The theory behind the extraction of a solution containing benzoic acid, cellulose, and methyl orange involves many components pertaining to the fundamental ideas of solubility and polarity. Using the concepts of like dissolving like and acid base reactions, a solution of organic acid (benzoic acid), a water soluble compound cellulose, and an organic soluble compound methyl orange, can be separated and benzoic acid can be isolated by a method of extraction.
At the fundamental level, organic solvents separate from aqueous solutions based on their varying densities, typically the organic layer being less dense and therefore on top of the aqueous layer1. Therefore any solutes in those solutions are also separated and can be isolated from one another. This phenomenon is the basis for the liquid-liquid extraction and leads into the concept of the partition coefficient. According to MtCg the ratio of concentrations of a solute in each layer is defined by the partition coefficient K, where K = C2 / C1. The distribution coefficient can therefore be viewed as the ratio of the concentration of the compound in organic solvent to the concentration of the same compound in aqueous solution. This constant allows for the calculation of dissolved compound in each layer of the solution, so that after several extractions, the yield can be sufficient for the purposes of the experiment.
A second type of extraction, acid-base extraction, involves the addition of acids and bases in solutions to change the polarity of organic acids and bases to their corresponding water-soluble salts2. This allows us to take advantage of the liquid-liquid extraction to separate organic acids and bases from solution mixtures. Such extraction can be considered chemically active extraction because the polarity of one substance is altered to increase solubility in water. This type of extraction is necessary when both compounds are non-polar and dissolved well in organic
References: MtCg pg. 129 MtCg pg. 131