Determine the molecular formula for the compound with the empirical formula P2O3 if the molar mass is 219.90 g/mol.
The Correct Answer and Explanation is:
To determine the molecular formula of a compound, you need to compare the empirical formula mass to the given molar mass.
Step 1: Determine the empirical formula mass of P₂O₃
- Phosphorus (P) atomic mass = 30.97 g/mol
- Oxygen (O) atomic mass = 16.00 g/mol
Empirical formula: P₂O₃
Empirical formula mass = (2 × 30.97) + (3 × 16.00)
= 61.94 + 48.00
= 109.94 g/mol
Step 2: Compare empirical formula mass to molar mass
Given molar mass = 219.90 g/mol
Empirical formula mass = 109.94 g/mol
Now calculate the ratio:
219.90 ÷ 109.94 ≈ 2.00
This means the molecular formula contains two empirical units.
Step 3: Multiply the subscripts in the empirical formula
Empirical formula: P₂O₃
Multiply each subscript by 2:
Molecular formula = P₄O₆
✅ Final Answer: P₄O₆
Explanation
The empirical formula of a compound represents the simplest whole-number ratio of atoms in the molecule. In this problem, the empirical formula is P₂O₃, which means the compound contains two atoms of phosphorus for every three atoms of oxygen. However, this may not reflect the actual number of atoms in a single molecule of the substance. To find the true molecular formula, you must compare the empirical formula mass with the actual molar mass of the compound.
First, calculate the mass of the empirical formula. Two phosphorus atoms contribute a total mass of 61.94 g/mol and three oxygen atoms add up to 48.00 g/mol, giving a total empirical formula mass of 109.94 g/mol. When you divide the given molar mass of 219.90 g/mol by the empirical formula mass, you get a factor of approximately 2.00. This factor tells you how many times the empirical formula must be multiplied to reach the true molecular formula.
By multiplying each subscript in P₂O₃ by 2, the molecular formula becomes P₄O₆. This new formula reflects the actual number of atoms in one molecule, and its mass matches the given molar mass. P₄O₆ is also known as tetraphosphorus hexoxide and is a well-known phosphorus oxide. This step-by-step process demonstrates how understanding the relationship between empirical and molecular formulas allows chemists to determine molecular composition based on measurable properties like molar mass.
