Equilibrium, chemical single-phase systems

We identified the equilibrium state for several chemical reactions occurring in a single-phase system at constant temperature and pressure by finding the state for which G = N Gi was equal to a minimum subject to the stoichiometric constraints... 

Chemical Equilibrium in a Single-Phase System 713 Thus, Eq. 13.1-17 can be rewritten as... 

One can see that the force between the walls is attractive because in equilibrium, /7 [cfc] must be a maximum if the single-phase system is to be stable — i.e., if there were another value of the composition with the same chemical potential, where 77 = — fb[cb] were the same or higher... 

If a mixture of monomers is not in equilibrium, any polymerization that occurs at constant temperature, T, and constant pressure, P, must lead to a decrease in the total Gibbs free energy of the system. A reaction variable may be defined. The fundamental property relation for a single phase system for the total differential of the Gibbs free energy can be written as a function of temperature, pressure, and chemical potential as follows ... 

For the case of equilibrium with respect to chemical reaciion within a single-phase closed system, combination of Eqs. (4-16) and (4-271) leads immediately to... 

The fundamental differences between the chemical reactions when compressing a single liquid phase and when compressing a gas-liquid two-phase system are best explained by comparing the rate and equilibrium equations (Equation (1) and (2), respectively) of the reaction... 

A phase boundary for a single-component system shows the conditions at which two phases coexist in equilibrium. Recall the equilibrium condition for the phase equilibrium (eq. 2.2). Letp and Tchange infinitesimally but in a way that leaves the two phases a and /3 in equilibrium. The changes in chemical potential must be identical, and hence... 

In this first example, a single-component system consisting of a liquid and a gas phase is considered. If the surface between the two phases is curved, the equilibrium conditions will depart from the situation for a flat surface used in most equilibrium calculations. At equilibrium the chemical potentials in both phases are equal ... 

The general criterion of chemical reaction equilibria is the same as that for phase equilibria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a single-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The independendy variable quantities are just the r reaction coordinates, and thus the equilibrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = l, ll,..., r ... 

For any pure chemical species, there exists a critical temperature (Tc) and pressure (Pc) immediately below which an equilibrium exists between the liquid and vapor phases (1). Above these critical points a two-phase system coalesces into a single phase referred to as a supercritical fluid. Supercritical fluids have received a great deal of attention in a number of important scientific fields. Interest is primarily a result of the ease with which the chemical potential of a supercritical fluid can be varied simply by adjustment of the system pressure. That is, one can cover an enormous range of, for example, diffusivities, viscosities, and dielectric constants while maintaining simultaneously the inherent chemical structure of the solvent (1-6). As a consequence of their unique solvating character, supercritical fluids have been used extensively for extractions, chromatographic separations, chemical reaction processes, and enhanced oil recovery (2-6). 

Next consider the triple point of the single-component system at which the solid, liquid, and vapor phases are at equilibrium. The description of the surfaces and tangent planes at this point are applicable to any triple point of the system. At the triple point we have three surfaces, one for each phase. For each surface there is a plane tangent to the surface at the point where the entire system exists in that phase but at the temperature and pressure of the triple point. There would thus seem to be three tangent planes. The principal slopes of these planes are identical, because the temperatures of the three phases and the pressures of the three phases must be the same at equilibrium. The three planes are then parallel. The last condition of equilibrium requires that the chemical potential of the component must be the same in all three phases. At each point of tangency all of the component must be in that phase. Consequently, the condition... 

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