LIQUAC model

Based on the UNIQUAC equation, an electrolyte model has been developed by Li et al [21], called LIQUAC. 

In the LIQUAC model, the excess Gibbs energy is calculated by three contributions taking into account the long-range (LR), the middle-range (MR), and the short-range (SR) interactions  

The LR term represents the interactions caused by the Coulomb electrostatic forces, expressed by a modified Debye-Hiickel term. The physical validity of the term is limited to the very dilute region. The purpose of this term is just to provide the true limiting law at infinite dilution. 

The activity coefficient caused by the LR interactions for the ions and the solvent is calculated by the following equations in the LIQUAC model  

For a binary mixture, e can be calculated using Osters rule ( 2- 1)(2 2 + 1) 

---

The MR term is the contribution of the indirect effects of the charge interactions, such as the charge-dipole interactions and charge-induced dipole interactions, to the excess Gibbs energy. In the LIQUAC model, the MR term is given by... 

In the LIQUAC model By represents all indirect effects caused by the charges, where the ionic strength dependence is described by the following simple relation ... 

In the LIQUAC model the interactions between like-charged ions are neglected in the MR part, so that Eq. (7.107) can be simplified to... 

Table 7.4 Selected interaction parameters for the LIQUAC model [21],...

For the SR part in the LIQUAC model, the UNIQUAC equation is used (see Chapter 5), where the relative van der Waals surface areas and volumes of the ions were fixed to one. This means that the activity coefficients are split into a combinatorial (C) and a residual part (R) ... 

Predict the mean activity coefficient of Na2S04 in a 1.5 molal aqueous solution at 298.15 K using the LIQUAC model. For the calculation the following properties should be used ... 

This value is in good agreement with the experimental value, as can be seen from Figure 7.6, where the available mean activity coefficients of Na2S04 are shown as a function of the salt concentration together with the predicted values using the LIQUAC model at a temperature of 298.15 K. 

Calculate the ideal solubility (y = 1) of NaCl, KCl, and NH4CI in water at 25 "C with the help of the standard thermodynamic properties listed in Table 8.1. What are the solubilities when the deviation from ideal behavior is taken into account using the LIQUAC model. 

In Figure 8.13 the ideal solubilities of the three salts are shown as a function of temperature together with the experimental data and the results of the LIQUAC model. It can be seen that the predicted solubilities of NaCl at 25 ""C in contrast to the calculated solubilities of KCl and NH4CI assuming ideal behavior (y = 1) are nearly identical with the experimental values. This is caused by the fact that accidentally the mean activity coefficient of NaCl for the calculated solubility of about 6 mol/kg is approx. 1 (see Figure 8.14). 

For selected salts and ions in water the thermodynamic standard properties are listed in Table 8.1. To be able to determine the salt solubility from the solubility product, only an electrolyte model, such as Pitzer, Electrolyte NRTL, LIQUAC [8], or LI FAC [9] for the calculation of the mean activity coefficients y , and in the case of hydrated salts additionally the activity of water is required (see Chapter 7). 

State, such as Predictive Soave-Redlich-Kwong (PSRK) and Volume-Translated Peng-Robinson (VTPR), or electrolyte models (LIQUAC and LIFAC). ... 

---