Solids equilibrium

Kn = vapor-solid equilibrium constant for hydrocarbon component n... 

The vapor-solid equilibrium constant is determined experimentally and is defined as the ratio of the mol fraction of the hydrocarbon component in gas on a water-free basis to the mol fraction of the hydrocarbon component in the solid on a water-free basis. That is ... 

Graphs giving the vapor-solid equilibrium constants at various temperatures and pressures are given in Figures 4-1 through 4-4. For nitrogen and components heavier than butane, the equilibrium constant is taken as infinity. 

Figure 4-1. Vapor-solid equilibrium constant for (a) methane, (b) ethane, and n-butane. (From Gas Processors Suppliers Association, Engineering Data Book.)...

The equilibrium pressure when (solid + vapor) equilibrium occurs is known as the sublimation pressure, (The sublimation temperature is the temperature at which the vapor pressure of the solid equals the pressure of the atmosphere.) A norma) sublimation temperature is the temperature at which the sublimation pressure equals one atmosphere (0.101325 MPa). Two solid phases can be in equilibrium at a transition temperature (solid + solid) equilibrium, and (liquid + liquid) equilibrium occurs when two liquids are mixed that are not miscible and separate into two phases. Again, "normal" refers to the condition of one atmosphere (0.101325 MPa) pressure. Thus, the normal transition temperature is the transition temperature when the pressure is one atmosphere (0.101325 MPa) and at the normal (liquid + liquid) solubility condition, the composition of the liquid phases are those that are in equilibrium at an external pressure of one atmosphere (0.101325 MPa). 

It should be noted that the curves of humidity plotted against either temperature or enthalpy have a discontinuity at the point corresponding to the freezing point of the humidifying material. Above the temperature 90 the lines are determined by the vapour liquid equilibrium and below it by the vapour-solid equilibrium. 

Vapour-solids equilibrium 753 Variable area flowmeters 257... 

The thermodynamics of solid equilibrium with gas atmospheres is considered in many textbooks of thermodynamics and, often, with useful examples, in textbooks of metallurgy and geology. The thermodynamics of many metal-oxygen systems are especially well characterized in view of their industrial importance. Two old but extremely useful descriptions of gas-solid equilibria are ... 

Equilibrium between simple salts and aqueous solutions is often relatively easily demonstrated in the laboratory when the composition of the solid is invariant, such as occurs in the KCI-H2O system. However, when an additional component which coprecipitates is added to the system, the solid composition is no longer invariant. Very long times may be required to reach equilibrium when the reaction path requires shifts in the composition of both the solution and solid. Equilibrium is not established until the solid composition is homogeneous and the chemical potentials of all components between solid and aqueous phases are equivalent. As a result, equilibrium is rarely demonstrated with a solid solution series. 

Finally, we must be certain we are observing vapor-liquid equilibrium in the column not vapor-solid equilibrium. Braun and Guillet (1976) reported that a discontinuity in a plot of Jin (V°) vs 1/T (where V° is the retention volume at 273.15 K) indicated a phase transition. We calculated V° from the following relationship... 

Figure 3.10. Phase diagrams of attractive monodisperse dispersions. Uc is the contact pair potential and (j) is the particle volume fraction. For udk T = 0, the only accessible one-phase transition is the hard sphere transition. If Uc/hgT 0, two distinct scenarios are possible according to the value of the ratio (range of the pair potential over particle radius). For < 0.3 (a), only fluid-solid equilibrium is predicted. For % > 0.3 (b), in addition to fluid-solid equilibrium, a fluid-fluid (liquid-gas) coexistence is predicted with a critical point (C) and a triple point (T).

J. Bibette, D. Roux, and F. Nallet Depletion Interactions and Fluid-Solid Equilibrium in Emulsions. Phys. Rev. Lett. 65, 2470 (1990). 

Additional Factors Influencing Decay. Numerous other factors may influence the observed change in activity of catalyst. These include pore mouth blocking by deposited solid, equilibrium, or reversible poisoning where some activity always remains, and the action of regeneration (this often leaves catalyst with an active exterior but inactive core). 

