You found that naphthalene is more soluble in petroleum ether than water. how do you account for this difference in solubility?

Naphthalene is a nonpolar molecule, therefore it is more soluble in the nonpolar solvent, petroleum ether, than the polar solvent, water. 

The general solubility principle is that "like dissolves like." Naphthalene is a nonpolar hydrocarbon, which means that it has no unequal distribution of charges within its molecular structure, giving it no partially charged regions. Petroleum ether is a nonpolar hydrocarbon also, and thus, since they are both alike in "nature" (nonpolar), then naphthalene will dissolve in the petroleum ether solvent. 

On the other hand, water is a polar molecule, which means that there is an unequal distribution of charge within the molecular structure, giving it a partial positive and a partial negative region. Being polar, it is unlike naphthalene in nature and will therefore not dissolve the said solute.