MSA-NRTL

The Born term is no more necessary, as the reference state for the ions is not the pure aqueous solution but the infinite dilution of ions in the solvent mixture. Thus, the MSA-NRTL has only two terms ... 

MSA-NRTL model for the description of the thermodynamic properties of electrolyte solutions. Phys Chem Chem Phys 4 4435-4443... 

Nonelectrolyte G mcxlels only account for the short-range interaction among non-charged molecules (—One widely used G model is the Non-Random-Two-Liquid (NRTL) theory developed in 1968. To extend this to electrolyte solutions, it was combined with either the DH or the MSA theory to explicitly account for the Coulomb forces among the ions. Examples for electrolyte models are the electrolyte NRTL (eNRTL) [4] or the Pitzer model [5] which both include the Debye-Hiickel theory. Nasirzadeh et al. [6] used a MSA-NRTL model [7] (combination of NRTL with MSA) as well as an extended Pitzer model of Archer [8] which are excellent models for the description of activity coefficients in electrolyte solutions. Examples for electrolyte G models which were applied to solutions with more than one solvent or more than one solute are a modified Pitzer approach by Ye et al. [9] or the MSA-NRTL by Papaiconomou et al. [7]. However, both groups applied ternary mixture parameters to correlate activity coefficients. Salimi et al. [10] defined concentration-dependent and salt-dependent ion parameters which allows for correlations only but not for predictions or extrapolations. 

Simonin JP, Krebs S, Kunz W (2006) Inclusimi of ionic hydration and association in the MSA-NRTL model for a description of the thcmnodynamic properties of aqueous ionic solutions application to solutions of associating acids. Ind Eng Chtan Res 45 4345 354... 

Here, we describe the application and typical modelling results for a G model (MSA-NRTL) as well as for an EOS (ePC-SAFT). In addition to strong electrolytes which are almost fully dissociated, we also consider some weak electrolytes (acids like HE or ion-paired electrolytes) that do only partially dissociate in aqueous solution. Here, ion pairing is accounted for by an association/dissociation equilibrium between the ion pair and the respective free ions in solution. 

The following chapters will introduce the two models we focus on the (remodel MSA-NRTL and the equation of state ePC-SAFT, both of which composed of different terms for the SR and for the LR contributions in Eq. (1). After that, we will apply the two models to electrolyte solutions in order to describe thermodynamic properties of strong and weak electrolytes. 

Papaiconomou et al combined the NRTL model with the semi-restricted version of the MSA model adapted to the Gibbs energy formalism. Simonin ct applied the MSA-NRTL to strong electrolytes... 

Here, v+ and v denote the stoichiometric factor of the anion and the cation, respectively. All six parameters needed within the MSA-NRTL approach are effectively mixture parameters, as they reflect interactions between two species, with r vcy c(l) being even concentration-dependent. All these parameters were obtained in Ref 5 by adjusting them to experimental MIAC data for the investigated system at 25°C. 

Here v is the stoichiometric factor of the anion and cation. For electrolytes in solution, the MSA-NRTL model describes the mole-fraction based MIAC as ... 

The fact that both the DH k as well as the MSA F in the Coulom-bic contributions in Eq. (12) (ePC-SAFT) and in Eq. (2) (MSA-NRTL) are expressed in terms of the dielectric constant e makes clear that these contributions follow the approach of so-called primitive models . This... 

In case of ePC-SAFT, dispersive (short-range) interactions were only considered for water-water, water-ion, and water-ion pairs but not among ions. Within the ion-specific MSA-NRTL approach, attractive short-range forces are also assumed to occur between anions and cations. 

As mentioned before, ion-specific instead of salt-specific parameters are used here for both models. Thus, the ionic parameters determined for an ion are applicable to all electrolytes containing this ion. Obtaining such a universal set of parameters requires a simultaneous regression of several electrolyte solutions, which is described in Refs. 5 and 15 for both models, MSA-NRTL and ePC-SAFT. 

Using ePC-SAFT, liquid densities, vapour pressures [directly obtained by Eq. (16) not included in the parameter estimation], and solute activity coefficients (MIAC) are modelled whereas only activity coefficients will be presented for MSA-NRTL as this quantity is the only one that can be obtained by a G -model. Any deviations from experimental data will be given by absolute relative deviations (ARD) ... 

In the following, we will give some examples of modelling results obtained with MSA-NRTL and ePC-SAFT. 

Fig. 2. Activity coefficients in a LiBr solution at 25° C. Lines are modelled with MSA-NRTL symbols are experimental data from Hamer and Wu. (a) MIAC of LiBr, and (b) activity coefficients of water in an aqueous LiBr solution.

