* Benzoic acid's reaction with ions: Benzoic acid (C6H5COOH) is a weak acid. When it reacts with a strong base, like sodium hydroxide (NaOH), it forms the benzoate ion (C6H5COO-) and water. The benzoate ion is more water-soluble than the original benzoic acid.
* Ether extraction: Ether is a non-polar solvent, while water is polar. When you have a mixture of benzoic acid and benzoate ions in ether, the benzoate ions are much more likely to dissolve in the water layer during an extraction process.
* The point of extraction: The main purpose of extracting an organic layer with aqueous sodium hydroxide (or other bases) is to remove acidic impurities. Since you're starting with benzoic acid, the goal is to *remove* benzoic acid from the organic layer, not introduce it.
So, what would you extract with sodium hydroxide? If you were trying to separate a mixture containing benzoic acid and a neutral organic compound, you'd extract the ether layer with sodium hydroxide. This would remove the acidic benzoic acid into the aqueous layer, leaving the neutral compound behind in the ether.
In summary: Extracting an ether layer with sodium hydroxide is useful for removing acidic impurities, but it's not necessary when reacting benzoic acid to form the benzoate ion because the benzoate ion will preferentially dissolve in the water layer.