Fugacity coefficient from Redlich-Kwong

In the gas law for real gases, the molar volume can be expressed with one or two virial coefficients according to the equations from Redlich-Kwong or Prausnitz [18, 19], With low pressures, the dependency of the fugacity coefficient can be neglected. 

The Redlich-Kwong equation is pressure-explicit, so we compute the fugacity coefficient from (4.4.24). We find the Redlich-Kwong expression for (p to be... 

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. 

Calculate the compressibility factor for the mixture. In a manner similar to that used in the previous problem, an expression for the fugacity coefficient in vapor mixtures can be derived from any equation of state applicable to such mixtures. If the Redlich-Kwong equation of state is used, the expression is... 

The fugacity coefficient is usually obtained by solving an equation of state (e.g., Peng-Robinson Redlich-Kwong). The activity coefficient is obtained from a liquid phase activity model such as Wilson or NRTL (see Walas, 1985). 

The fugacity coefficient can be calculated using a suitable EOS. The Soave—Redlich—Kwong EOS (SRK EOS) will be employed in this paper. Starting from the SRK EOS... 

In the Chao-Seader correlation, the fugacity coefficient in the gas mixture is obtained from the Redlich-Kwong eos and is as follows ... 

Fugacity coefficients are important in considering the boiling of hydrothermal fluids, and have been approached from the virial equation as well as from numerous modifications of the van der Waals equation, the best known of these being the (modified) Redlich-Kwong equation. However, they are of minor importance in most environmental situations, and are routinely assumed to be 1.0, so that the activity of gaseous solution components is equal to the partial pressure (Equation (3.14)). 

Fugacity coefficients of species in liquid or vapor mixtures can be obtained from (4-52). If the R-K equation of state is applied, a rather tedious procedure, as given by Redlich and Kwong, leads to the following working equations. 

Use the Soave-Redlich-Kwong equation of state to predict for each phase the density, mixture fugacity coefficients, and enthalpy. Also predict the K-values and compare them to the experimental values derived from the above data. 

The fugacity is obtained from the Redlich-Kwong equation by evaluating (4.4.23) for the fugacity coefficient and then applying FFF 1. The result from (4.4.23) is... 

If an equation of state is to be used for the calculation, it is often better to introduce the fugacity coefficient This is particularly important if there is no expression for the Gibbs energy as in the case of empirical cubic equations of state like Soave-Redlich-Kwong and Peng-Robinson. In usual thermodynamics the fugacity coefficient may be calculated from... 

Fugacity coefficients define the deviation from non-ideal to ideal gas behavior and can be determined from generalized compressibility charts or from suitable equations of state [e.g., Soave-Redlich-Kwong, Eq. (6.11.61) for details see Soave (1972)] ... 

To obtain the fugacity coefficient for component 1 from equations (7.4) and (7.5) the differential coefficient ((3P/3wi)r, v.nj) is required. For this purpose it is convenient to rewrite the Redlich-Kwong equation and its mixing rules in terms of total volumes (V=wym) and numbers of moles of components 1 and 2 (ri and W2) giving... 

The calculated curve was obtained via equation (7.35), the fugacity coefficient /i being taken from the Redlich-Kwong expression (7.30). The parameters G22 and b2 for the supercritical component (CO2) were evaluated from the critical constants as described in section 7.2.2.3. 

Redlich and Kwong (1949) derived the following expression from equation (26) for the fugacity coefficient of a pure fluid ... 

Vapor phase fugacity coefficients are calculated using the Redlich-Kwong equation of state, while the activity coefficients are calculated from the regular solution theory of Hildebrand (Hildebrand and Scott, 1964) ... 

Consider a mixture of CH4 and HgS at 444 K and 70 bar. Use the results of Table 7.1 to plot the fugacity coefficient of methane as a function of methane mole fraction using the Redlich— Kwong equation of state with van der Waals mixing rules. Compare the result with that obtained from the text software, ThermoSolver, using the Peng-Robinson equation of state. 

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