So working through this.
If some of the benzoic acid goes into the aqueous layer in extraction 1 then you just extract again in extraction 2. So by Stochiometry I get that by the end of extraction 2, all the Benzoic Acid should be precipitated, there is no more left over for extraction 3. So theoretical yield is just 2 g by this method.
I however think, that the question may be asking more so about the partition coefficient. However, I'm not sure I understand it fully. Do I have the necessary information to calculate the partition coefficient? I don't think I do as i have the solubilities however I do not have the solubilities in each of the different layers (only have solubilities in aqueous, not for organic layer).
Am I correct in thinking I cannot calculate the partition coefficient with the information given to me?