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
By stoichiometry it is still around 1/3 of benzoic acid to remove from solution.
In reality - slightly less due to it's solubility, but this is unimportant.
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).
Solubility in CH2
won't help you either, as the partition coefficient is ratio of concentration in organic solvent and water.
Concentration ≠ solubility.https://en.wikipedia.org/wiki/Partition_coefficient#Log_P_from_log_S
If the solubility of an organic compound is known or predicted in both water and 1-octanol, then log P can be estimated as log P = log So - log SH2O
But this is only an estimation.