When two liquids are mixed in different proportions at certain temperature and pressure conditions, two liquid phases are produced in different concentrations that reach a thermodynamic equilibrium, which is best known a liquid-liquid equilibria. (LLE). The thermodynamic description of the LLE is in terms of pressure, temperature and fugacity for each chemical species in both phases. The liquid-liquid systems are characterized by a variety of behaviors. At equilibrium, temperature and pressure are the same, so according to the Gibbs phase rule, the system has 3 degrees of freedom. Therefore, to establish the system’s thermodynamic equilibrium can be reached by fixing the concentration of any phase, besides the temperature and pressure.
Partial miscibility
Two liquids are considered partially miscible if shaking equal volumes of the liquids together results in a meniscus visible between two layers of liquid, but the volumes of the layers are not identical to the volumes of the liquids originally added.
Example:
At 50° C the solubility (weight percent) of n-butyl alcohol in water is 6.5 percent, whereas that of water in n-butyl alcohol is 22.4 percent. At 127° C, the upper consolute temperature, complete miscibility is attained: above 127° C the two liquids mix in all proportions, but below 127° C they show a miscibility gap. Thus, if n-butyl alcohol is added to water at 50° C, there is only one liquid phase until 6.5 weight percent of the mixture is alcohol; when more alcohol is added, a second liquid phase appears the composition of which is 22.4 weight percent water. When sufficient alcohol is present to make the overall composition 77.6 weight percent alcohol, the first phase disappears, and only one liquid phase remains.
Solid-liquid Equilibrium
At solid-liquid equilibrium (SLE) in a binary system, the composition in both solid and liquid phases changes with temperature at a given pressure.
Two liquids are considered partially miscible if shaking equal volumes of the liquids together results in a meniscus visible between two layers of liquid, but the volumes of the layers are not identical to the volumes of the liquids originally added.
Example:
At 50° C the solubility (weight percent) of n-butyl alcohol in water is 6.5 percent, whereas that of water in n-butyl alcohol is 22.4 percent. At 127° C, the upper consolute temperature, complete miscibility is attained: above 127° C the two liquids mix in all proportions, but below 127° C they show a miscibility gap. Thus, if n-butyl alcohol is added to water at 50° C, there is only one liquid phase until 6.5 weight percent of the mixture is alcohol; when more alcohol is added, a second liquid phase appears the composition of which is 22.4 weight percent water. When sufficient alcohol is present to make the overall composition 77.6 weight percent alcohol, the first phase disappears, and only one liquid phase remains.
Solid-liquid Equilibrium
At solid-liquid equilibrium (SLE) in a binary system, the composition in both solid and liquid phases changes with temperature at a given pressure.
Ternary diagrams
Represent the equilibrium between the phases that form in a three component system as a function of temperature. Since pressure isn’t an indispensable variable while constructing ternary diagrams, it’s represented at a constant value of 1 atm.
Liquid-Liquid Extraction
In this process, the solute is transferred from one liquid phase to a immiscible or partially miscible liquid in a way that both phases are in contact. Since both phases are chemically different, components get separated according to their distribution in both phases.
Equilibrium Relations in Extraction
1. Phase ruleThree minimum components are needed in a liquid-liquid system, where two phases are in equilibrium. In a ternary system, there are three degrees of freedom, which can be calculated using the phase rule:
F=C-P+2
3-2+2=3
2. Triangular coordinates and equilibrium dataThe equilibrium data is often expressed in triangular coordinates due to the three components that have to be considered. The methods that are used to interpret such ternary composition diagrams are:
In this process, the solute is transferred from one liquid phase to a immiscible or partially miscible liquid in a way that both phases are in contact. Since both phases are chemically different, components get separated according to their distribution in both phases.
Equilibrium Relations in Extraction
1. Phase ruleThree minimum components are needed in a liquid-liquid system, where two phases are in equilibrium. In a ternary system, there are three degrees of freedom, which can be calculated using the phase rule:
F=C-P+2
3-2+2=3
2. Triangular coordinates and equilibrium dataThe equilibrium data is often expressed in triangular coordinates due to the three components that have to be considered. The methods that are used to interpret such ternary composition diagrams are:
Extra for understanding how to interpret ternary compositions:
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References.
Babylon10. (2014). Partial miscibility. [Online]. Available at: http://dictionary.babylon-software.com/partial_miscibility_(partially_miscible)/ [Accessed 23 Nov 2016].
Kurosawa, I. (2004). SOLID-LIQUID EQUILIBRIUM IN MULTI SOLUTE SYSTEMS. [Online]. Available at: https://smartech.gatech.edu/bitstream/handle/1853/4993/kurosawa_izumi_200408_phd.pdf [Accessed 23 Nov 2016].
Ternary Phase Diagrams [Internet]. Brocku.ca. 2016 [cited 20 November 2016]. Available from: https://brocku.ca/earthsciences/people/gfinn/petrology/ternary3.htm
RMP Lecture Notes [Internet]. Facstaff.cbu.edu. 2016 [cited 20 November 2016]. Available from: http://facstaff.cbu.edu/rprice/lectures/extract.html
Babylon10. (2014). Partial miscibility. [Online]. Available at: http://dictionary.babylon-software.com/partial_miscibility_(partially_miscible)/ [Accessed 23 Nov 2016].
Kurosawa, I. (2004). SOLID-LIQUID EQUILIBRIUM IN MULTI SOLUTE SYSTEMS. [Online]. Available at: https://smartech.gatech.edu/bitstream/handle/1853/4993/kurosawa_izumi_200408_phd.pdf [Accessed 23 Nov 2016].
Ternary Phase Diagrams [Internet]. Brocku.ca. 2016 [cited 20 November 2016]. Available from: https://brocku.ca/earthsciences/people/gfinn/petrology/ternary3.htm
RMP Lecture Notes [Internet]. Facstaff.cbu.edu. 2016 [cited 20 November 2016]. Available from: http://facstaff.cbu.edu/rprice/lectures/extract.html