Mixed Solvent System

Mixed solvent systems

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. The total Gibbs energy of a solution is the sum of the ideal solution Gibbs energy and the excess Gibbs energy. When the standard state properties are modified, the ideal part of the Gibbs energy changes. This change needs to be reflected in a similar change in the excess Gibbs energy also avoid discontinuities.  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. This method 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. It is based on two basic thermodynamic concepts:

  • Choice of standard states: Water is considered to be the 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 method for modeling mixed solvent electrolyte solutions was described in the following publications, which also contain the required model parameters:

  1. 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
  2. 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 
  3. 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
  4. Kaj Thomsen, Martin Due Olsen, Lucas FF Corrêa, Modeling vapor-liquid-liquid-solid equilibrium for acetone-water-salt systems, Pure and Applied Chemistry (2020) https://doi.org/10.1515/pac-2019-1013
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