Yes, if you have some additional information, such as the molecular weight. For instance, the molecules C2H4 and C4H8 have exactly the same percent composition, but they are very different molecules. So you need some other information to tell them apart than the percent composition.
Answer Expanded
This is kind of a trick question. By knowing the percent composition, you would easily be able to determine its empirical formula, but molecular formula is a bit different. The molecular formula is the actual number of atoms in a molecule, so in order to find the specific molecular formula of a substance, you would also need to know how many grams there is of that substance.
(This explains the difference between C2H4 and C4H8)
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