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334 Analytical Chemistry 2.0Extraction Efficiency1008060402000 2 4 6 8 10Number of ExtractionsFigure 7.27 Plot of extractionefficiency versus the number ofextractions for the liquid–liquidextraction in Example 7.15.log( 0. 001) = nlog( 0. 400)n = 754 .we find that a minimum of 8 extractions is necessary.The last two examples provide us with an important observation—forany extraction efficiency, we need less solvent if we complete several extractionsusing smaller portions of solvent instead of one extraction using alarger volume of solvent. For the conditions in Example 7.14 and Example7.15, an extraction efficiency of 99.9% requires one extraction with 9990mL of chloroform, or 120 mL when using eight 15-mL portions of chloroform.Although extraction efficiency increases dramatically with the firstfew multiple extractions, the effect quickly diminishes as we increase thenumber of extractions (Figure 7.27). In most cases there is little improvementin extraction efficiency after five or six extractions. For the conditionsin Example 7.15, we reach an extraction efficiency of 99% after fiveextractions and need three additional extractions to obtain the extra 0.9%increase in extraction efficiency.Practice Exercise 7.8To plan a liquid–liquid extraction we need to know the solute’s distributionratio between the two phases. One approach is to carry out theextraction on a solution containing a known amount of solute. Afterextracting the solution, we isolate the organic phase and allow it to evaporate,leaving behind the solute. In one such experiment, 1.235 g of asolute with a molar mass of 117.3 g/mol is dissolved in 10.00 mL ofwater. After extracting with 5.00 mL of toluene, 0.889 g of the solute isrecovered in the organic phase. (a) What is the solute’s distribution ratiobetween water and toluene? (b) If we extract 20.00 mL of an aqueoussolution containing the solute with 10.00 mL of toluene, what is theextraction efficiency? (c) How many extractions will we need to recover99.9% of the solute?Click here to review your answer to this exercise.7G.3 Liquid–Liquid Extractions Involving Acid–Base EquilibriaAs shown by equation 7.21, in a simple liquid–liquid extraction the distributionratio and the partition coefficient are identical. As a result, the distributionratio does not depend on the composition of the aqueous phaseor the organic phase. Changing the pH of the aqueous phase, for example,will not affect the solute’s extraction efficiency.If the solute participates in an additional equilibrium reaction withina phase, then the distribution ratio and the partition coefficient may notbe the same. For example, Figure 7.28 shows the equilibrium reactions affectingthe extraction of the weak acid, HA, by an organic phase in which