Aqueous Salt Solutions

Solutions containing electrolytes and more than one solvent are often called "mixed solvent systems". Mixed solvent systems containing one salt have been considered pseudo binary solutions consisting of "mixed solvent" and salt. This view makes it difficult to model "mixed solvent systems" because the standard chemical potentials of ions are functions of the solvent composition. It is necessary to know the numerical values of the standard chemical potentials of ions at the current solvent composition in order to perform solid-liquid equilibrium and liquid-liquid equilibrium calculations in such systems. With this approach, two models are actually required: one for the variation of the standard state properties with composition and another for the excess Gibbs function. An example of this type of modeling is the model by Pérez-Salado Kamps, "Model for the Gibbs Excess Energy of Mixed-Solvent (Chemical-Reacting and Gas-Containing) Electrolyte Systems, Ind. & Eng. Chem. Res., 44(2005)201-225, DOI:10.1021/ie049543y.

A more straightforward method for modeling mixed solvent systems is presented here. It is based on two basic thermodynamic concepts:

- Choice of standard states: Water is considered the only solvent, electrolytes and non-electrolytes are solutes. The standard state for all solutes is the aqueous standard state. Standard state properties as Gibbs energy of formation and enthalpy of formation are therefore not dependent on composition. Thus no additional model for the standard state properties is required.
- Modeling the effect of the variation of the relative permittivity with composition: The relative permittivity (electric constant) is used for calculating the electrostatic contribution to the interaction between ions in an aqueous solution. It can be determined experimentally that the relative permittivity varies with the solution composition. The effect of solutes on the activity of other components in the solution , including the variation of the relative permittivity, is accounted for through the energy interaction parameters in the excess Gibbs function.

This view makes it possible to calculate solid-liquid-equilibria, vapor-liquid equilibria, and liquid-liquid equilibria with great accuracy using the same set of parameters using the relatively simple thermodynamic model, the Extended UNIQUAC model. Some results of this type of modeling are shown below.

This method for modeling mixed solvent electrolyte solutions was described in the following publications, which also contains the required model parameters:

- Kaj Thomsen and Peter Rasmussen, Modeling of vapor - liquid - solid Equilibria in gas - aqueous electrolyte systems, Chemical Engineering Science Vol. 54(1999)1787-1802, DOI:10.1016/S0009-2509(99)00019-6
- Maria Iliuta, Kaj Thomsen and Peter Rasmussen, Extended UNIQUAC model for correlation and prediction of vapour-liquid-solid equilibria in aqueous salt systems containing non-electrolytes . Part A. Methanol - water - salt systems, Chemical Engineering Science, 55(2000)2673-2686, DOI:10.1016/S0009-2509(99)00534-5
- Kaj Thomsen, Maria Iliuta, and Peter Rasmussen, Extended UNIQUAC model for correlation and prediction of vapor-liquid-liquid-solid equilibria in aqueous salt systems containing non-electrolytes. Part B. Alcohol (Ethanol, Propanols, Butanols) - water - salt systems. (Chemical Engineering Science 59(2004)3631-3647, issue 17), DOI:10.1016/j.ces.2004.05.024

The following five systems are considered on this page:

- Methanol-K
_{2}SO_{4}-H_{2}O at 60°C - Ethanol-K
_{2}SO_{4}-H_{2}O at 25°C - 1-Propanol-K
_{2}SO_{4}-H_{2}O at 45°C - i-Propanol-K
_{2}SO_{4}-H_{2}O at 50°C - NH
_{3}-K_{2}SO_{4}-H_{2}O at 60°C

The phase diagrams below show solubility isotherms for these five systems. The
solubility isotherms describe compositions of each system in equilibrium
with solid potassium sulfate. In all these systems, K_{2}SO_{4}
is being salted out by the addition of an extra solvent. 'Salted out' means
that the solubility decreases and an excess of salt precipitates.

In the triangular diagrams shown below, lines of constant mass %
potassium sulfate are lines parallel to the right hand side of the triangle.
This side is opposite to the corner representing pure K_{2}SO_{4}
and represents potassium sulfate free solutions. A decreasing solubility of
K_{2}SO_{4} is characterized by solubility lines getting
closer to the right side of the diagram.

Of the five solvents added one by one in each of the five diagrams,
ammonia has a stronger salting out effect on K_{2}SO_{4}
than the four alcohols. In all the depicted phase diagrams, the red circles
represent experimental data while the solubility equilibrium lines were
calculated with the Extended UNIQUAC model. Notice that the temperatures
vary between the diagrams.

In all the above graphs, the focus is on the H_{2}O corner of the
phase diagram. The lower part of the diagrams are therefore not shown, even
though in some of the systems experimental data are available for the
solubility of potassium sulfate in pure or almost pure non-electrolyte.