Find the molar mass of alum (KAl(SO₄)₂ · 12H₂O).
The Correct Answer and Explanation is :
The molar mass of alum, potassium aluminum sulfate dodecahydrate, KAl(SO₄)₂ · 12H₂O, can be calculated by summing the atomic masses of all the atoms in its formula.
Step-by-step Calculation:
- Potassium (K): 1 atom
Atomic mass of K = 39.10 g/mol - Aluminum (Al): 1 atom
Atomic mass of Al = 26.98 g/mol - Sulfur (S): 2 atoms
Atomic mass of S = 32.07 g/mol
Total mass of sulfur = 2 × 32.07 = 64.14 g/mol - Oxygen (O): 8 atoms (from the sulfate ions)
Atomic mass of O = 16.00 g/mol
Total mass of oxygen in SO₄²⁻ = 8 × 16.00 = 128.00 g/mol - Water molecules (H₂O): 12 molecules
Molecular mass of water = 2 × 1.008 (H) + 16.00 (O) = 18.016 g/mol
Total mass of 12 H₂O = 12 × 18.016 = 216.19 g/mol
Now, adding everything together:
- Potassium (K): 39.10 g/mol
- Aluminum (Al): 26.98 g/mol
- Sulfur (S): 64.14 g/mol
- Oxygen (O): 128.00 g/mol
- Water (12 H₂O): 216.19 g/mol
Total molar mass of KAl(SO₄)₂ · 12H₂O = 39.10 + 26.98 + 64.14 + 128.00 + 216.19 = 474.41 g/mol
Explanation:
Alum, KAl(SO₄)₂ · 12H₂O, is a double sulfate salt containing potassium (K), aluminum (Al), and two sulfate (SO₄²⁻) ions along with 12 water molecules (H₂O) of hydration. Each component contributes to the overall mass of the compound. Potassium and aluminum are the metals that combine with the sulfate ions to form the main framework of the alum crystal. Sulfate ions (SO₄²⁻) contribute both sulfur and oxygen atoms. The water molecules (12 H₂O) are part of the structure, hydrating the ions and helping maintain the crystalline form.
The molar mass is important because it allows chemists to calculate the number of moles of the substance in a given mass, which is crucial for stoichiometric calculations in reactions involving alum, such as in water purification, dyeing, or as an astringent in various applications.