We assume that there are 100 g unknown, and work out the proportion of phosphorus and oxygen atoms.
In 100⋅g of stuff there are 43.64⋅g phosphorus and 56.36⋅g oxygen.
We divide thru by the ATOMIC masses of each constituent:
O: 56.36⋅g16.00⋅g⋅mol−1 = 3.52⋅mol oxygen
P: 43.64⋅g31.00⋅g⋅mol−1 = 1.41⋅mol phosphorus.
We divide thru by the SMALLEST molar quantity, we want to get whole numbers:
3.52⋅mol1.41⋅mol = 2.5 oxygen
1.41⋅mol1.41⋅mol = 1 phosphorus
A formula of PO2.5 is no good to us at all. Why, because as we have specified, the empirical formula is the simplest WHOLE NUMBER RATIO defining constituent atoms in a species. So, we simply double the ration to give P2O5 as required. If the molecular mass of this material is 283.89 g⋅mol−1, what is the molecular formula of this material???
