An Interpretation of the Vapor Phase Second Virial Coefficient Isotope Effect:  Correlation of Virial Coefficient and Vapor Pressure Isotope Effects

Abstract

Experimental data on vapor phase second virial coefficient isotope effects (VCIEs) are reviewed and then interpreted using the general theory of isotope effects. Useful correlations are developed between -∆(Bb o )/(Bb o ) ) (-VCIE) and [ln(f c /f g )]*, where [ln(f c /f g )]* is the reference condensed phase reduced isotopic partition function ratio, and B is the second virial coefficient, b o ) 2πσ 3 /3, σ is the Lennard-Jones size parameter, and ∆ denotes an isotopic difference, light-heavy. [ln(f c /f g )]* can be straightforwardly obtained from measurements of vapor pressure isotope effects for T R ) T/T CRITICAL < 0.7. We show (-VCIE) ) ln(f p /f g 2 ) where ln(f p /f g 2 ) is the reduced isotopic partition function ratio associated with the equilibrium between isolated gas-phase monomer species and interacting pairs. At temperatures well removed from crossovers in ln(f p /f g 2 ) or [ln(f c /f g )]*, ln(f p /f g 2 ) ) (0.4 ( 0.2) [ln(f c /f g )]*. * To whom correspondence may be addressed.µ′ cµ c ) -RT ln(〈Q′ c 〉/〈Q c 〉) + (P′V′ c -PV c ) (1) 9284

Isotope effects on VLE properties of fluids and corresponding states: Critical point shifts on isotopic substitution

“…B II and B II are well defined, but in poor agreement with experiment [1]. For VdW1, however, α is adjustable over the range (1.75 < α < 2.25).…”

“…These effects share a common origin in quantum effects on vibrational properties. Recently we discussed the molecular origins of the virial coefficient IE [1], illustrating the close relationship between virial coefficient and vapor pressure IE's by comparing standard state free energy differences between average condensed phase molecules or average gasphase dimers, on one hand, and the dilute gas-phase reference on the other. The approach clarified a long-standing confusion arising from the convenience of expressing virial coefficients (and their IE's) using parameter sets that define an intermolecular potential (and IE's) (ε, σ, ε/ε, σ/σ) [2][3][4][5][6], as compared to the use of a complete set of vibrational frequencies and their isotope dependences [7][8][9][10] to describe vapor pressure IE's.…”

i&lt;sub&gt;N&lt;/sub&gt;RACM: incorporating &lt;sup&gt;15&lt;/sup&gt;N into the Regional Atmospheric Chemistry Mechanism (RACM) for assessing the role photochemistry plays in controlling the isotopic composition of NO&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;, NO&lt;sub&gt;&lt;i&gt;y&lt;/i&gt;&lt;/sub&gt;, and atmospheric nitrate

“…For example, α NO/NO 2 is the temperature-dependent isotope fractionation factor (EIE) for NO + 15 NO 2 ←→ 15 NO + NO 2 . In this case, at 298 K β NO = 1.0669, β NO 2 = 1.1064, and α NO/NO 2 = β NO /β NO 2 = 0.9643 (Walters and Michalski, 2015).…”

i&lt;sub&gt;N&lt;/sub&gt;RACM: Incorporating &lt;sup&gt;15&lt;/sup&gt;N into the Regional Atmospheric Chemistry Mechanism (RACM) for assessing the role photochemistry plays in controlling the isotopic composition of NO&lt;sub&gt;x&lt;/sub&gt;, NO&lt;sub&gt;y&lt;/sub&gt;, and atmospheric nitrate.

“…Isotopologues partition differently between phases giving rise to the VPIE. This is most notable in gas-liquid systems [Van Hook et al, 2001], but also can occur in gas-solid equilibrium.…”