William P. answered • 08/16/21
Biochemistry student with expertise in STEM curriculum
Liquid-liquid extraction relies on differences in solubility, usually taking advantage of the change of charge between a conjugate acid and conjugate base. The equilibrium equation ΔG° = RT ln(Keq) describes the free energy change between equilibrium at standard conditions (1M for all solutes when in solution and standard temperature and pressure). Keq, then, is the ratio of products to reactants (the "mass-action expression"). This expression can have any value equal than or greater than 0, as concentrations are always positive. A Keq of 0 implies that the process does not occur at all, which in the case of a solubility problem means a compound is completely insoluble. The limit as Keq → ∞ is approached as the concentration of reactants (the denominator) nears 0. This would be a process that goes entirely to completion. For liquid-liquid extraction, the process is the exchange of solutes from one solvent to another. As Keq approaches but never equals infinity, the reactant concentration is always greater than 0 (even if it is infinitesimal). Secondly, while a Keq of 0 is defined, ln(0) is undefined - the concentration of products is likewise always greater than 0. These characteristics of equilibria means that there is some solubility of every solute in the mixture being purified. The best a chemist can do is maximize the target product's solubility, and minimize the solubility of the probable contaminants. Even in the most ideal practical case, some contaminants will transfer to the extracting solvent, and the result will be impurity.
A fun fact related to this is that purity is one criteria distinguishing US Pharmaceutical Grade from Food Grade (and other grades). It is possible to achieve high levels of purity, but these often rely on techniques other than liquid-liquid extraction.
