Calculate the molar mass of ALUM

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Calculate the molar mass of ALUM, KAl(So4)2 .2H2O or potassium aluminum sulfate dodecahydrate. Be sure to include the twelve waters of hydration in the molar mass 

The Correct Answer and Explanation is :

To calculate the molar mass of potassium aluminum sulfate dodecahydrate, KAl(SO₄)₂·12H₂O (commonly referred to as alum), we need to sum the molar masses of all the components, including the potassium (K), aluminum (Al), sulfate ions (SO₄²⁻), and the twelve water molecules (H₂O) in the hydrate form.

Step-by-Step Calculation:

  1. Potassium (K):
    • The molar mass of potassium (K) is 39.10 g/mol.
    • There is one potassium atom in KAl(SO₄)₂·12H₂O.
    39.10 g/mol×1=39.10 g/mol39.10 \, \text{g/mol} \times 1 = 39.10 \, \text{g/mol}
  2. Aluminum (Al):
    • The molar mass of aluminum (Al) is 26.98 g/mol.
    • There is one aluminum atom in KAl(SO₄)₂·12H₂O.
    26.98 g/mol×1=26.98 g/mol26.98 \, \text{g/mol} \times 1 = 26.98 \, \text{g/mol}
  3. Sulfate (SO₄²⁻):
    • The molar mass of a sulfate ion (SO₄) is calculated by adding the molar masses of sulfur (S) and oxygen (O):
      • Sulfur (S): 32.07 g/mol
      • Oxygen (O): 16.00 g/mol
      • Molar mass of SO₄ = 32.07 + (4 × 16.00) = 96.07 g/mol
    • There are two sulfate ions in KAl(SO₄)₂·12H₂O.
    96.07 g/mol×2=192.14 g/mol96.07 \, \text{g/mol} \times 2 = 192.14 \, \text{g/mol}
  4. Water (H₂O):
    • The molar mass of water (H₂O) is 18.02 g/mol.
    • There are 12 water molecules in KAl(SO₄)₂·12H₂O.
    18.02 g/mol×12=216.24 g/mol18.02 \, \text{g/mol} \times 12 = 216.24 \, \text{g/mol}

Total Molar Mass:

Now, add up all the components: 39.10+26.98+192.14+216.24=474.46 g/mol39.10 + 26.98 + 192.14 + 216.24 = 474.46 \, \text{g/mol}

Thus, the molar mass of potassium aluminum sulfate dodecahydrate (KAl(SO₄)₂·12H₂O) is 474.46 g/mol.

Explanation:

  • Potassium (K) contributes to the overall molar mass because it is a component of the formula unit of the alum.
  • Aluminum (Al) is part of the structure, bound to sulfate ions.
  • Sulfate (SO₄) is an important ion in the compound and appears twice in the formula, making its contribution significant.
  • Water (H₂O) plays a role as part of the hydrate, where twelve molecules of water are included per formula unit. These water molecules are bound to the other ions through hydrogen bonding, which is a key feature of hydrated salts.

By considering all the atoms and molecules in the structure, we can determine the molar mass of KAl(SO₄)₂·12H₂O as 474.46 g/mol.

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