Equations of state for mixtures

These mixing rules, when joined with the Redlich-Kwong equation of state, will constitute the Redlich-Kwong equation of state for mixtures that is consistent with the statistical mechanical basis of the van der Waals mixing rules. 

In obtaining the expression for the activity coefficient part of the chemical potential, we have considered droplets of a single size represented by the most populous size (corresponding to the maximum in the size distribution). A more formal equation allowing for droplets of various sizes can be written according to the Mansoori—Carnahan—Starling equation of state for mixtures of hard spheres.26 The results based on such an expression are not expected to be essentially different from those obtained on the basis of a single droplet size. 

The critical properties for both carbon dioxide and toluene are given in Table 6.6-1. The binary interaction parameter for the COi-toluene mixture is. not given in Table 9,4-1. However, as the value for CO -benzene is 0.077 and that for COi-rt-heptane is 0.10, we estimate that the COi-toluene interaction parameter will be 0.09. Using this value and the bubble point pressure calculation in either the programs or the MATHCAD worksheet for the Peng-Robinson equation of state for mixtures (de.scribed in Appendix B and on the CD-ROM accompanying this book), the following values were obtained ... 

A one-fluid theory is generally superior to a two-fluid theory in generalizing the LHW equation of state for mixtures. In the one-fluid theory the same form of equation is used for the mixture as for the components, but the equation of state parameters are assumed to be composition dependent. Van der Waals (VDW) forms, quadratic in mole fractions, prove satisfactory to describe this composition dependence for simple species. 

R.J. Magya, S. Root, T.R. Mattsson, Equations of state for mixtures results from density functional (DFT) simulations compared to high accuracy validation experiments on Z, J. Phys. Conf. Ser. 500 (2014). Article 162004. 

In Chapter 4, the important terms for the description of the thermodynamics of mixtures are explained, including the mixing rules, which have become the main progress of modern equations of state for mixtures. 

The hard-sphere contribution is represented by the Boublik-Mansoori hard-sphere equation of state for mixtures of hard spheres, Eq. (84) [74, 75]. 

Song Y, Lambert SM, Prausnitz JM (1994) Equation of state for mixtures of hard sphere chains including copolymers. Macromolecules 27 441 148... 

Figure 16. Vapor-phase equation of state for mixtures containing water (de Santis and Breedveld)...

There are no equations of state for mixtures with an accuracy comparable to that available for pure fluids. In practice, mixture properties are almost always predicted, using a variety of different equations of state and different mixing rules. This section lists a number of references to aid the reader when entering this very extensive literature. A general text, which discusses many different methods for the prediction of mixture properties, is to be found in the fourth edition of the volume by Reid, Prausnitz Poling (1987). 

If the equations of state for mixtures are valid for both the vapour and the liquid, activity coefficients and fugacities can be derived because... 

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