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The empirical formula of a compund differs from the molecular formula in that it shows only the correct ratio of one atom to another. The molecular formula correctly lists the actual number of atoms in one molecule of that compound. For example, glucose has a molecular formula of C6H12O6, but it's empirical formula is CH2O, because the ratio of carbon to hydrogen to oxygen is 1:2:1.
So, to calculate the empirical formula of your mystery compound, we need to use the percentages supplied, along with the mass of each atom. Something times 12 equals the 48.38 for carbon. If we divide the 48.38 by 12, we get 4.03, so I vote 4 atoms of carbon.
If we divide 8.12 by 1 for the mass of hydrogen, we get 8.12, so I think 8 atoms of hydrogen.
Then if we divide 33.5, the remainder, by 16 for the mass of oxygen, we get 2.72, which could be rounded up to 3 atoms for oxygen.
That would give us a molecular formula of C4H8O3. The empirical formula would be something like CH2O(1.5). That is based upon the percentage numbers stated in your problem.
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