Thermodynamic Aspects Phase Equilibrium

The phase equilibrium constitutes a thermodynamic limitation of transfer processes. Therefore, the knowledge of phase equilibrium is an essential precondition for specification and calculation of high-pressure processes. 

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The thermodynamic aspects of hydride formation from gaseous hydrogen are described by means of pressure-composition isotherms in equilibrium (AG = 0). While the solid solution and hydride phase coexist, the isotherms show a flat plateau, the length of which determines the amount of H2 stored. In the pure P-phase, the H2 pressure rises steeply vfith increase in concentration. The two-phase region ends in a critical point T, above which the transition from the a- to the P-phase is continuous. The equilibrium pressure peq as a function of temperature is related to the changes AH° and AS° of enthalpy and entropy ... 

These considerable solvent-dependent shifts demonstrate that for molecules with such pronounced conformational ambiguity, the equilibration of conformations has to be taken into account in the calculation of thermodynamic phase-equilibrium data. In order to enable a consistent treatment, we have implemented an automated conformation equilibration scheme in COSMO therm. A compound X can be represented by a set of COSMO-files for the conformers, and a multiplicity ojx(i) can be assigned to each con-former based on geometrical degeneration aspects. Then the population of a conformer, i, in a solvent S is calculated as... 

Most quantitative theories and calculations in engineering sciences rely on a combination of three fundamental concepts balances (e. g., mass, energy, elemental, momentum), equilibria (e.g., force, reaction, phase equilibria), and kinetics (e. g., momentum, mass and heat transfer, enzymatic and growth kinetics). While balances and kinetic models are used extensively by biotechnologists, the same is not true for thermodynamics, and the equilibrium aspects and non-equilibrium thermodynamics appear to be largely disregarded by many of them. 

Thermodynamic Aspects of Solubility At equilibrium in a saturated solution, the chemical potential, or partial molal free energy, of the solute must be the same in the solution as in the solid phase. If we consider two different saturated solutions, there-fore, both in equilibrium with the same solid phase, the chemical potential of the solute must be the same in both. The chemical potential ( ) and activity (c) are related by the equation p — po — RT In o, where Po is the chemical potential of the substance in the standard state. Hence, if the same standard state is chosen for all the solutions considered, the activity of the solute must be the same in all. 

One last concept must be considered with respect to the thermodynamic aspects of solubility—the condition of equilibrium in mixtures that contain two or more phases. What specific conditions must be met for a particular mixture to be regarded as being in thermodynamic equilibrium A particularly important requirement is that the chemical potential of each component must be the same in all the phases that are present. Numerous boundary conditions apply to this requirement, which have been discussed elsewhere [34]. By introducing the concepts of field and density thermodynamic variables, Griffiths and Wheeler were able to restate the condition of equilibrium for heterogeneous mixtures in a particularly simple, rigorous, and elegant form [35,36]. 

With these concepts in hand, we may now briefly consider some thermodynamic aspects of solubility. Suppose (as above) one starts with pure solute (say, sodium chloride crystals) and pure solvent (water) and adds the salt crystals to the water at constant temperature. Just at the point when they are brought together, a nonequilibrium state exists, because salt has a finite solubility in water but has not yet dissolved. The concentration profile at this time is the step-function described in Fig. 1. The process of dissolving salt in water has a negative free energy, and thus occurs irreversibly until the liquid is saturated. As the concentration of salt in the liquid phase increases, so does its chemical potential, as seen from Eq. (4), and so the driving force for dissolution (the difference between the chemical potential at any given time and the equilibrium chemical potential) steadily decreases. Finally, a concentration is reached at which the chemical potential of sodium... 

At particular critical points (Tq, Pc) on the phase diagram of a substance, two phases can be found in thermodynamic equilibrium. Therefore, upon application of a pressure or a temperature gradient, a transformation occurs from one phase into the other. This is a phase transition, in many aspects similar to a transformation implying the change of aggregation state. However, the extent of the changes in a solid to solid transformation is much smaller. For example, latent heat or latent volumes associated with the transformations are quite small, sometimes even difficult to detect. 

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