Final answer:
To find the percent water in CaCl₂·2H₂O, calculate the molar masses of both calcium chloride and water. Add these to obtain the molar mass of the hydrate, and then divide the mass of water by this total molar mass and multiply by 100%, resulting in approximately 24.5%.
Step-by-step explanation:
To calculate the percent water in the hydrate CaCl₂·2H₂O (calcium chloride dihydrate), we must first determine the molar mass of the entire hydrate and the mass of the water within it. The molar mass of calcium chloride dihydrate is the sum of the molar masses of calcium chloride and two water molecules. The molar mass of calcium (Ca) is 40.08 g/mol, chlorine (Cl) is 35.45 g/mol (and there are two chlorine atoms in calcium chloride), and water (H₂O) has a molar mass of 18.02 g/mol.
The molar mass of calcium chloride (CaCl₂) is:
40.08 g/mol (Ca) + 2 × 35.45 g/mol (Cl) = 40.08 g/mol + 70.90 g/mol = 110.98 g/mol.
The total mass of two water molecules is:
2 × 18.02 g/mol (H₂O) = 36.04 g/mol.
Therefore, the total molar mass of calcium chloride dihydrate is:
110.98 g/mol (CaCl₂) + 36.04 g/mol (2H₂O) = 147.02 g/mol.
The mass percent of water in the compound is:
((2 × 18.02 g/mol) / 147.02 g/mol) × 100% ≈ 24.5%.
This means that approximately 24.5% of the mass of calcium chloride dihydrate is made up of water molecules.