a) Considering the given percentages, 100 g of the compound contains:
49.5 g or 49.5 / 12.01 = 4.12 mol of Carbon
5.2 g or 5.2 / 1.01 = 5.15 mol of Hydrogen
28.8 g or 28.8 / 14.01 = 2.06 mol of Nitrogen
16.5 g or 16.5 / 16.00 = 1.03 mol of Oxygen
The C : H : N : O mole ratio is 4.12 : 5.15 : 2.06 : 1.03 = 4 : 5 : 2 : 1
Therefore, the empirical formula is C4H5N2O
b) M = 9.71g / 0.050mol = 194.2 g/mol
c) The molecular mass of one empirical formula unit is 12.01*4 + 1.01*5 + 14.01*2 + 16 = 97.1 g/mol.
The molecular mass of the given compound is twice the molecular mass of one empirical formula unit: 194.2 / 97.1 = 2. Therefore, subscripts of the empirical formula should be multiplied by 2. The formula needed is C8H10N4O2.
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