A sample of magnesium phosphate Mg3(PO4)2 contains 72 g of magnesium in the sample. Calculate the number of moles of oxygen molecules in the sample.
The Correct Answer and Explanation is:
To calculate the number of moles of oxygen molecules in the sample, we must first clarify what is being asked. Magnesium phosphate, with the formula Mg₃(PO₄)₂, contains oxygen atoms, but these are part of the compound, not free O₂ molecules. Since there are no molecular oxygen (O₂) molecules present in the compound, the question likely means the number of moles of oxygen atoms present in the compound. We’ll proceed with that interpretation.
Step 1: Molar mass of magnesium (Mg)
The atomic mass of magnesium is 24 g/mol.
Given:
Mass of Mg in the sample = 72 g
Moles of Mg = 72 g / 24 g/mol = 3 moles
Step 2: Determine the moles of Mg₃(PO₄)₂
From the formula Mg₃(PO₄)₂, we see that each formula unit contains 3 moles of Mg.
Therefore:
Moles of Mg₃(PO₄)₂ = Moles of Mg / 3
= 3 moles / 3 = 1 mole of Mg₃(PO₄)₂
Step 3: Determine the number of moles of oxygen atoms
Each formula unit of Mg₃(PO₄)₂ contains 2 phosphate (PO₄³⁻) groups.
Each PO₄ group contains 4 oxygen atoms.
So, total oxygen atoms per formula unit = 2 × 4 = 8 oxygen atoms
Therefore, 1 mole of Mg₃(PO₄)₂ contains 8 moles of oxygen atoms.
Final Answer:
8 moles of oxygen atoms
Explanation
This problem involves determining the number of moles of oxygen atoms in a compound when only the amount of magnesium is given. The compound in question is magnesium phosphate, with the chemical formula Mg₃(PO₄)₂. To solve this, we begin by examining the atomic composition and stoichiometry of the compound.
Magnesium phosphate contains three magnesium (Mg) atoms for every two phosphate (PO₄³⁻) groups. The molar mass of elemental magnesium is 24 grams per mole. If the sample contains 72 grams of magnesium, we divide this by the molar mass to find the number of moles of magnesium present: 72 grams divided by 24 grams per mole gives 3 moles of magnesium.
Since the chemical formula shows that three magnesium atoms are present in each unit of Mg₃(PO₄)₂, the number of moles of magnesium phosphate is calculated by dividing the moles of magnesium by three. This gives 1 mole of Mg₃(PO₄)₂.
Next, we analyze the oxygen content. Each phosphate ion contains four oxygen atoms, and there are two phosphate ions in each unit of Mg₃(PO₄)₂. Therefore, each formula unit has 8 oxygen atoms. Since we have one mole of Mg₃(PO₄)₂, we have 8 moles of oxygen atoms in total.
It’s important to note that these are not free oxygen molecules like O₂, but rather oxygen atoms chemically bonded within the phosphate groups of the compound. If the question had asked for molecular oxygen (O₂), the answer would be zero because no O₂ molecules are present in this salt. However, as interpreted, the sample contains 8 moles of oxygen atoms.