Fig. 3. Water activity coefficients of (a) three bronfide and (b) three hydroxide aqueous salt solutions at 25°C as function of salt molality. Experimental data Li+ — squares, Na+ — circles, K+ — triangles. The lines represent MSA-NRTL calculations. Activity coefficients decrease with decreasing size of the cation K+ > Na+ > Li+ for bromide solutions but in the reversed order for hydroxide solutions.

This behaviour can quantitatively be captured with MSA-NRTL using a single parameter set per ion (Fig. 3). In Sec. 3.2.2 we will see that the acetate anion also causes a reverse in the WAC (or MIAC) series compared to alkali halides. However, no acetate parameters exist for MSA-NRTL so that we cannot provide direct comparisons for the acetates. 

Although accurate results are obtained with the MSA-NRTL, it should be mentioned that applying an ion-specific treatment gives rise to an ARD value which is threefold compared to a salt-specific treatment for modelling the MIAC which was shown for 19 salts in water. ... 

Section 3.2.1 describes fiilly dissociated electrolytes. For electrolytes that do not completely dissociate into the respective ions, a chemical-reaction mechanism is implemented in the ePC-SAFT framework (Sec. 3.2.2). Modelling of systems that can form multiple ion pairs is described in Sec. 3.2.3. Finally, we will discuss the experimental behaviour of strong and weak acids and present a respective model strategy (Sec. 3.2.4). Whereas so far activity coefficients of 19 electrolyte systems have been modelled by the MSA-NRTL, the properties of more than 120 systems have been studied with ePC-SAFT. The latter contains not only activity coefficients but also solution densities, which are important quantities for both process design and validation of model parameters. 

Until now the calculations showed that both MSA-NRTL and ePC-SAFT are powerful models for the calculation of thermodynamic properties that are required for designing technical processes. In this section, we finally focus on the meaning of the model parameters and how they can be used to interpret experimentally observed phenomena. 

However, the cation-size series of ePC-SAFT and MSA-NRTL differ in their sequence. Obviously, the adjusted MSA-NRTL parameters do not reflect the series of the Pauling diameters. This is due to the fact that they directly reflect the strength of hydration and that no volumetric properties were used for the respective parameter estimation. Thus, the most strongly hydrated cation (Li+) within the alkali halide series considered here seems to have the largest diameter. In contrast, the ePC-SAFT diameters for the alkali cations were obtained by adjusting them to MIAC and volumetric data (solution densities). They follow the same trend and are in the same order of magnitude as the Pauling diameters are. 

The second parameter which is used in the electrolyte models is a parameter representing the short-range interactions between water and an ion. In Table 4, anion-water and cation-water parameters are compared for the two models. Both the ePC-SAFT ujk, as well as the MSA-NRTL TW-ion interaction parameters directly reflect the strength of ionic hydration. The higher and the more negative rw-ion are, the more strongly hydrated the ion is (strong interaction with water) within the considered alkali halides. 

Table 3. Comparison of hydrated-ion sizes Experimental values from X-ray and neutron diffraction measurements versus ePC-SAFT and MSA-NRTL parameters.

Table 4. Comparison of water/ion interaction parameters for ePC-SAFT and MSA-NRTL.

Obviously, the smallest cation but the largest anion interact most strongly with water within the considered systems. Analysing the experimental activity coefficients of water, these parameter series can be confirmed (Fig. 5 and accompanying text). Additionally, it is obvious that the cations are much stronger hydrated than the anions, which is also reflected by the ePC-SAFT and MSA-NRTL parameters u/k and t where the general relation is valid ... 

In this study, the ePC-SAFT EOS as well as the MSA-NRTL model were applied to describe thermodynamic properties of numerous aqueous electrolyte solutions. Whereas only activity coefficients are obtained by the G model, volumetric properties can be calculated with an EOS. Ion-specific parameters were used independent of the electrolyte which the ions are part of. The model parameters possess a physical meaning and show reasonable trends within the ion series. Two ion parameters are needed in ePC-SAFT, whereas six parameters are necessary for applying MSA-NRTL. Next to the standard alkali halide electrolyte systems, both models even capture the non-ideal behaviour of solutions containing acetate or hydroxide anions where a reversed MIAC series is experimentally observed. Until now, thermodynamic properties of more than 120 aqueous systems could be successfully modelled with ePC-SAFT. The MSA-NRTL parameter set has also been applied to a couple of systems (so far 19 solutions). Implementing an ion-pairing reaction in ePC-SAFT,... 

Simonin JP, Bernard O, Papaiconomou N, Runz W. (2008) Description of dilution enthalpies and heat capacities for aqueous solutions within the MSA-NRTL model with ion solvation. Fluid Phase Equilibr 264 211-219. 

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