Vapor-Liquid- and Solid-Liquid-Equilibria of Electrolyte Systems (LIQUAC Model)


The presence of a dissolved salt changes the phase equilibrium behavior of a mixture significantly. This phenomenon is often referred to as the "salt effect". It can be applied to optimize separation processes like destillation (shifting of azeotropic points), extraction (shifting of miscibility gaps, changing distribution coefficients), absorption and fractional crystallization.

During the last years thermodynamic models were developed for the calculation of phase equilibria of salt-containing mixtures. However, in most cases the application is restricted to aqueous systems. Reliable methods for the calculation of non-aqueous systems -including solvent mixtures are scarce. Therefore a model has been established, that is based on an expression for the excess Gibbs energy [1,2]. The so called LIQUAC model takes into account all interactions that occur in electrolyte solutions, and calculates the excess Gibbs energy as the sum of :

  1. an electrostatic contribution (representing Coulomb interactions based on the theory of Debye and Hückel)

  2. a short-range contribution (using the UNIQUAC equation for the description of short-range interactions)

  3. a contribution for ion-dipole effects (so called middle range interactions) based on Pitzer's theory.

The model parameters only take into account binary interactions which were fitted to a large data base. Recently this data base was extended with the help of literature data and own measurements using the head-space gaschromatography and ebulliometry. New interaction parameters have been fitted, so that the applicability of the method was largely extended. The present status of the parameter matrix is shown in Fig. 1.


Fig. 1. LIQUAC-Parametermatrix

The method is suitable for the description of both single and mixed solvent systems and it provides more reliable results compared to other models, in particular at high electrolyte concentration. Typical results for VLE together with the experimental data are given in Fig.2.


Fig. 2. Experimental and predicted y-x' phase diagrams for different mixed solvent / salt systems

See more details of Fig. 2 

For the prediction of solid-liquid equilibria (SLE) of salt containing mixtures the solubility product Ksp for the reaction has to be known. It can be calculated from tabulated thermodynamic data:




In equilibrium the following equation has to be satisfied: <dir><dir><dir><dir>



To meet the requirements of precise prediction of the saturation molality, it is very important that the model is not only able to describe the activity coefficient of the solvents, but also the mean activity coefficient of the electrolytes.

Fig. 3 shows some typical results. The mean activity coefficient and the molal osmotic coefficient of a copper chloride solution are calculated with the help of the LIQUAC model and compared with experimental data and calculation results using published parameters for the Pitzer and Bromley method.


Fig.3 Mean activity coefficient and molal osmotic coefficient of an aqueous copper (II) chloride solution, T=298.15 K.


<1> Jiding Li, H.-M. Polka, J. Gmehling, Fluid Phase Equilibr., 94, 89-114(1994).
<2> H.-M. Polka, Jiding Li, J. Gmehling, Fluid Phase Equilibr. , 94,115-127(1994).

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