The molecular formula for aspartame is C14H18N2O5, and its molar mass is about 294 g/mol. 1.2 g / 294 g/mol = 4.08 X 10-3 moles aspartame. Since each mole of aspartame has 2 moles of nitrogen, you have 8.16 X 10-3 moles of N in your 1.2 grams of aspartame.
