Phase equilibrium of methane and nitrogen at low temperatures: Application to Titan

Abstract

Methane and nitrogen are partially miscible in the condensed phase. Although there are experimental data on the vapor-liquid equilibria of methane-nitrogen mixtures at the low temperatures characterizing much of Titan's lower atmosphere, in many cases only the temperature, total vapor pressure, and composition of the liquid phase have been measured. The composition of the vapor phase is uniquely determined as a consequence of the Gibbs phase rule, and we compute the vapor composition for these data by integration of the Gibbs-Duhem equation. We examine the thermodynamic consistency of published measurements and calculations of the vapor phase composition. Using the profile of Titan's atmospheric temperature derived from Voyager radio occultation measurements, we also compute the saturated mole fraction of gaseous methane as a function of altitude up to the 700-mbar level. We find that it lies approximately halfway between that computed from Raoult's Law for a gas in equilibrium with an ideal solution of liquid nitrogen and methane and that for a gas in equilibrium with pure liquid methane. Above this level, the equilibrium condensed phase will freeze. If, however, a supercooled liquid phase is assumed, the experimental measurements can be extrapolated to a lower pressure and temperature, and the vertical profile of gaseous methane can be extended to the cold trap near 344 mbar, where the saturated mole fraction of tropospheric methane is a minimum. If uniform mixing of methane above this level is assumed, the occultation measurements may be adjusted for the presence of this constituent in the stratosphere. At the cold trap the mole fraction of methane in equilibrium with supercooled droplets in a nitrogen-methane atmosphere is 0.017 ± 0.001.