Review of absorption and adsorption in the hydrogen–palladium system

Abstract

The hydrogen–palladium system has been the subject of much study, both experimentally and computationally. In this review article the authors have set out to draw a comparison between the experimentally determined thermodynamic data for this system and the calculated energies, in order to attempt to bridge the gap between computational chemistry and experimental work and so gain insight into the absorption and adsorption of hydrogen on palladium. Rigorous thermodynamic analysis of the data for the absorption of hydrogen into palladium metal shows that although constant volume measurements have been made, the analysis that has been applied in the literature in several instances is valid only for a constant pressure system. Re-analysis of the data has lead to a heat of formation for β-palladium hydride which is not a function of composition and a weak function of temperature. Values for the internal energy of absorption of −36.7, −35.2 and −34.4 kJ/mol of H 2 were obtained at 0 °C and in the temperature ranges from 200 to 313 °C and from 366 to 477 °C, respectively. There is a good agreement between these values and the calculated values. The implicit assumptions that underpin the integrated form of the Clausius–Clapeyron equation are that an isobaric system is being analyzed, and that the enthalpy is not a function of composition or temperature. Since heat of adsorption is known to be a function of surface coverage and is generally measured in a constant volume system, the application of the integrated Clausius–Clapeyron equation to determine the enthalpy of adsorption as a function of surface coverage has been questioned and an alternative thermodynamic analysis has been proposed that enables one to calculate the differential change in internal energy of adsorption with surface coverage. It has been found that the internal energy of adsorption varies with increasing surface coverage in a similar manner to the way in which internal energy varies as two atoms approach each other. It is noted that the variation in internal energy with surface coverage (0.1 < θ < 0.94) calculated in this work is of the order of 100 J/mol, while the heat of adsorption in the literature is of the order of −87,000 J/mol. Thus, except at very high coverages, the change in internal energy or enthalpy of adsorption with changes in surface coverage is very small compared to the overall heat of adsorption. The computationally determined energies of adsorption do not reflect this trend and appear to under estimate the electrostatic repulsion (or over estimate the attraction) between gas phase molecules and atoms that are already adsorbed on the surface for this system.