Calculate the formula weight and molar mass of Al2(SO4)3 (aluminum sulfate), once used as a common antiperspirant.
The Correct Answer and Explanation is:
To calculate the formula weight and molar mass of aluminum sulfate, Al₂(SO₄)₃, we need to add up the atomic masses of all the atoms present in one formula unit.
Step-by-step calculation:
- Aluminum (Al): Atomic mass ≈ 26.98 g/mol
Number of Al atoms = 2
Total = 2 × 26.98 = 53.96 g/mol - Sulfur (S): Atomic mass ≈ 32.07 g/mol
Number of S atoms = 3
Total = 3 × 32.07 = 96.21 g/mol - Oxygen (O): Atomic mass ≈ 16.00 g/mol
Number of O atoms = 12 (4 per SO₄, 3 SO₄ groups)
Total = 12 × 16.00 = 192.00 g/mol
Adding them together:
53.96 (Al) + 96.21 (S) + 192.00 (O) = 342.17 g/mol
So, the formula weight and molar mass of Al₂(SO₄)₃ is 342.17 grams per mole.
Explanation
Aluminum sulfate, Al₂(SO₄)₃, is a compound made of two aluminum ions and three sulfate ions. To determine its molar mass or formula weight, one must calculate the sum of the atomic masses of all atoms in its chemical formula. This is important in chemistry because molar mass allows scientists to convert between the mass of a substance and the number of moles, which are essential for stoichiometric calculations in chemical reactions.
The process begins by examining the chemical formula. Al₂(SO₄)₃ indicates there are two aluminum atoms, three sulfur atoms, and twelve oxygen atoms. The atomic mass of each element can be found on the periodic table. Aluminum has an atomic mass of about 26.98 g/mol. With two atoms, its contribution becomes 53.96 g/mol. Sulfur, at 32.07 g/mol, with three atoms contributes 96.21 g/mol. Oxygen, with twelve atoms at 16.00 g/mol each, adds 192.00 g/mol. Summing all these gives the total molar mass: 342.17 g/mol.
Molar mass is the mass of one mole of a substance. For aluminum sulfate, this means that one mole of Al₂(SO₄)₃ weighs 342.17 grams. This value is the same as its formula weight because formula weight refers to the mass of the compound’s formula unit in atomic mass units, and in grams per mole for practical laboratory use, both values are numerically equal.
Understanding molar mass is crucial for laboratory work, particularly when preparing solutions or performing quantitative chemical reactions. Aluminum sulfate has also been widely used in water treatment and previously in antiperspirants, which makes knowledge of its molar mass important in both industrial and medical contexts.
