Stable phase chemical equilibrium

Figure 1 shows the percentage distribution of aluminum between its major gases and the condensed phases that are stable at chemical equilibrium in a solar composition gas as a function of temperature at a total pressure of 10 4 bar. This pressure is representative of that in the inner regions of protoplan-etary accretion disks (such as the solar nebula) and photospheric regions of cool stars. 

Reversible processes are those processes that take place under conditions of equilibrium that is, the forces operating within the system are balanced. Therefore, the thermodynamics associated with reversible processes are closely related to equilibrium conditions. In this chapter we investigate those conditions that must be satisfied when a system is in equilibrium. In particular, we are interested in the relations that must exist between the various thermodynamic functions for both phase and chemical equilibrium. We are also interested in the conditions that must be satisfied when a system is stable. 

At kinetically controlled reactive conditions (Da = 1), Fig. 4.28(b) shows that the stable node moves into the composition triangle, as in reactive distillation (Fig. 4.27(b)). This point is termed the kinetic arheotrope because its location in the phase diagram depends on the membrane mass transfer resistances and also on the rate of chemical reaction. The kinetic arheotrope moves towards the B vertex with increasing C-selectivity of the membrane. At infinite Damkohler number, the system is chemical equilibrium-controlled (Fig. 4.28(c)), and therefore the arheotrope is located exactly on the chemical equilibrium curve. In this limiting case, it is called a reactive arheotrope . 

When a piece of aluminum is added to clear, transparent molten cryolite, foglike streamers spread out from the metal and they soon render the melt completely opaque [188-195], It is clear that the metal fog is not a stable chemical phase in equilibrium with the electrolyte, since it dissipates when it rises from the molten... 

Types of Phases in Binary Systems.—A two-component system, like a system with a single component, can exist in solid, liquid, and gaseous phases. The gas phase, of course, is perfectly simple it is simply a mixture of the gas phases of the two components. Our treatment of chemical equilibrium in gases, in Chap. X, includes this as a special case. Any two gases can mix in any proportions in a stable way, so long as they cannot react chemically, and we shall assume only the simple case where the two components do not react in the gaseous phase. 

Figure 4.3a-d shows the phase diagrams of an Si-C-Cl-H system at temperatures of 1473, 1500, 1600 and 1700 K respectively. A constant total pressure of 105 Pa and a ratio of Cl/Si = 3 are used to generate the four diagrams. The gaseous phase equilibrium with all combinations of condensed phases is implicitly shown for all four conditions. Curves are used to mark the boundary between the stable phase fields. For this chemical system, there are no more than two condensed phases in each field. 

When a drying temperature is selected, the relative humidity should not be too low so as to initiate calcination, or too high so as to promote surface adsorption and capillary condensation. In addition the drying conditions of temperature and relative humidity must not affect the chemical equilibrium. However, since each calcium sulfate compound has its own stability region in the phase diagram, the drying conditions must be in a region where all the phases present in the sample remain stable. 

Chemical equilibrium calculations predict the distribution of each element between its gaseous, solid, and liquid compounds as a function of temperature, pressure, and bulk elemental composition. These calculations are often called condensation calculations because they show the stable phases that condense out of a cooling gas with solar system elemental abundances. However, chemical equilibrium calculations are path independent because the Gibbs energy is a state function, i.e., its differential dG is an exact (or perfect) differential. Thus, the results of chemical equilibrium calculations apply equally well to heating or cooling of a solar composition system. 

The formation of a disperse system as a result of the generation and successive growth of primary particles (nuclei) of a new stable phase may take place in any metastable system. The metastability, arising as conditions shift away from normal equilibrium conditions, may arise from deviations in the chemical composition of the phases (supersaturation) as well as from physicochemical action (changes in the temperature and pressure). 

The temperature axis is divided into three intervals. Below 7 the solid has the lowest chemical potential. Between 7 and 7J, the liquid has the lowest chemical potential. Above Tfj the gas has the lowest chemical potential. The phase with the lowest value of the chemical potential is the stable phase. If liquid were present in a system at a temperature below 7, Fig. 12.2, the chemical potential of the liquid would have the value while the solid has the value. Thus, liquid could freeze spontaneously at this temperature, since freezing will decrease the Gibbs energy. At a temperature above 7 the situation is reversed the p of the solid is greater than that of the liquid and the sohd melts spontaneously to decrease the Gibbs energy of the system. At 7 the chemical potentials of solid and liquid are equal, so neither phase is preferred they coexist in equilibrium. The situation is much the same near Tjj. Just below liquid is stable, while just above 7 the gas is the stable phase. 

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