Fugacity, definition equilibrium

Hydrogen Electrode an electrode at which the equilibrium (aq.) + jHj, is established. By definition, at unit activity of hydrogen ions and unit fugacity of hydrogen gas the potential of the standard hydrogen electrode h+/y//2 =... 

Equilibrium. Equilibrium between compartments can be expressed either as partition coefficients K.. (i.e. concentration ratio at equilibrium) or in the fugacity models as fugacity capacities and Z. such that K.. is Z./Z., the relationships being depicted in Figur 1. Z is dellned as tfte ratio of concentration C (mol/m3) to fugacity f (Pa), definitions being given in Table I. 

The exact definition of the equilibrium constant given by IUPAC requires it to be defined in terms of fugacity coefficients or activity coefficients, in which case it carries no units. This convention is widely used in popular physical chemistry texts, but it is also common to find the equilibrium constant specified in terms of molar concentrations, pressure or molality, in which cases the equilibrium constant will carry appropriate units. 

Determination of gas pressures in expired air or blood depends on the application of certain physical principles (Table 27-4). The partial pressure of a gas dissolved in blood is by definition equal to the partial pressure of the gas in an imaginary ideal gas phase in equilibrium with the blood. At equilibrium, the partial pressure (tension) of a gas is the same in erythrocytes and plasma, so that the partial pressure of a gas is the same in whole blood and plasma. The partial pressure of a gas in a gas mixture is defined as the substance fraction of gas (mole fraction) times the total pressure. The tension of a gas in a liquid is, in fact, a measure of the chemical activity of the gas in the liquid. In the physicochemical literature, it is called the fugacity. 

The fugacity function has been introduced because its relation to the Gibbs energy makes it useful in phase equilibrium calculations. The present criterion for equilibrium between two phases, (Eq. 7.1-9c) is C = C , with the restriction that the temperature and pressure be constant and equal in the two phases. Using this equality and the definition of the fugacity (Eq. 7.4-6) gives... 

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... 

Ideal solution is often chosen as reference in analysis. In this case we may write for the fugacity of a component the relations f/ (HL) = XjHj and fj LR) = X/fk vhere HL stands for Henry law and L-R for Lewis-Randall assumption. The problem is now how to express the phase equilibrium A possible approach would be to use Henry law for solute, and Lewis-Randall rule for solvent. For this reason such definition of Ai-values is considered asymmetric. 

Equilibrium Composition of Nonideal Gases. In order to provide equations which would be useful for all substances, Lpwis and RandalP defined a term, fugacity. This is an arbitrarily defined term that may be substituted for pressure in the preceding equation and which will make it applicable for all substwces. The mathematical definition of fugacity / is... 

Level I Model The components of a multimedia model are illustrated in the schematic (Fig. 10.10) with the four major compartments being, air, water, sediment, and soil. The equilibrium distribution of a fixed quantity of chemical among these compartments is defined by the Level 1 model, and by definition, the fugacities in each compartment would be equal... 

Standard potential values are usually those of ideal unimolal solutions at a pressure of 1 atm (ignoring the deviations of fugacity and activity from pressure and concentration, respectively). A pressure of 1 bar = 10 Pa was recommended as the standard value to be used in place of 1 atm = 101 325 Pa (the difference corresponds to a 0.34-mV shift of potential). If a component of the gas phase participates in the equilibrium, its partial pressure is taken as the standard value if not, the standard pressure should be that of the inert gas over the solution or melt. In a certain case, a standard potential can be established in a system with nonunity activities, if the combination of the latter substituted in the Nemst equation equals unity. For any sohd component of redox systems, the chemical potential does not change in the course of the reaction, and it remains in its standard state. In contrast to the common thermodynamic definition of the standard state, the temperature is ignored, because the potential of the standard hydrogen (protium) electrode is taken to be zero at any temperature in aqueous and protic media. The zero temperature coefficient of the SHE corresponds to the conventional assumption of... 

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. 

The fiigacity has the dimension of pressure. Often we want a nondimensional representation of the fugacity, for example, in mass-action (chemical equilibrium) calculations. We will see in Chapter 12 that this requirement leads naturally to the definition of the activity. Furthermore, when we apply the ideal solution idea to nonideal solutions, we will need a measure of departure from ideality, just as the compressibility factor z is a measure of departure from ideal gas behavior. The logical choice for that measure is the activity coefficient, defined below. We will see that the activity and activity coefficient are dimensionless, and that for ideal solutions and many practical solutions the activity is equal to the mol fraction. 

Equation 11.1, which we applied to LLE, applies to any phase equilibrium, so it must apply to LSE, with phase 1 being the liquid and phase 2 being the solid. Substituting the definition of the fugacity in terms of the standard state fugacity and solving for the mol fraction of dissolved solid, we find... 

Equilibrium phenomena of liquid and vapour phases of binary and ternary mixtures, as well as the analytical and graphic representation of the equilibrium of the two phases have been discussed in the introduction written b) Hausen. The introduction also contains discussion of the thermodynamic basis of phase equilibria, definitions of the characteristic concepts of the activity coefficient and the fugacity as well as equations that represent phase equilibria. More references can be found in the papers quoted in the next section entitled "References on the Thcrmodjmamics of the Liquid-Vapour Equilibrium . 

Consider, now, the case of liquid water at 100°C and 1 atm, in equilibrium with its vapor, i.e. saturated water. According to Webster s definition of fugacity we would expect that, due to the equilibrium between the two phases, the molecules of the liquid are as "apt to flee" their... 

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