See the explanation below.
Work Step by Step
Notice that in this scenario, both of the compounds are soluble in methyl chloride and are both insoluble in water. The acid is soluble in aqueous bases, because it reacts with the base to form polar salt known as sodium benzoate. Therefore, the aqueous base is used to remove the benzoic acid from the mixture of the 2 dissolved compounds in methyl chloride. Also notice that the hydrocarbon is neutral and does not dissolve in the base, remaining behind in the methyl chloride. Notice that evaporation of the methyl chloride leaves the naphthalene as crystals. Then, you can add hydrogen chloride to make the aqueous sodium benzoate solution acidic. The salt is then considered to be prorated and once again you have benzoic acid crystals, which are insoluble in water and you can collect by filtration.