A compound is composed of 13% carbon, 4.3% hydrogen, 30.4% nitrogen, and 52.2% oxygen. The mystery compound has a molar mass of 184 grams per mole. What is the molecular formula of the compound

C₂H₈N₄O₆ is the molecular formula for the compound

Explanation:

Data from the problem:

13 g of C in 100 g of compound

4.3 g of H in 100 g of compound

30.4 g of N in 100 g of compound

52.2 g of O in 100 g of compound

Firstly we determine, the mass of each in 184 g of compound, which is 1 mol

(13 g / 100 g) . 184 g  = 24 g C

(4.3 g  / 100 g) . 184 g  = 7.91 g H ≅ 8 g H

(30.4 g / 100 g) . 184 g  = 56 g N

(52.2 g  / 100 g) . 184 g  = 96 g O

And now, we divide the mass by the molar mass of each to determine the moles:

24 g C / 12 g/mol = 2 mol C

8g H / 1 g/mol = 8 mol H

56 g N / 14 g/mol = 4 mol N

96 g O / 16 g/mol = 6 mol O

So the molecular formula of the compound is C₂H₈N₄O₆