### Abstract

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.

Original language | English (US) |
---|---|

Article number | 96 |

Journal | Astrophysical Journal |

Volume | 816 |

Issue number | 2 |

DOIs | |

State | Published - Jan 10 2016 |

### Fingerprint

### Keywords

- methods: analytical
- planets and satellites: atmospheres

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*816*(2), [96]. https://doi.org/10.3847/0004-637X/816/2/96

**ATMOSPHERIC CHEMISTRY for ASTROPHYSICISTS : A SELF-CONSISTENT FORMALISM and ANALYTICAL SOLUTIONS for ARBITRARY C/O.** / Heng, Kevin; Lyons, James; Tsai, Shang Min.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 816, no. 2, 96. https://doi.org/10.3847/0004-637X/816/2/96

}

TY - JOUR

T1 - ATMOSPHERIC CHEMISTRY for ASTROPHYSICISTS

T2 - A SELF-CONSISTENT FORMALISM and ANALYTICAL SOLUTIONS for ARBITRARY C/O

AU - Heng, Kevin

AU - Lyons, James

AU - Tsai, Shang Min

PY - 2016/1/10

Y1 - 2016/1/10

N2 - 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.

AB - 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.

KW - methods: analytical

KW - planets and satellites: atmospheres

UR - http://www.scopus.com/inward/record.url?scp=84954501659&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84954501659&partnerID=8YFLogxK

U2 - 10.3847/0004-637X/816/2/96

DO - 10.3847/0004-637X/816/2/96

M3 - Article

AN - SCOPUS:84954501659

VL - 816

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

M1 - 96

ER -