Preliminaries to Reaction-Equilibrium Calculations

In this section we discuss standard states commonly chosen for reacting systems ( 10.4.1), then we show how values for standard-state properties can be determined from properties of formation ( 10.4.2). Lastly we develop computational forms used in applying the stoichiometric ( 10.4.3) and nonstoichiometric ( 10.4.5) approaches. 

Before a reaction-equilibrium calculation can be performed, we must select an appropriate standard state for each species. Moreover, we must clearly distinguish quantities, such as fugacities and activities, that depend on the final equilibrium state (T, P, x ), from those quantities, such as equilibrium constants, that depend only on the equilibrium temperature T, the standard-state pressures P , and the phase. Typically, the standard-state pressure and phase are chosen according to whether the real substance is gas, liquid, or solid at the equilibrium conditions. Those three possibilities are discussed, in turn, here, and each discussion culminates with a particular expression for the activity. Those expressions can be used either in the stoichiometric development, via (10.3.14), or in the nonstoichiometric development, via (10.3.38). We emphasize that when we use the stoichiometric approach, the standard states used for the fugacities must be consistent with those associated with the equilibrium constant. 

Standard states for gases. When species i is a gas at the equilibrium conditions, the standard state is usually taken to be the pure ideal gas at the equilibrium temperature T and P, = 1 bar. (Caution in older literature, the standard pressure was usually taken as 1 atm = 1.0133 bar.) Then, the standard-state fugacity becomes 

The activity is dimensionless, and therefore, since the standard-state pressure P° was specified in bars, the value for the system pressure P used in (10.4.3) must also be in bars. Values for the fugacity coefficients (p,- appearing in (10.4.3) would be, as usual, computed from a volumetric equation of state. The expression (10.4.3) for the activity can be used both in (10.3.14) of the stoichiometric development and in (10.3.38) of the nonstoichiometric development. 

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Although in principle one could choose a set of arbitrary values for the solvent coordinates sm, solve the eigenvalue equation (2.23), and compute the free energy (2.12), in practice a preliminary aquaintance with the equilibrium solvation picture for the target reaction system serves as a computationally convenient doorway for the calculations in the nonequilibrium solvation regime. We show this below in the section dedicated to an illustration of the method for a two state case reported in BH-II. 

Although there are no industrial sources of COCIF emissions, natural emissions of COCIF from volcanoes have been predicted by equilibrium thermodynamic models [1990a]. COCIF may also be generated environmentally from the photochemical decomposition of CCI3F (CFC-11). Subsequent removal can be assumed to be effected by its reaction with 0( D) [1994], and by further photolysis (the preliminary photodissociation step has been examined by ab initio methods [677a]). Using calculated production and removal rates, an altitude profile for COCIF was calculated maximum COCIF formation was noted to occur at an altitude of about 25 km [1994]. 

The rates of production/consumption of ions have to be calculated in this step as independent phenomena from the previous step. According to the proposed hypotheses, these rates are high enough to consider that the local equilibrium is reached. In the present case, this means that concentration changes of the ions and species considered in this model can be calculated using the action mass equations of the involved chemical reactions. After the transport step, a set of preliminary values of concentrations, which are not at chemical equilibrium, is known for each volume element (C, ). The solution in each cell of the mass conservation equations, together... 

The present chapter is concerned primarily with measured molecular structural effects on reactions 2 and 4 in the gas phase. These have been obtained only very recently from direct equilibrium-constant determinations. Work in this area is still in a very active state, so that this chapter serves as a preliminary progress report. Useful comparison can now be made of structural effects on equation 2 with the following related topics (1) proton-transfer equilibria in condensed phases (2) other Lewis acid-base equilibria in the gas phase (3) theoretical calculations of proton-transfer energetics (4) hydrogen-atom transfer equilibria between cation radicals and saturated cations (5) hydrogen-bonded complex formation, in hydrocarbon solvents and (6) gas-phase equilibria for attachment of neutral molecules to cations and anions. Each of these topics is considered at least briefly. 

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