The reaction enthalpy of hydrogen dissociation calculated with the Small System Method from simulation of molecular fluctuations

Abstract

We show how we can find the enthalpy of a chemical reaction under non-ideal conditions using the Small System Method to sample molecular dynamics simulation data for fluctuating variables. This method, created with Hill's thermodynamic analysis, is used to find properties in the thermodynamic limit, such as thermodynamic correction factors, partial enthalpies, volumes, heat capacities and compressibility. The values in the thermodynamic limit at (T,V, μ_j) are then easily transformed into other ensembles, (T,V,N_j) and (T,P,N_j), where the last ensemble gives the partial molar properties which are of interest to chemists. The dissociation of hydrogen from molecules to atoms was used as a convenient model system. Molecular dynamics simulations were performed with three densities; ρ = 0.0052 g cm⁻³ (gas), ρ = 0.0191 g cm⁻³ (compressed gas) and ρ = 0.0695 g cm⁻³ (liquid), and temperatures in the range; T = 3640–20 800 K. The enthalpy of reaction was observed to follow a quadratic trend as a function of temperature for all densities. The enthalpy of reaction was observed to only have a small pressure dependence. With a reference point close to an ideal state (T = 3640 K and ρ = 0.0052 g cm⁻³), we were able to calculate the thermodynamic equilibrium constant, and thus the deviation from ideal conditions for the lowest density. We found the thermodynamic equilibrium constant to increase with increasing temperature, and to have a negligible pressure dependence. Taking the enthalpy variation into account in the calculation of the thermodynamic equilibrium constant, we found the ratio of activity coefficients to be in the order of 0.7–1.0 for the lowest density, indicating repulsive forces between H and H₂. This study shows that the compressed gas- and liquid density values at higher temperatures are far from those calculated under ideal conditions. It is important to have a method that can give access to partial molar properties, independent of the ideality of the reacting mixture. Our results show how this can be achieved with the use of the Small System Method.