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Predictive synthesis of aqueous organic solutions with desired liquid–solid phase equilibria could drive progress in industrial chemistry, cryopreservation, and beyond, but is limited by the predictive power of current solution thermodynamics models. In particular, few analytical models enable accurate liquidus and eutectic prediction based only on bulk thermodynamic properties of the pure components, requiring instead either direct measurement or costly simulation of solution properties. In this work, we demonstrate that a simple modification to the canonical ideal solution theory accounting for the entropic effects of dissimilar molecule sizes can transform its predictive power. Incorporating a Flory-style entropy of mixing term that includes both the mole and volume fractions of each component, we derive size-dependent equations for the ideal chemical potential and liquidus temperature, and use them to predict the binary phase diagrams of water and 10 organic solutes of varying sizes. We show that size-dependent prediction outperforms the ideal model in all cases, reducing average error in the predicted liquidus temperature by 59% (to 5.6 K), eutectic temperature by 45% (to 9.7 K), and eutectic composition by 43% (to 4.7 mol%), as compared to experimental data. Furthermore, by retaining the ideal assumption that the enthalpy of mixing is zero, we demonstrate that, for aqueous organic solutions, much of the deviation from ideality that is typically attributed to molecular interactions may in fact be explained by simple entropic size effects. These results suggest an underappreciated dominance of mixing entropy in these solutions, and provide a simple approach to predicting their phase equilibria.

Phase stability, and the limits thereof, are a central concern of materials thermodynamics. However, the temperature limits of equilibrium liquid stability in chemical systems have only been widely characterized under constant (typically atmospheric) pressure conditions, whereunder these limits are represented by the eutectic. At higher pressures, the eutectic will shift in both temperature and chemical composition, opening a wide thermodynamic parameter space over which the absolute limit of liquid stability, i.e., the limit under arbitrary values of the thermodynamic forces at play (here pressure and concentration), might exist. In this work, we use isochoric freezing and melting to measure this absolute limit for the first time in several binary aqueous brines, and nodding to the etymology of “eutectic”, we name it the “cenotectic” (from Greek “κοινός-τῆξῐς”, meaning “universal-melt”). We discuss the implications of our findings on ocean worlds within our solar system and cold ocean exoplanets; estimate thermodynamic limits on ice crust thickness and final ocean depth (of the cenotectic or “endgame” ocean) using measured cenotectic pressures; and finally provide a generalized thermodynamic perspective on (and definition for) this fundamental thermodynamic invariant point.