Solution phase thermodynamic aspects

The algorithm used to equilibrate ice, COy-bHoO, and CH4 6H2O with the solution phase uses aspects of several of the above techniques. First, the model calculates the fugacity coefficients for CC>2(g) and CH4(g) using the approach outlined in Eqs. 3.36 to 3.48 and 3.72 to 3.74. Then the model calculates which of the phases - ice, C02-6H20, or CH4-6H20 - is thermodynamically most stable by selecting the phase that minimizes the activity of water (aw). The reaction,... 

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 ... 

The relative stability of the tautomers of purine and pyrimidine bases is of fundamental importance to the structure and functioning of nucleic acids. The occurrence of rare tautomers was considered a factor responsible for the formation of mismatches leading to spontaneous mutations in the genetic code fl,2]. Cytosine, in particular, has been the subject of several studies, both experimental [3-5] and theoretical [5-15] which have provided a reliable picture of the relative stability of its tautomers, both in the gas phase and in solution. Tautomerization is generally the result of proton transfer (PT) reactions whose activation barriers may exert a kinetic control over the formation of some tautomers. As far as cytosine is concerned, a large majority of the studies available in the literature focus on the thermodynamic aspects of tautomerization and quite a few [16-19] are devoted to the elucidation of the kinetic aspects. The tautomerization of cytosine in the gas phase, with a special attention to the activation energy of the proton transfer reactions, has been afforded by this group in a previous paper [19]. By comparison with experimental data [4,5] it was... 

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. 

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... 

The development of colloid science has b en based partly on the concept of the two-phase system and partly on the concept of ordinary solutions. This will be set forth in more detail in chapter I of volume II. Wc will here only consider some thermodynamic aspects of the problem. 

Theoretically, chromatography may be described as a combination of thermodynamic and kinetic processes. The thermodynamic aspects control the retention and shape of the peak whilst the kinetic aspects control the sharpness of the band. Together they define the resolution between components. The fundamental thermodynamic parameter is the distribution coefficient of the solute between the phases. This is given as the ratio between the concentrations of a solute in the stationary and mobile phases. 

The title of this chapter is somewhat misleading. In one sense it is too broad, in another sense too restrictive. We shall really discuss in detail only the phase separation and osmostic pressure of polymer solutions a variety of other thermodynamic phenomena are ignored. In this regard the chapter title would better read Some aspects of. . . . Throughout this volume only a small part of what might be said about any topic is actually presented, so this modifying phrase is taken to be understood and is omitted. 

The problem of transport of molecules through swollen gels is of general interest. It not only pertains to catalysis, but also to the field of chromatographic separations over polymeric stationary phases, where the partition of a solute between the mobile phase (liquid phase) and a swollen polymeric stationary phase (gel phase) is a process of the utmost importance. As with all the chemical and physicochemical processes, the thermodynamic and the kinetic aspect must be distinguished also in partition between phases. 

Agee, L. J., S. Banerjie, R. B. Duffey, and E. D. Hughes, 1978, Some Aspects of Two-Phase Models for Two-Phase Flow and Their Numerical Solutions, in Transient Two-Phase Flow, Proc. 2nd Specialists Meeting, OECD Committee for the Safety of Nuclear Installations, Paris, Vol. 1, pp. 27-58. (3) Ahmadi, G., and D. Ma, 1990, A Thermodynamical Formulation for Disposed Multiphase Turbulent Flows I. Basic Theory, Int. J. Multiphase Flow 16 323. (3)... 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

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