Final answer:
Approximately 90.84ml of the organic solvent must be used to effect 90% separation in one extraction. If two extractions were made, each using half of this volume, approximately 681.3% of the organic compound could be recovered.
Step-by-step explanation:
To calculate the volume of the organic solvent needed for 90% separation in one extraction, we can use the equation:
V solute / V solution = K / (1-K)
Given that 2.7g of the compound dissolves in 100ml of water, we can assume that the remaining 97.3g of the solution is the organic solvent. Using the given K value of 15, we can solve for V solute / V solution to find the volume of the organic solvent:
(V solute / V solution) = 15 / (1-15) = 15/14 = 1.07
To find the volume of the organic solvent, we can set up the equation:
(97.3g organic solvent) / (V organic solvent) = 1.07
Solving for V organic solvent:
V organic solvent = (97.3g organic solvent) / 1.07 = 90.84 ml
Therefore, approximately 90.84ml of the organic solvent must be used to effect 90% separation in one extraction.
Now, let's calculate the percentage of the organic compound that could be recovered if two extractions were made, each time using half of the volume calculated in step 2.
Half of the volume of the organic solvent is 90.84ml / 2 = 45.42ml.
Solving for the volume of the solute in each extraction, we have:
45.42ml organic solvent x 15 (K) = 681.3ml solute for each extraction.
Since the original solute volume is 100ml, we can determine the percentage of the solute that could be recovered by dividing 681.3ml by 100ml and multiplying by 100:
Percentage of the solute recovered = (681.3ml / 100ml) x 100% = 681.3%