To verify the empirical formula and calculate the molecular formula of the compound, we can follow these steps:
1. Calculate the moles of phosphorous (P) and oxygen (O) in the compound:
- Mass of phosphorous = 0.500 g
- Mass of oxygen = (Mass of the compound) - (Mass of phosphorous) = 1.145 g - 0.500 g = 0.645 g
Moles of phosphorous (P) = (Mass of phosphorous) / (Molar mass of phosphorous)
The molar mass of phosphorous is 31.0 g/mol.
Moles of phosphorous (P) = 0.500 g / 31.0 g/mol ≈ 0.0161 mol
Moles of oxygen (O) = (Mass of oxygen) / (Molar mass of oxygen)
The molar mass of oxygen is 16.0 g/mol.
Moles of oxygen (O) = 0.645 g / 16.0 g/mol ≈ 0.0403 mol
2. Divide the moles of each element by the smallest number of moles to get the simplest whole number ratio:
Divide moles of phosphorous (P) and oxygen (O) by 0.0161 (the smallest number of moles):
Moles of P = 0.0161 mol / 0.0161 mol ≈ 1
Moles of O = 0.0403 mol / 0.0161 mol ≈ 2.5
So, the empirical formula would be P2O5.
To find the molecular mass, we need the empirical formula, which we have already determined as P2O5.
3. Calculate the empirical formula weight:
The empirical formula weight is the sum of the atomic masses of all the atoms in one empirical formula unit.
Molar mass of P = 31.0 g/mol
Molar mass of O = 16.0 g/mol
Empirical formula weight = (2 * Molar mass of P) + (5 * Molar mass of O)
= (2 * 31.0 g/mol) + (5 * 16.0 g/mol)
= 62.0 g/mol + 80.0 g/mol
= 142.0 g/mol
4. Determine the molecular formula:
To find the molecular formula, we need to compare the empirical formula weight (142.0 g/mol) to the given molecular mass (285 amu).
Molecular formula weight = 285 amu
The molecular formula mass must be a whole number multiple of the empirical formula weight:
Whole number multiple = Molecular formula weight / Empirical formula weight
= 285 amu / 142.0 g/mol
≈ 2
So, the molecular formula would be twice the empirical formula: (P2O5)2, which simplifies to P4O10.
Therefore, the empirical formula of the compound is P2O5, and its molecular formula is P4O10.