Condensed-phase species equation

STANJAN The Element Potential Method for Chemical Equilibrium Analysis Implementation in the Interactive Program STANJAN, W.C. Reynolds, Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA, 1986. A computer program for IBM PC and compatibles for making chemical equilibrium calculations in an interactive environment. The equilibrium calculations use a version of the method of element potentials in which exact equations for the gas-phase mole fractions are derived in terms of Lagrange multipliers associated with the atomic constraints. The Lagrange multipliers (the element potentials ) and the total number of moles are adjusted to meet the constraints and to render the sum of mole fractions unity. If condensed phases are present, their populations also are adjusted to achieve phase equilibrium. However, the condensed-phase species need not be present in the gas-phase, and this enables the method to deal with problems in which the gas-phase mole fraction of a condensed-phase species is extremely low, as with the formation of carbon particulates. 

With reference to Figs. 3.9 and 3.10, the energy and the species equations are condensed-phase energy equation ... 

The condensed phase energy equation, being decoupled from the species... 

Of special interest in stable isotope geochemistry are evaporation-condensation processes, because differences in the vapour pressures of isotopic compounds lead to significant isotope fractionations. For example, from the vapour pressure data for water given in Table 1.2, it is evident that the lighter molecnlar species are preferentially enriched in the vaponr phase, the extent depending upon the temperature. Such an isotopic separation process can be treated theoretically in terms of fractional distillation or condensation under equilibrium conditions as is expressed by the Rayleigh (1896) equation. For a condensation process, this equation is... 

Quinone oximes and nitrosoarenols are related as tautomers, i.e. by the transfer of a proton from an oxygen at one end of the molecule to that at the other (equation 37). While both members of a given pair of so-related isomers can be discussed separately (see, e.g., our earlier reviews on nitroso compounds and phenols ) there are no calorimetric measurements on the two forms separately and so discussions have admittedly been inclusive—or very often sometimes, evasive—as to the proper description of these compounds. Indeed, while quantitative discussions of tautomer stabilities have been conducted for condensed phase and gaseous acetylacetone and ethyl acetoacetate, there are no definitive studies for any pair of quinone oximes and nitrosoarenols. In any case. Table 4 summarizes the enthalpy of formation data for these pairs of species. 

We may, with appropriate attention to the reference state, develop the relations in terms of components between the intensive variables pertinent to multiphase systems that contain species other than the components. Such relations would be rather complex, because no account would be taken of the effect of the chemical reactions that occur in the system. All deviations from ideality would appear either in the activity coefficients for substances in condensed phases or in the coefficients used in some equations of state for the gas phase. Simpler relations are obtained when the conditions of phase equilibrium are based on species rather than components, once the species have been identified. 

There are six variables and five equations, and the system is univariant. We wish to determine the change of the partial pressure of the species A2B with change of composition of the condensed phase that is, the derivative (din PAB/dx1)T- In the solution of the set of Gibbs-Duhem equations, we therefore must retain nAB and or expressions equivalent to these quantities. The solution can be obtained by first eliminating n2 and fiB from Equations (11.167) and (11.168) by use of Equations (11.169) and (11.171). The expressions... 

This equation is for reactions involving only gaseous reactants and products. If some species are in condensed phases, appropriate heats of vaporization of sublimation must be included. 

Whereas aldehydes and ketones are one of the most important classes of organic compounds containing multiple bonds, no species with a E=0 double bond with E = Si, Ge, Sn, Pb could be isolated as a pure compound in the condensed phase . The ger-manone Tbt(Tip)Ge=0 116 prepared by Tokitoh s group could be detected in solution only. At room temperature, however, by insertion of the Ge=0 bond into a C—Si bond of an ortho-hsi substituent of the employed Tbt ligand, it rearranges quickly to a mixture of diastereomeric benzogermacyclobutanes (equation 13) . ... 

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. ... 

Since the quantity in brackets in equation (56) is always positive, the sign of (Pi/Pi 1/ 2) is the same as the sign of dp /dX,. Hence, the vapor is richer in species 1 in regions where dp /dX, > 0, and the condensed phase is richer in species 1 where dp /dX, < 0. The vapor and condensed phase have the same composition where dp /dX, = 0, a condition under which the mixture is said to be azeotropic. 

For the above reaction scheme, the following kinetic equations are applicable. It is assumed that a saturated vapor of gas Ai is in equilibrium with its condensed phase containing species Ai to A12. Other assumptions are as in case 3.13-5 above, where H is the rate of supply of A1 in moles/sec from the vapor phase into the condensed phase. 

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