Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O

Heng, Kevin; Lyons, James R.; Tsai, Shang-Min (2016). Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O. Astrophysical journal, 816(2), p. 96. Institute of Physics Publishing IOP 10.3847/0004-637X/816/2/96

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We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.

Item Type:

Journal Article (Original Article)


08 Faculty of Science > Physics Institute > Space Research and Planetary Sciences
10 Strategic Research Centers > Center for Space and Habitability (CSH)

UniBE Contributor:

Heng, Kevin and Tsai, Shang-Min


500 Science > 520 Astronomy
500 Science > 530 Physics
600 Technology > 620 Engineering




Institute of Physics Publishing IOP




Danielle Zemp

Date Deposited:

19 Jul 2017 08:14

Last Modified:

19 Jul 2017 08:14

Publisher DOI:





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