Calculation of fugacities

This equation may be integrated from a low pressure where the fugacity is equal to the pressure to a higher pressure P giving 

For gases that deviate only moderately from perfect-gas behaviour a more convenient approximate relation can be used  

Fugacities calculated using this equation for nitrogen at 273 K are compared with the exact values in Table 8.1. 

Calculate the final volume and the work done when 5 x 10 3 m3 of a perfect (monatomic) gas at 273 K is reversibly expanded from 10 atm to 1 atm pressure (a) isothermally and (b) adiabatically. What is the final temperature after the adiabatic expansion Assume Cy = 3R/2. 

Calculate the final temperature and the work done if 5 x 10 3m3 of a perfect (monatomic) gas at 273 K and at 10 atm pressure is allowed to expand suddenly (irreversibly and adiabatically) against an external pressure of 1 atm. 

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The data base contains provisions for a simple augmentation by up to eight additional compounds or substitution of other compounds for those included. Binary interaction parameters necessary for calculation of fugacities in liquid mixtures are presently available for 180 pairs. 

Chapter 3 discusses calculation of fugacity coefficient < ). Chapter 4 discusses calculation of adjusted activity coefficient Y fugacity of the pure liquid f9 [Equation (24)], and Henry s constant H. 

Vugacity Coefficients. An exact equation that is widely used for the calculation of fugacity coefficients and fugacities from experimental pressure—volume—temperature (PVT) data is... 

Activity coefficient models offer an alternative approach to equations of state for the calculation of fugacities in liquid solutions (Prausnitz ct al. 1986 Tas-sios, 1993). These models are also mechanistic and contain adjustable parameters to enhance their correlational ability. The parameters are estimated by matching the thermodynamic model to available equilibrium data. In this chapter, vve consider the estimation of parameters in activity coefficient models for electrolyte and non-electrolyte solutions. 

The values allow the calculation of fugacity and, thence, the chemical potential of the gaseous component at the P and T of interest, applying... 

In order to calculate solubility from Equation 29 we need to choose an expression for the fugacity coefficient. Generally for calculation of fugacity coefficient an equation of state with appropriate mixing rules is used (12) in the following expression ... 

Calculation of Fugacity, f, using the Virial Equation for a Gas at Moderate Pressures... 

Because of the equality of fugacities of saturated liquid and vapor, calculation of fugacity for species i as a compressed liquid is done in two ste First, one calculates the fugacity coefficient of saturated vapor = by integrated form of Eq. (11.20), evaluated for P = P . Then by Eqs. (11. and (11.23),... 

Although we have omitted an identifying subscript in the preceding equations, their application so far has been to the development of generated correlations for pure gases only. In the remainder of this section we show how the virial equation may be generalized to allow calculation of fugacity coefficients < , of species in gas mixtures. 

The calculation of fugacity coefficients and the use of generalized charts are discussed in the standard thermodynamics texts. If the fugacity coefficients are known then in the nonideal case we find that... 

Fugacity coefficients are dimensionless they are identically uni for ideal gases. For nonreacting real gases, their values approach unity as pressure approadies zero. Table 1.2-2 summarizes general thermodynamic relationships for the fugacity coefficients. Section 1.3 discusses the calculation of fugacity coefficients from PVTx equations of state. 

Another commonly used equation of state is the virial equation. We discuss the calculation of fugacity from virial coefficients in Chapter 13, 13.5.1. 

Mackay [43] proposed the calculation of fugacities in the various environmental compartments through the concentrations and fugacity capacities of the compounds in the compartments. According to this approach ... 

Of course, the equilibrium partition approach has some limitations (a) it considers only a phase equilibrium situation and does not take into account the rate of transport between air and soil, (b) the fine distribution of compounds within surface soils may influence the calculation of fugacities and (c) it provides only a snap-shot for a given set of enviromnental conditions. 

Calculation of fugacity coefficient from equation of state in typical case. We shall take as example the general Redlich-Kwong equation (equation 7.19) applied to a mixture of two components 1 and 2. The simple van der Waals mixing rules (7.11) and (7.13) will be used. 

CALCULATION OF FUGACITIES FROM PRESSURE-EXPLICIT EOSs... 

Fully revised and expanded, this new edition deeply explores physical and chemical equilibrium, including a new appendix on the Bridgman Table and its uses, a new chapter on Equilibrium in Biochemical Reactions, and new sections on minimum work, eutectics and hydrates, adsorption, buffers and the charge-balance method of computing them. Its appendix on Calculation of Fugacities from Pressure-explicit EOSs shows clearly how modern computer equilibrium programs actually do their work using the SRK and related equations. 

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