To find the molar mass of a hydrate, you calculate the molar mass of the anhydrous salt and add the molar mass of the water molecules included in the hydrate formula.
Here's a step-by-step breakdown:
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Identify the Chemical Formula of the Hydrate: A hydrate's formula indicates the anhydrous salt and the number of water molecules associated with each formula unit. For example, copper(II) sulfate pentahydrate is written as CuSO4 • 5H2O.
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Determine the Molar Mass of the Anhydrous Salt:
- Look up the atomic masses of each element in the anhydrous salt (the part before the • symbol) from the periodic table.
- Multiply each element's atomic mass by its subscript in the chemical formula.
- Sum the results to get the molar mass of the anhydrous salt.
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Calculate the Molar Mass of the Water Molecule (H2O):
- Atomic mass of Hydrogen (H) ≈ 1.01 g/mol
- Atomic mass of Oxygen (O) ≈ 16.00 g/mol
- Molar mass of H2O = (2 × 1.01 g/mol) + (1 × 16.00 g/mol) = 18.02 g/mol
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Determine the Total Molar Mass of the Water Molecules in the Hydrate: Multiply the molar mass of water by the number of water molecules indicated in the hydrate formula (the coefficient after the • symbol). For example, in CuSO4 • 5H2O, you would multiply 18.02 g/mol by 5.
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Calculate the Molar Mass of the Hydrate: Add the molar mass of the anhydrous salt (from step 2) to the total molar mass of the water molecules (from step 4).
Example: Copper(II) Sulfate Pentahydrate (CuSO4 • 5H2O)
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Anhydrous Salt (CuSO4):
- Copper (Cu): 1 × 63.55 g/mol = 63.55 g/mol
- Sulfur (S): 1 × 32.07 g/mol = 32.07 g/mol
- Oxygen (O): 4 × 16.00 g/mol = 64.00 g/mol
- Molar mass of CuSO4 = 63.55 + 32.07 + 64.00 = 159.62 g/mol
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Water (5H2O):
- Molar mass of H2O = 18.02 g/mol
- Molar mass of 5H2O = 5 × 18.02 g/mol = 90.10 g/mol
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Hydrate (CuSO4 • 5H2O):
- Molar mass of CuSO4 • 5H2O = 159.62 g/mol + 90.10 g/mol = 249.72 g/mol
Therefore, the molar mass of copper(II) sulfate pentahydrate is approximately 249.72 g/mol.
