Potential, Fugacity and Activity

The theory and conditions for phase equilibrium are well established. If more than one phase is present, then the chemical potential of a component is the same in all phases present. As chemical potential is linked functionally to the concepts of fugacity and activity, models for phase behavior prediction and correlation based on chemical potentials, fugacities, and activities have been developed. Historically, phase equilibrium calculations for hydrocarbon mixtures have been fragmented with liquid-vapor, liquid-liquid, and other phase equilibrium calculations, subject to separate and diverse treatments depending on the temperature, pressure, and component properties. Many of these methods and approaches arose to meet specific needs in the chemical process industries. Poling, Prausnitz,... 

The brief survey presented here must necessarily begin with a discussion of thermodynamics as a language most of Section 1.2 is concerned with the definition of thermodynamic terms such as chemical potential, fugacity, and activity. At the end of Section 1.2, the phase-equilibrium problem is clearly staled in several thermodymunic forms each of these forms is particularly suited for a particular situation, as indicated in Sections 1.S, 1.6, and 1.7. 

Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

In Chapter 6, fugacity and activity are defined and described and related to the chemical potential. The concept of the standard state is introduced and thoroughly explored. In our view, a more aesthetically satisfying concept does not occur in all of science than that of the standard state. Unfortunately, the concept is often poorly understood by non-thermodynamicists and treated by them with suspicion and mistrust. One of the firm goals in writing this book has been to lay a foundation and describe the application of the standard state in such a way that all can understand it and appreciate its significance and usefulness. 

One of your friends has difficulty understanding what the chemical potential of a given compound in a given system expresses. Try to explain it in words to him or her. What do the quantities fugacity and activity describe How are they related to the activity coefficient ... 

It has been said chemists have solutions 3 Solutions are involved in so many chemical processes1 that we must have the mathematical tools to comfortably work with them, and thermodynamics provides many of these tools. Thermodynamic properties such as the chemical potential, partial molar properties, fugacities, and activities, provide the keys to unlock the description of mixtures. 

Standard (electrode) potential — (E ) represents the equilibrium potential of an electrode under standard-state conditions, i.e., in solutions with the relative activities of all components being unity and a pressure being 1 atm (ignoring the deviations of fugacity and activity from pressure and concentration, respectively) at temperature T. A pressure of 1 bar = 105 Pa was recommended as the standard value to be used in place of 1 atm = 101,325 Pa (the difference corresponds to 0.34 mV shift of potential). If a component of the gas phase participates in the equilibrium, its partial pressure is taken as... 

LT is the standard cell potential difference, which is determined only by the reactants in definited standard states. This quantity results as the difference of standard electrode potentials. The power term Ila contains the corrected composition quantities a, (fugacities and activities) with the stoichiometric coefficients v, of the gases and condensed substances taking part in the cell reaction [10,12]. If a sensor at equilibrium delivers signals in agreement with Equation (25-7) then we have a reaction celt. In this case at solid electrolytes with oxide ion vacancies Vo> two reactions can be found besides... 

Note that the argument of the logarithm is a proper quotient of fugacity and activity for the electrode reaction if the presence of the electrons is ignored in constructing the quotient. From Eq. (17.33) we can calculate the potential, relative to SHE, of a hydrogen electrode at which/h2 and h+ have any values. 

Fugacity and activity are basically compositional terms. In ideal solutions they are not necessary pressure and various composition terms can be directly linked to the Gibbs energy. Real solutions have a variety of intermolecular forces, so that ideal solution models need correction factors. These corrections can be made either to the composition terms (fugacity and activity coefficients) or to the thermodynamic potentials (excess functions), and efforts to model these correction factors in mathematical terms have always been, and likely always will be, an important research field. 

The form taken by the equilibrium constant depends on the type of expression which is substituted in the above equation for the purpose of expressing the chemical potentials in terms of the composition this in its turn dex>ends on additional physical knowledge concerning whether or not the real system in question may be approximately represented by means of a model, such as the perfect gas or the ideal solution. If the system does not approximate to either of these models it is still possible, of course, to formulate an equilibrium constant in terms of fugacities or in terms of mole fractions and activity coefficients. However, this isapurely formal process the fugacities and activity coefficients are themselves defined in terms of the chemical potentials and therefore the knowledge contained in equation (10 1) is in no way increased, but is obtained in a more convenient form. 

The absolute values of die chemical potentials can not be determined experimentally, however, the difference between die chemical potential of a given component and die chemical potential of the same component in a well-defined standard state, at given conditions, can be expressed in terms of two auxiUary thermodynamic functions, namely fugacity and activity (77IUP1). 

Chemical equilibrium is achieved when chemical is distributed among environmental media (including organisms) according to the chemical s physico-chemical partitioning behavior. Thermodynamically, an equilibrium is defined as "a condition where the chemical s potentials (also chemical activities and chemical fugacities) are equal in the environmental media." At equilibrium, chemical concentrations in static environmental media remain constant over time. 

Chemical Potentials of Real Gases Fugacity, f, Activity, a and Activity Coefficient, [Pg.122]

The connection between chemical potential and activity is made by way of the concept of fugacity 2 The fiigacity / of a gas can be defined by... 

Activity and Activity Coefficient. —When a pure liquid or a mixture is in equilibrium with its vapor, the chemical potential of any constituent in the liquid must be equal to that in the vapor this is a consequence of the thermodynamic requirement that for a system at equilibrium a small change at constant temperature and pressure shall not be accompanied by any change of free energy, i.e., (d( )r. p is zero. It follows, therefore, that if the vapor can be regarded as behaving ideally, the chemical potential of the constituent i of a solution can be written in the same form as equation (7), where p,- is now the partial pressure of the component in the vapor in equilibrium with the solution. If the vapor is not ideal, the partial pressure should be replaced by an ideal pressure, or fugacity, but this correction need not be considered further. According to Raoult s... 

The fugacity fi = Pyi4>i P,yi) is determined from an equation of state (EOS) for the pure bulk gas. The adsorbed-phase activity coefficients are functions of the grand potential (0) and composition, where = -Q/RT. The form of Eq. (2) allows the grand potential to be calculated analytically [4] ... 

Express the chemical potential as a function of concentration and activity coefficients for liquid and solid phase (Eq. 17) or as a function of partial pressure and fugacity coefficients for the gas phase (Eq. 18). Define appropriate secondary reference states. 

The grand canonical partition function for a system of volume V, temperature T, and chemical potential g (the chemical potential and fugacity or activity z are related by z = exp ) is given by... 

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