To find the molar mass of alum, KAl(SO₄)₂·12H₂O, we need to calculate the sum of the atomic masses of all the atoms in the formula. Here’s how you can do it step by step:
1. **Identify the elements and their counts:**
– Potassium (K): 1 atom
– Aluminum (Al): 1 atom
– Sulfur (S): 2 atoms (since there are two SO₄ groups)
– Oxygen (O): 20 atoms (8 from the two SO₄ groups and 12 from the 12H₂O)
– Hydrogen (H): 24 atoms (from the 12H₂O)
2. **Find the atomic masses:**
– 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
3. **Calculate the molar mass:**
– Potassium (K): 1 × 39.10 = 39.10 g/mol
– Aluminum (Al): 1 × 26.98 = 26.98 g/mol
– Sulfur (S): 2 × 32.07 = 64.14 g/mol
– Oxygen (O): 20 × 16.00 = 320.00 g/mol
– Hydrogen (H): 24 × 1.01 = 24.24 g/mol
4. **Sum the masses:**
– Total molar mass = 39.10 + 26.98 + 64.14 + 320.00 + 24.24 = 474.46 g/mol
So, the molar mass of alum KAl(SO₄)₂·12H₂O is **474.46 g/mol**.