what is the molecular formula of a compound with the empirical formula of P2O3 and a gram molecular mass of 284 grams?

The answer is: the molecular formula of a compound is P₄O₁₀.

M (P₂O₅) = 2 · Ar (P) + 5 · Ar (O) · g/mol.

M (P₂O₅) = 2 · 31 + 5 · 16 · g/mol.

M (P₂O₅) = 142 g/mol; molar mass of empirical formula.

M (PₓOₙ) = 284 g/mol; molecular mass of unknown compound.

M (PₓOₙ) : M (P₂O₅) = 284 g/mol : 142 g/mol.

M (PₓOₙ) : M (P₂O₅) = 2 : 1.

P5O8

Explanation:

The formula to be used here is

(mass of the emperical formula) n = molecular mass

n is a number that is unknown

The atomic mass of phosphorus (P) is 31 g/mol while that of oxygen is 16 g/mol

molecular mass of the compound is 284g

(P2O3) n = 284g

[ (31 x 2) + (16 x 3) ]n = 284

(110) n = 284

n = 284/110

n = 2.58

If n = 2.58, the molecular formula is (P2O3) 2.58

which is then P (2 x 2.58) = P (5.16) ⇔ P5 and

O (3 x 2.58) = O (7.74) ⇔ O8

= P5O8

NOTE: 5.16 was rounded up to 5 while 7.74 was rounded up to 8