One of the most effective methods for evaluating the purity of chemical substances is that involving determination of the freezing point, with appropriate observation of the temperature of the liquid-solid equilibrium as a function of the fraction of sample frozen or melted. 

Figures 5 and 6 show the results of the calculations, and they are compared with the actual data distribution as shown by a dashed bounding line. With both calcite and dolomite, colder waters match conditions of carbon dioxide pressure greater than atmospheric, and high temperature conditions match carbon dioxide pressure nearly the same as the atmosphere. It appears the degree of mixing and the rate of carbon dioxide diffusion is of prime importance when considering approach to liquid, gas, and solid equilibrium.

Source Considerations. Many CVD sources, especially sources for or-ganometallic CVD, such as Ga(CH3)3 and Ga(C2H5)3, are liquids at near room temperatures, and they can be introduced readily into the reactor by bubbling a carrier gas through the liquid. In the absence of mass-transfer limitations, the partial pressure of the reactant in the gas stream leaving the bubbler is equal to the vapor pressure of the liquid source. Thus, liquid-vapor equilibrium calculations become necessary in estimating the inlet concentrations. For the MOCVD of compound-semiconductor alloys, the computations have also been used to establish limits on the control of bubbler temperature to maintain a constant inlet composition and, implicitly, a constant film composition (79). Similar gas-solid equilibrium considerations govern the use of solid sources such as In(CH3)3. 

The interaction parameter, ft, is a fitting parameter in the regular solution model that can be found from liquid-solid equilibrium data (93). With the DLP model, the interaction parameter is calculated from the lattice parameters of the binary compounds. For a compound semiconductor AiJB C, ft is computed from the lattice constants aAC and aBC of the binary compounds from the following expression... 

Mann, S.L., McClure, L.M., Poettmann, F.H., Sloan, E.D., Vapor-Solid Equilibrium Ratios for Structure I and Structure II Natural Gas Hydrates, in Proc. 68th Annual Gas Processing Association Convention, San Antonio, TX, March 13-14 (1989). 

The dashed lines in Figure 9.4 represent the formulation dilution (eroof Formulation A and Formulation B. Both Formulations A and B have the same concentration of drug and both are well below the equilibrium solubility of the drug in either formulation because they are well below the solid equilibrium solubility line. However, because Formula B has more cosolvent, it has less area above the solid solubility limit line and therefore, should be less prone to precipitation on injection. 

An extensive process data base has been accumulated which includes (1) vapor-liquid-solid equilibrium data for binary... 

Several different measurements were made as a result of the different phase behavior observed for the two binary mixtures. Gas-solid equilibrium was observed for mixtures of TPP and pentane at conditions near the critical point of pentane. Hence, solid solubilities for TPP in supercritical pentane were measured. 

However, for mixtures of TPP and toluene, a third (liquid) phase forms in the presence of the gas and the solid, at pressures well below the critical pressure of toluene. At higher pressures, gas-liquid and solid-liquid equilibria were observed, rather than gas-solid equilibrium. Thus, phase compositions for gas-liquid equilibrium were measured for this binary mixture to give TPP solubilities in each of the fluid phases. Pressures and temperatures for three-phase, solid-liquid-gas equilibrium were also measured for both binary mixtures. 

The melting behavior for TPP in the presence of compressed pentane (Figure 1) is characterized by an interrupted three-phase, SLG equilibrium line which terminates at a LCEP. This behavior is characteristic of a gas and a solid with low mutual solubility, and is expected when the triple-point temperature of the solid is much greater than the critical temperature of the gas (3). At temperatures just above the LCEP temperature, TPP does not melt in the presence of compressed pentane, and gas-solid equilibrium is observed at pressures up to two hundred atmospheres (Figure 3). 

Figure 10.2 Scheme of liquid-solid equilibrium in a cylindrical pore of radius Rp with the creation of an adsorbed layer of thickness t. 

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