Final answer:
The empirical formula of the unknown compound x with 38.8% calcium, 20.0% phosphorus, 41.3% oxygen is Ca3(PO4)2. This was determined by converting percentage compositions to moles and finding the simplest whole number ratio.
Step-by-step explanation:
To determine the empirical formula of the unknown compound x, which consists of calcium, phosphorus, and oxygen, we must first convert the percentage composition to moles. We know that the compound consists of 38.8% calcium, 20.0% phosphorus, and 41.3% oxygen by mass. To convert these percentages to moles, we divide each percentage by the respective atomic weight of each element (Ca=40.08 g/mol, P=30.97 g/mol, O=16.00 g/mol):
- Calcium: (38.8 g / 40.08 g/mol) = 0.968 moles
- Phosphorus: (20.0 g / 30.97 g/mol) = 0.646 moles
- Oxygen: (41.3 g / 16.00 g/mol) = 2.581 moles
To find the simplest whole number ratio, divide each mole value by the smallest mole value obtained, which in this case is for phosphorus (0.646 moles). This results in approximately:
- Calcium: 0.968 / 0.646 ≈ 1.5
- Phosphorus: 0.646 / 0.646 = 1
- Oxygen: 2.581 / 0.646 ≈ 4
We then multiply each number by 2 to get whole numbers:
- Calcium: 1.5 * 2 = 3
- Phosphorus: 1 * 2 = 2
- Oxygen: 4 * 2 = 8
The empirical formula of the unknown compound x is therefore Ca3(PO4)2.