Molar mass of KAl(SO4)^2·12H2O
The Correct Answer and Explanation is:
To calculate the molar mass of potassium aluminum sulfate dodecahydrate, commonly referred to as KAl(SO₄)₂·12H₂O, we first need to determine the molar masses of each individual component in the compound.
Step 1: Identify the Components
- Potassium (K): 1 atom
- Aluminum (Al): 1 atom
- Sulfur (S): 2 atoms
- Oxygen (O): In two sulfate groups (SO₄²⁻), so 8 atoms total
- Water (H₂O): 12 water molecules
Step 2: Molar Mass of Each Element
Using the periodic table:
- Potassium (K): 39.10 g/mol
- Aluminum (Al): 26.98 g/mol
- Sulfur (S): 32.07 g/mol
- Oxygen (O): 16.00 g/mol
- Hydrogen (H): 1.01 g/mol
Step 3: Calculate Molar Mass of Each Component
- Potassium (K):
(1 \times 39.10 = 39.10 \, \text{g/mol}) - Aluminum (Al):
(1 \times 26.98 = 26.98 \, \text{g/mol}) - Sulfur (S):
(2 \times 32.07 = 64.14 \, \text{g/mol}) - Oxygen in Sulfate (O):
(8 \times 16.00 = 128.00 \, \text{g/mol}) - Water (H₂O):
[
12 \times (2 \times 1.01 + 16.00) = 12 \times 18.02 = 216.24 \, \text{g/mol}
]
Step 4: Total Molar Mass Calculation
Adding all these values together gives us the total molar mass of KAl(SO₄)₂·12H₂O:
[
39.10 + 26.98 + 64.14 + 128.00 + 216.24 = 474.46 \, \text{g/mol}
]
Conclusion
Thus, the molar mass of potassium aluminum sulfate dodecahydrate, KAl(SO₄)₂·12H₂O, is 474.46 g/mol. This compound is often utilized in various applications such as water purification, as a food additive, and in the textile industry. Understanding its molar mass is essential for stoichiometric calculations in chemical reactions, as it enables chemists to convert between grams and moles effectively, allowing for precise measurements and formulations in laboratory settings.