Finding the molecular formula through molar mass

Question

Compound X  has a molar mass of 316.29·gmol−1 and the following composition:

Phosporus: 39.17%

Sulfur:60.83%

Write the molcecular formula of X.

Answer 1

From the % composition, we can just assume we have 100 g of material. Then the % is equal to grams. Our goal is to find the number of MOLES of each element and thus find the empirical formula. Once we know the empirical formula, we can find out how many of those fit into 1 molecular formula.

P: 39.17 g x 1 mol/30.97 g = 1.265 moles P

S: 60.83 g x 1 mol/32.07 g = 1.897 moles S

Since these are not whole numbers, we divide both by 1.265 to try to get whole numbers.

P: 1.265 moles/1.265 moles = 1 mole P

S: 1.897 moles/1.265 moles = 1.5 moles S

Now, we can simply multiply both by 2 to get whole numbers.

P = 2

S = 3

Empirical formula = P₂S₃

The molar mass of 1 empirical formula is (2x30.97) + (3x32.07) = 61.94 + 96.21 = 158.15 g/mole

How many of these fit into a compound with molar mass of 316.29?

316.29/158.15 = 1.999 = 2

Therefore, the molecular formula of compound X is twice the empirical formula or P₄S₆