In this work an equation of state applicable to the system containing electrolytes has been developed by coupling the perturbed chain statistical associating fluid theory (PC-SAFT) with the primitive mean spherical approximation. The resulting electrolyte equation of state is characterized by 4 ion parameters for each of the cation and anion contained in aqueous solutions, and 4 ion specific parameters for each of six cations (Li + , Na + , K + , Rb + , Mg 2+ and Ca 2+ ) and six anions (Cl − , Br − , I − , HCO 3 − , NO 3 − and SO 4 2− ) were estimated, based upon the individual ion approach, from the fitting of experimental densities and mean ionic activity coefficients of 26 aqueous single-salt solutions at 298.15 K and 1 bar. The present equation of state with the estimated individual ion parameters has been found to satisfactorily describe not only the densities and mean ionic activity coefficients, but also osmotic coefficients and water activities of single-salt aqueous solutions. Furthermore, the present model was extended to two-salt aqueous solutions, and it has been found that thermodynamic properties such as mentioned above, of two-salt solutions, can be well predicted with the present model, without any additional adjustable parameters.
Perturbed-hard-sphere-chain-association (PHSC-AS) equation of state, which is defined by incorporating the association term of the statistical associating fluid theory (SAFT) model into the PHSC equation of state with van der Waals-type dispersion term, is used to calculate the liquid−liquid equilibrium (LLE) for complex associating mixtures such as alcohol/alkane, water/alkane, acetic acid/alkane, alcohol/water, and carboxylic acid/water systems. In this work, the PHSC-AS models with two different chain terms have been investigated. One is the original model proposed by Song et al. [Macromolecules 1994, 27 (2), 441−448], and the other is the modified model whose chain term was replaced with that of the SAFT model. The calculated results of LLE for associating mixtures are compared with those by the purturbed-chain-SAFT (PC-SAFT) model as well. The results with PHSC-AS and PC-SAFT equation of state are in acceptable agreement with the experimental data. Despite the simple dispersion equation with van der Waals-type, PHSC-AS models show a reasonable calculation performance for LLE of associating fluid mixture. ■ INTRODUCTIONThe calculation of liquid−liquid equilibria (LLE) is of importance in the design and development of new separation processes, such as extraction and extractive distillation, and is also a challenge for nonideal mixtures with strong attractive interaction owing to hydrogen bonding. For accurate process modeling and design, the reliable model for associating fluids is essentially required and important.A great number of theoretical studies (i.e., excess Gibbs energy models, conductor-like screening model (COSMO)-based model, and equation of state (EOS)) have been mainly focused on theoretical models to account for the effects of solvation and association on the bulk properties and phase behaviors. Correlations of LLE has been done usually by using the excess Gibbs free energy (g E ) models, such as nonrandom two-liquid (NRTL), 1 universal quasichemical (UNIQUAC), 2 and UNIQUAC functional-group activity coefficients (UNI-FAC), 3 which have been successfully applied for the prediction and correlation of several liquid−liquid systems. The UNIFAC model is most extensively used as a predictive model because of the universal binary interaction parameters between each functional group. 4−6 More recently, COSMO-based models obtained from the results of quantum mechanical calculations, such as COSMO-RS (real solvents) 7,8 and COSMO-SAC (segment activity coefficient), 9,10 have been shown to provide reliable predictions for the various thermodynamic properties for many molecules. 11,12 Aside from excess Gibbs free energy models, the EOS provides a useful tool for describing phase equilibria of mixtures regardless of magnitude of pressure. The advance in statistical mechanics results in perturbation theories capable of accurately describing the thermodynamic properties for nonideal fluids. Wertheim 13,14 proposed the thermodynamic perturbation theory (TPT1) for hydrogen bonding fluids. The statistical-asso...
Perturbed-chain statistical associating fluid theory (PC-SAFT) was applied for modeling the thermodynamic properties of aqueous amino acid solutions. To account for the association phenomena of amino acids occurring in the aqueous solution, the zwitterionic forms of amino acids are assumed to be associating species with proton donor and acceptor sites. Also, in order to reduce the number of adjustable parameters of PC-SAFT equation of state (EoS) for amino acids from five to three, it is assumed that segment numbers of amino acids are linearly related with the molecular weight of amino acids, and the association volume parameters of amino acids can be set to a fixed value. Thus, 3-parameters of PC-SAFT EoS for amino acids were estimated by simultaneously fitting the activity coefficients of amino acid and densities data in the aqueous amino acid solutions. The PC-SAFT EoS with estimated 3-parameters of amino acid is found to well describe activity coefficients of amino acid and densities of the aqueous amino acid solutions. Also, this equation was used for predicting solubilities of amino acids as well as the water activities and osmotic coefficients in the aqueous amino acid solutions. The predicted values of these properties are in good agreement with the experimental data.
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