Equilibrium constant vapor-solid

If the composition of the stream is known, the hydrate temperature can be predicted using vapor-solid (hydrate) equilibrium constants. The basic equation for this prediction is ... 

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.)...

At a given temperature, the pressure of iodine vapor is constant, independent of the amount of solid iodine or any other factor. The equilibrium constant expression is... 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

Since solid carbon vaporizes as a result of its vapor pressure, p p,c, the chemical equilibrium constant s defined as... 

Figure 7.18 gives the ratio (K /K)s4 s4 of the calculated equilibrium constants for solution-phase ammonium nitrate compared to the solid salt product at various temperatures and water activities. As the water activity, i.e., water vapor pressure above the solution, increases, the equilibrium constant falls. That is, at higher relative humidities, relatively less HNO, and NH, are found in the vapor phase at equilibrium. This may be why relatively more ammonium nitrate in particles collected on filters evaporates at lower RHs compared to higher ones. 

The melting point of ammonium hydrosulphide in a closed vessel was found by E. Briner to be 120° and, in the presence of an excess of hydrogen sulphide, the m.p. is a triple point NHiSHv HgS+NHg, and the equilibrium constant is K=0 04 at 22°. The heat of vaporization of the solid hydrosulphide, in consequence of dissociation, will be equal to the heat of formation of the solid from the component gases, viz., 22 4 Cals., as found by J. Thomsen. According to F. Isambert, the heat of vaporization between 77° and 132° is 23 Cals., and, according to J. H. van t Hoff, calculated between 9 5° and 25 1° at constant press., 22 7 Cals. J. Walker and J. S. Lumsden find that the value of this constant increases with a rise of temp., being 19 7 Cals, between 4 2° and 18°, and 22 0° between 30 9° and 44 4°. 

The vapor pressure of a compound is not only a measure of the maximum possible concentration of a compound in the gas phase at a given temperature, but it also provides important quantitative information on the attractive forces among the compound s molecules in the condensed phase. As we will see below, vapor pressure data may also be very useful for predicting equilibrium constants for the partitioning of organic compounds between the gas phase and other liquid or solid phases. Finally, we should note that knowledge of the vapor pressure is required not only to describe equilibrium partitioning between the gas phase and a condensed phase, but also for quantification of the rate of evaporation of a compound from its pure phase or when present in a mixture. 

When the system is heterogeneous—i.e., the temperature and pressure are such that solid carbon exists in equilibrium with its vapor, the value of Pci is uniquely determined by the temperature and can be calculated directly from the equilibrium constant Ki. Hence in a heterogeneous system, the partial pressure of cyanogen radicals and of cyanogen depend only on the temperature... 

On the other hand, equilibrium constant for this reaction at the temperatures of study is rather small. But it is suspected that with the fixed-bed operation and with the possibility of some sulfur vapor adsorption on the solid, nonequilibrium conditions may be prevailing in the system. As a result, high sulfur yields could be obtained. This plausible explanation is only speculative, and more studies are necessary before a definite conclusion can be drawn. At WVU studies are in progress to obtain the kinetics of the reactions involved in this scheme. 

The LCM was accurate within 20 percent error in SO- vapor pressure for the 50°C data, as well as data at 35, 70, and 90°C. The solid line shows the general trend of the LCM predictions. Figure 4 plots the apparent equilibrium constant as a function of ionic strength for a calcium sulfite/bisulfite system at 25, 50, and 60 C... 

Since/i and Xi become unity at infinite dilution, i.e., for the pure solvent, it follows from equation (11) that the chemical potential of a pure liquid becomes equal to m2(d, and hence is a constant at a given temperature and pressure. By considering the equilibrium between a solid and its vapor, it can be readily shown that the same rule is applicable to a pure solid. 

Let us consider vapor-liquid (or vapor-solid) equilibria for binary mixtures. For the sake of simplicity it will be assumed that all gases are ideal. In addition to the vapors of each component of the condensed phase, the gas will be assumed to contain a completely insoluble constituent, the partial pressure p of which may be adjusted so that the total pressure of the system, p, assumes a prescribed value. Therefore, C = 3, P = 2, and, according to equation (51), F = 3. Let us study the dependence of the equilibrium vapor pressures of the two soluble species p and P2 on their respective mass fractions in the condensed phase X and X2 at constant temperature and at constant total pressure. Since it is thus agreed that T and p are fixed, only one remaining variable [say X ( = l — "2)] is at our disposal p, P2 and the total vapor pressure p = p + p2 will depend only on X. ... 

Heterogeneous physical equilibria, e.g., between a pure solid and its vapor or a pure liquid and its vapor, can be treated in a manner similar to that just described. If the total pressure of the system is 1 atm., the fugacity of the vapor is here also equivalent to the equilibrium constant. The variation of In/ with temperature is again given by equation (33.16), where MP is now the ideal molar heat of vaporization of the liquid (or of sublimation of the solid) at the temperature T and a pressure of 1 atm. If the total pressure is not 1 atm., but is maintained constant at some other value, the dependence of the fugacity on the temperature can be expressed by equation (29.22), since the solid or liquid is in the pure state thus,... 

Because the equilibrium constant Keq ranges from zero, when the system is all solid, to infinity, when it is all liquid, (strictly, one should include vaporization, neglected here) it is convenient to introduce another related function, a ratio we call D (for distribution), which contains the same information but ranges from — 1 to +1 D = (Keq — l)/(Keq +1). This allows us to portray graphically the behavior of a system in terms of the amount of each of two phases as a function of temperature. This is done in Fig. 1, for a small system (a), a mid-size system (b), and a large but not truly macroscopic system (c). However, even case (c) in this figure does not... 

For an equilibrium constant of a heterogeneous chemical reaction where the components are present in separate phases, the standard states of each component may be different. Let there be a reaction between a pure solid, say component 1, and additional components all present in the vapor phase. The equilibrium constant is now expressed as... 

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