On the behavior of the osmotic second virial coefficients of gases in aqueous solutions: Rigorous results, accurate approximations, and experimental evidence

We present a novel molecular-based approach for the determination of the osmotic second virial coefficients of gaseous solutes in dilute binary solutions, according to a recently proposed molecular thermodynamic formalism of gas solubility [A. A. Chialvo, J. Chem. Phys. 148, 174502 (2018) and Fluid Phase Equilib. 472, 94 (2018)]. We discuss relevant solvation fundamentals and derive new expressions including (i) the relations among infinite-dilution solvation quantities leading to a novel self-consistent route to the calculation of the osmotic second virial coefficients, (ii) the new microstructural interpretation of the resulting osmotic second virial coefficients based on Kirkwood Buff integrals, the unambiguous discrimination between short- and long-range contributions, and their limiting behavior as the solvent approaches its critical conditions, (iii) new rigorous expressions for the calculation of the osmotic second virial coefficients using standard reference thermodynamic data, and (iv) their underlying interdependence based on the constrained state variable invoked in the density expansion. We then invoke the proposed formalism to shed some light on the inaccuracies behind current calculations of osmotic second virial coefficients from molecular theory and simulation as well as macroscopic correlations. To advance the microscopic understanding and illustrate the functional relationship between the osmotic second virial coefficients, Henry's law constant, and the solute-solvent inter molecular asymmetry as a source of solution non-ideality, we use data for the microstructural and thermodynamic behavior of infinitely dilute Lennard-Jones systems obtained self-consistently via integral equations calculations. The newly derived relationships leading to the proposed formalism offer novel routes for the accurate determination of osmotic second virial coefficients of any type of solutes in dilute solutions regardless of the type and nature of the intermolecular interactions. However, for illustration purposes in the current work, we dealt with aqueous solutions of simple gases to exploit the abundance of standard thermodynamic data for the orthobaric Henry's law constant and solute distribution coefficients, as well as the availability of results from molecular based calculations and macroscopic correlations.