HR: 0800h
AN: A51C-0800    [Abstracts]
TI: Theoretical Calculations of Exchange Equilibria Involving Multiply-Substituted Isotopologues of Molecular Gases
AU: * Wang, Z
EM: wzhr@gps.caltech.edu
AF: Caltech, Division of Geological and Planetary Sciences, M/C 100-23, Pasadena, CA 91125 United States
AU: John, E M
EM: eiler@gps.caltech.edu
AF: Caltech, Division of Geological and Planetary Sciences, M/C 100-23, Pasadena, CA 91125 United States
AU: Schauble, E A
EM: schauble@ess.ucla.edu
AF: UCLA, Department of Earth and Space Sciences, P.O. Box 951567, Los Angeles, CA 90095 United States
AB: Heavy stable isotopes are not randomly distributed among molecules in thermodynamically equilibrated mono-molecular gases (e.g., O$_{2}$, N$_{2}$, or CO$_{2}$), but instead preferentially concentrate into bonds with each other (e.g., $^{18}$O-$^{18}$O, $^{15}$N-$^{15}$N, etc.). This occurs because such bonds have exceptionally low zero point energies and thus are comparatively more stable. This zero point energy effect is subtle (typically at per-mil level) but has recently been shown to be measurable. The abundances of isotopologues of molecular gases containing more than one rare isotope (`multiply-substituted isotopologues') could be used for a variety of geochemical applications, including geothermometry, and such applications will require a sound understanding of these zero-point energy effects. This study presents methods and data for theoretically estimating the strength of these effects, and discusses possible applications. Accompanying abstracts by Afek et al., Eiler et al., Ghosh et al. and Schauble et al. provide analytical details, analogous models for condensed phases, and illustrative applications. We have derived a method for systematically evaluating the influence of the zero point energy effect in the abundances of all isotopologues in thermodynamically equilibrated populations of O$_{2}, CO, N$_{2}$, NO, CO$_{2}$ and N$_{2}$O between 1000 and 193 to 77 K. This method uses Urey-type algorithms (based on simple harmonic oscillator and rigid rotor model) to evaluate partition functions and equilibrium constants of isotope exchange reactions, and simultaneously solves for abundance of each isotopologue of a given molecule constrained by all independent equilibria. We also examine the accuracy of the Urey-type models by comparison with direct summations over all experimentally or empirically determined energy levels to calculate partition functions. This comparison is only made for CO and CO$_{2}$ due to limitations in spectroscopic data, but in these cases there are no significant differences among methods. Calculation results also show that, in most cases, multiply-substituted isotopologues are predicted to be enriched relative to stochastic (random) distributions by ca. 1 to 2 per mil at earth-surface temperatures. This deviation, defined as \Delta$_{i}$ for isotopologue i, generally increases linearly with 1/T at temperatures $<$ 500 K, and with 1/T$^{2}$ at temperatures $>$ 500 K. An exception is N$_{2}$O, which shows complex temperature dependences and 10's of per-mil enrichments or depletions of abundances for some isotopologues. These theoretical calculations provide a basis for discriminating between fractionations controlled by equilibrium thermodynamics and other sorts of isotopic fractionations in the budgets of atmospheric gases. Moreover, because abundances of multiply-substituted isotopologues in thermodynamically equilibrated populations of molecules vary systematically with temperature, they can be used as geothermometers. Such thermometers are unusual in that they involve homogeneous rather than heterogeneous equilibria (e.g., isotopic distribution in gaseous CO$_{2}$ alone, rather than difference in isotopic composition between CO$_{2}$ and coexisting water). Also, multiple, independent thermometers exist for all molecules having more than one multiply-substituted isotopologue (e.g., thermometers based on abundances of $^{18}$O$^{13}$C$^{16}$O and $^{18}$O$^{12}$C$^{18}$O are independent); thus temperatures estimated by this method can be tested for internal consistency.
DE: 4825 Geochemistry
DE: 4870 Stable isotopes
DE: 1040 Isotopic composition/chemistry
DE: 0300 ATMOSPHERIC COMPOSITION AND STRUCTURE
DE: 0345 Pollution--urban and regional (0305)
SC: Atmospheric Sciences [A]
MN: 2004 AGU Fall Meeting