Fugacity approximation

II The increment in the free energy, AF, in the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are for a gas, fugacity (approximately equal to the pressure) of 1 atm for a pure liquid or solid, the substance at a pressure of 1 atm for a substance in aqueous solution, the hyj)othetical solution of unit molahty, which has all the properties of the infinitely dilute solution except the property of concentration. 

This discussion can be illustrated by Fig. 2, in which the fugacities (approximately vapor pressures) of the supercooled liquid, solid, and solution are plotted against the temperature. The system will be in equilibrium where the fugacity curve for the solid meets that of the... 

When it comes to physical meaning, parameters in the thermodynamic model sometimes have meanings that are difficult to relate to the real world, as we have seen, particularly in the case of standard states. The example most relevant here is oxygen fugacity, another measure of the state of oxidation of systems, which we will consider in a later section. Oxygen fugacity is often used as a parameter in systems which contain no O2, just as water contains no free electrons. Still, there are other. systems where fugacity approximates partial pressures, and this is a link to reality that... 

This is the Nernst equation, which expresses the exact emf of a cell in terms of activities of products and reactants of the cell. The activity, uu of a dissolved substance L is equal to its concentration in moles per thousand grams of water (molality) multiplied by a correction factor, y, called the activity coefficient. The activity coefficient is a function of temperature and concentration and, except for very dilute solutions, must be determined experimentally. If L is a gas, its activity is equal to its fugacity, approximated at ordinary pressures by the pressure in atmospheres. The activity of a pure solid is arbitrarily set equal to unity. Similarly, for water, with concentration essentially constant throughout the reaction, the activity is set equal to unity. 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

The computer subroutines for calculation of vapor-phase and liquid-phase fugacity (activity) coefficients, reference fugac-ities, and molar enthalpies, as well as vapor-liquid and liquid-liquid equilibrium ratios, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements and CDC 6400 execution times for these subroutines are given in Appendix J. 

This equation, known as the Lewis-RandaH rule, appHes to each species in an ideal solution at all conditions of temperature, pressure, and composition. It shows that the fugacity of each species in an ideal solution is proportional to its mole fraction the proportionaUty constant is the fugacity of pure species i in the same physical state as the solution and at the same T and P. Ideal solution behavior is often approximated by solutions comprised of molecules similar in size and of the same chemical nature. 

The fugacity coefficient departure from nonideaHty in the vapor phase can be evaluated from equations of state or, for approximate work, from fugacity/compressibiHty estimation charts. References 11, 14, and 27 provide valuable insights into this matter. 

The limits of the Lewis fugacity rule are not determined by pressure but by composition the Lewis rule becomes exact at any pressure in the limit as y( - 1, and therefore it always provides a good approximation for any component i which is present in excess. However, for a component with small mole fraction in the vapor phase, the Lewis rule can sometimes lead to very large errors (P5, R3, RIO). 

E6.2 The fugacity of liquid water at 298.15 K is approximately 3,17 kPa. Take the ideal enthalpy of vaporization of water as 43.720 TmoD1, and calculate the fugacity of liquid water at 300 K. 

We used the system (.vic-Q,H 1CH3 +. vic-CeH ) as an example of a system that closely approximates ideal behavior. Figure 6.5 showed the linear relationship between vapor pressure and mole fraction for this system. In this Figure, vapor pressure could be substituted for vapor fugacity, since at the low pressure involved, the approximation of ideal gas behavior is a good one, and... 

Since the standard state fugacity, f°, can be approximated by saturation vapor pressure, p , then equation (2) reduces to the well known relationship ... 

The QUASI fugacity model was then run for a trichlorobiphenyl in a lake the size of Lake Michigan, being approximately 60,000 times the size of the evaluative environment. A detailed justification for the selection of D values is beyond our scope here but in selecting values, we have relied on recent reports by Neely (11), Rogers (15), Armstrong and Swackhamer (16), Thomann (17), and Andren (18). 

Gas Pure gas at unit fugacity (for an ideal gas the fugacity is unity at 1 atm pressure this is a valid approximation for most real gases). 

In principle, this system of 20 equations can be solved provided the equilibrium constants, activities, Henry-constants and fugacities are available. While some results for most of these properties are available, there exists no approved method for calculating activities in concentrated aqueous solutions of weak electrolytes therefore, several approximations were developed. ... 

At low pressures the fugacity of a component can be replaced by its partial pressure so that Equation 1 can be approximated as follows. 

As the evaluation of Equation (10.86) requires a great deal of data, and as adequate data are available for only a few mixtures of gases, it is useful to have approximate relationships that can be used to estimate the fugacity of components in a solution of gases. 

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