Thermodynamics of Helium-4 Dimerization and Trimerization

Thermodynamics of the van der Waals Dimers of O2, N2 and the Heterodimer (N2)(O2) and Their Presence in Earth's Atmosphere

The dimerization thermodynamics of N2 and O2, the principal components of Earth's atmosphere, have been determined from the respective second virial coefficients of the bound and metastable dimers calculated using the method of Stogryn and Hirschfelder that utilizes the Lennard-Jones (LJ) potential to account for intermolecular interactions. In addition, the thermodynamic properties of the heterodimer (N2)(O2) have been obtained using the same approach, employing combining rules to construct the LJ potential. Thus, Keq, ΔH, and ΔS for the three dimers are reported between 80-120 K. Over this temperature range, the ranking of Keq is (N2)(O2) > (O2)(O2) > (N2)(N2). The same trend is found for the exoethalpicity of dimer formation. For example, at 100 K, the Keq values are, respectively, 0.0406(14), 0.0215(5), and 0.0181(10), and the corresponding ΔH values are -2401(5), -2344(7), and -2279(1) J/mol. The mole fraction composition of the dimers in the atmosphere was calculated for altitudes up to 20 km. These calculations show that in the troposphere and the lower stratosphere (up to 20 km), the three dimers rank fifth to seventh in abundance, between CO2 and Ne. In this region, the average mole fractions of (N2)(N2), (O2)(O2), and (N2)(O2) are calculated to be 3.4(2) × 10-4, 2.80(9) × 10-5, and 1.95(7) × 10-4, respectively.

Thermodynamic Properties of van der Waals Dimers and Trimers of Nonpolar Gases and Their Correlation with Lennard-Jones Potential Well Depths

A method of unifying the equilibrium thermodynamic properties ΔH^o and ΔG^o relating to the van der Waals dimers and trimers of 15 nonpolar gases (He-Xe, H₂, D₂, CH₄, CF₄, ethene, ethane, CO₂, SF₆, propane, and neopentane) is described. Values of ΔH^o and ΔG^o, obtained at the reduced temperature T_r = 0.7, show good correlation with the respective Lennard-Jones pair potential well depth, calculated from the monomer critical temperature and the acentric factor. Such relationships present the opportunity to estimate the van der Waals dimer and trimer thermodynamic properties of other nonpolar molecules, and examples of seven such applications are given. It is found that the enthalpies of dimerization and trimerization of the 15 gases are about 21 and 29% of the respective condensation enthalpies, providing information about the thermodynamics of small clusters in relation to liquefaction.

Equilibrium Thermodynamics of the Dimers and Trimers of H2 and D2 and Their Heterodimer (H2)(D2)

The equilibrium thermochemical properties of the dimers and trimers of H₂ and D₂ are obtained from the equations of state (EOSs) of normal H₂ and D₂. The standard dimer and trimer equilibrium constants K _D ^o and K _T ^o and ΔH _D, T ^o and ΔS _D, T ^o are reported for these weakly bound van der Waals molecules between 25 and 45 K. Statistical thermodynamics (ST) calculations of H₂ and D₂ dimerization using Morse pair potentials to account for intermolecular interactions, obtained from recent experimental work, are in qualitative agreement with the EOS results. The entropies of the H₂ and D₂ dimers and trimers are calculated from the EOS ΔS ^o values and ST calculations of the monomer entropies.