Final answer:
The formula of the calcium chloride hydrate that contains 3.06 g of water in a 12.5 g sample is CaCl2·2H2O, which means there are approximately 2 moles of water for every mole of calcium chloride.
Step-by-step explanation:
To find the formula of the hydrate of calcium chloride that contains 3.06 g of water in a 12.5 g sample, we first need to determine the mass of calcium chloride in the sample by subtracting the mass of water from the total mass of the hydrate:
Mass of CaCl₂ = Total mass of the hydrate - Mass of H₂O = 12.5 g - 3.06 g = 9.44 g
Now we need to convert these masses into moles using the molar mass of water (18.015 g/mol) and the molar mass of calcium chloride (110.98 g/mol, derived from the atomic masses of Ca and Cl).
Moles of H₂O = 3.06 g / 18.015 g/mol = 0.1698 mol
Moles of CaCl₂ = 9.44 g / 110.98 g/mol = 0.0851 mol
To find the mole ratio, we divide the moles of water by the moles of calcium chloride:
Mole ratio = Moles of H₂O / Moles of CaCl₂ = 0.1698 mol / 0.0851 mol ≈ 2
Since the mole ratio is approximately 2, this means there are about 2 moles of water for every mole of calcium chloride in the hydrate. The formula of the hydrate is therefore:
CaCl₂·2H₂O
Which corresponds to option (b) in the question provided.