structure and phase stability of a Pd crystal in thermodynamic equilibrium with molecular hydrogen gas at temperature T and pressure PH2 g. The pressurecomposition-temperature (PCT) curves were deduced under the extreme conditions of an open system (Pd crystal in equilibrium with a large-volume H2 gas reservoir) and a closed system (Pd crystal in equilibrium with H2 gas reservoir of infinitesimal volume). The PCT curves from the open simulations reproduce the experimental observations, including the ubiquitous hysteresis. The PCT curves from the closed-system simulations are continuous curves. Below a tricritical point, the Pd-H system decomposes into two coherent phases. We find excellent agreement between the present simulation results and the predictions of the Schwarz-Khachaturyan theory for the decomposition of a Pd-H alloy into two coherent hydride phases.