A general model for the solubilities of gases in liquids
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ORIGINAL PAPER
A general model for the solubilities of gases in liquids Jane S. Murray 1 & Paul G. Seybold 2 & Rubin Battino 2 & Peter Politzer 1 Received: 25 May 2020 / Accepted: 3 August 2020 / Published online: 20 August 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The solubility of a compound is one of its most important properties. Here, regression relationships are presented for solubilities of a series of gases in water and in four organic solvents, treating each solvent separately. The solubilities are related to the Coulombic intermolecular interactions arising from the intrinsic polarities of the solute molecules and the polarities induced in them by the solvent. As a measure of intrinsic polarity, a statistical quantity defined in terms of the solute’s molecular electrostatic potential is used, and the measure of induced polarity is taken to be the solute’s molecular polarizability. Regression analyses show that solubility in water is best expressed in terms of just the intrinsic polarities of the solutes, but for the organic solvents, it is necessary to take into account both the intrinsic and the induced polarities of the solutes. If the dielectric constant of the solvent is included in the regression analysis, then a single relationship can encompass all four organic solvents. Solute molecular volumes were not found to contribute significantly to the present relationships. Keywords Gaseous solubility . Aqueous solutions . Organic solvents . Electrostatic potentials . Polarizability . Coulombic interactions . Dispersion
Solubility and polarizability From various standpoints, ranging from medicinal and pharmacological to environmental, the solubilities of compounds are among their most important properties. It has been demonstrated that the solubilities of gases in organic solvents can be expressed quite well as linear functions of just the polarizabilities of the gas molecules [1]. The correlations can be improved by including quadratic polarizability terms. In the latter relationships, the linear polarizability term is dominant and has a positive sign; solubility increases with polarizability. However, the smaller quadratic term has a negative sign; i.e., it diminishes solubility. This may indicate that it is a correction for some other factor. The strong dependence upon polarizability suggests a prominent role for noncovalent solute-solvent attractive interactions involving induced polarities, such as are involved in
* Jane S. Murray [email protected] 1
Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA
2
Department of Chemistry, Wright State University, Dayton, OH 45459, USA
dispersion forces [2]. These are Coulombic in nature, whether described in terms of London’s [3] or Feynman’s [4] analysis. The situation becomes different when water is the solvent [1, 5]. Relating the aqueous solubilities of a series of gases to molecular polarizabilities simply produced a scatter plot [1]. Clearly, something else must be involved. We will
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