In this work, the exactly integrated form of the Clapeyron equation found by Mosselman et al. has been used in a systematic manner to derive a comprehensive set of equations describing the first-order transition curves of pure substances. The application of each of these equations requires the knowledge of only one (reference) point on the particular equilibrium line, of the corresponding enthalpy of transition, and some ancillary data (molar volumes and heat capacities of the phases at equilibrium). No fitting to ( p, T ) experimental data is needed. In this respect the equations developed here can be regarded as a source for calculating a priori the phase equilibrium curves. The results have been tested for a number of selected pure substances of variable molecular complexity, and the uncertainties attached to the calculations have been assessed. Empirical equations currently used for first-order transitions are compared with those obtained from the exact integration. As far as we are aware, no equation was previously proposed for solid + solid equilibrium lines.

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Between 2004 and 2007 the instruments of the CASSINI spacecraft, orbiting within the Saturn system, discovered dark patches in the polar regions of Titan. These features are interpreted as hydrocarbon lakes and seas with ethane and methane identified as the main compounds. In this context, we have developed a lake-atmosphere equilibrium model allowing the determination of the chemical composition of these liquid areas present on Titan. The model is based on uncertain thermodynamic data and precipitation rates of organic species predicted to be present in the lakes and seas that are subject to spatial and temporal variations. Here we explore and discuss the influence of these uncertainties and variations. The errors and uncertainties relevant to thermodynamic data are simulated via Monte-Carlo simulations. Global Circulation Models (GCM) are also employed in order to investigate the pos- sibility of chemical asymmetry between the south and the north poles, due to differences in precipitation rates. We find that mole fractions of compounds in the liquid phase have a high sensitivity to thermodynamic data used as inputs, in particular molar volumes and enthalpies of vaporization. When we combine all considered uncertainties, the ranges of obtained mole fractions are rather large (up to ∼ 8500%) but the distributions of values are narrow. The relative standard deviations remain between 10% and ∼ 300% depending on the compound considered. Compared to other sources of uncertainties and variability, deviation caused by surface pressure variations are clearly negligible, remaining of the order of a few percent up to ∼ 20%. Moreover no significant difference is found between the composition of lakes located in north and south poles. Because the theory of regular solutions employed here is sensitive to thermodynamic data and is not suitable for polar molecules such as HCN and CH 3 CN, our work strongly underlines the need for experimental simulations and the improvement of Titan's atmospheric models.