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.

Diglycolamic Acid-Functionalized MWCNT-Augmented Polymeric Beads for Efficient Separation of Trivalent Lanthanides and Actinides

“…Understanding the thermodynamics of sorption processes is a very important aspect that needs to be linvestigated. The values of the thermodynamic parameters such as Gibbs free energy (Δ G °), enthalpy (Δ H °), and entropy (Δ S °) are calculated by the following three equations , ln nobreak0em0.25em⁡ K D = normalΔ S ° R − normalΔ H ° RT normalΔ G = normalΔ H − T normalΔ S normalΔ G ° = prefix− italicRT 0.25em ln nobreak0em0.25em⁡ K D where K D is the conditional equilibrium constant, R is the universal gas constant (8.314 J mol –1 K –1 ), and T is the temperature in K . The plots of ln K D vs 1/ T are shown in Figure .…”

“…Understanding the thermodynamics of sorption processes is a very important aspect that needs to be linvestigated. The values of the thermodynamic parameters such as Gibbs free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°) are calculated by the following three equations 41,42…”

Effect of frozen storage on preservation of a silicone-based test food material

“…Moreover, lower temperatures slow down the natural degradation of the polymer by decreasing the activation energy for these reactions and also slowing the propagation of microorganisms. However, no uniform reduction in reaction rate has been observed as the temperature is lowered, although there is a certain extent of adherence to Van't-Hoff's rule (the velocity of a chemical reaction increases two-fold or more for each 10°C increase in temperature) 13 . The latter is generally true when a temperature approximates that at which a reaction normally occurs.…”

“…Polydimethylsiloxanes are organosilicon polymers that are composed of a Si-O-linked backbone, repeating units of -[(CH 3 ) 2 Si-O-] n , and silanol end groups 12 . As a result, silicone exhibits ther-mal stability, minimal temperature effects, and low-temperature performance 13 . This molecular configuration also provides excellent release features and surface activity, antifriction and lubricity, good damping behavior, shear stability, hydrophobic and physiological inertness, and weak intermolecular forces 12,13 .…”

Role of virial coefficients in chemical reaction

“…The resulting equation predicts that the logarithm of equilibrium constant K (ratio of rate constants associated to forward and backward reactions) is inversely proportional to temperature T . However this is not the case with some chemical reactions [2,3,4]. With these results in mind, here we revisit the van't Hoff equation by relaxing the ideal gas approximation.…”