Deviation from van’t Hoff Behavior of Solids at Low Temperature

Abstract

As a sequel to results obtained on the low-temperature behavior of liquids, a similar study is presented for solids. A molecule in a solid interacts with the other molecules of the crystal so that it is subjected to a specific multimolecular potential, kT0. At temperature T < T0, the molecules are localized, and at T > T0, they can participate in processes like self-diffusion and evaporation. As a consequence, the van ’t Hoff equation is disobeyed at a low temperature and properties like vapor pressure, diffusion rate, or reactivity are zero below the specific temperature, T0, which here can be interpreted as a temperature of thermal stability of the solid. To account for this view, the van’t Hoff equation, represented by the green curve in the figure, is extended with a suitable pre-exponential factor, leading to the red curve. Three examples, taken from the literature, are analyzed to demonstrate its applicability. These examples are: the thermal dissociation of calcium carbonate, the sublimation equilibrium pressure of naphthalene, and that of ice. For some other solids, equilibria and dynamic properties, X(T), are examined by means of extrapolations in the X(T) versus T domain, showing the presence of an arrest temperature, which coincides, within experimental accuracy, with the T0 value obtained from the corresponding vapor pressure. As with liquids, kT0 is found to be proportional to the molecular pair potential.