A sample contains 7.5 g of CaCl2·9H2O. How many grams of pure CaCl2 are present in this sample?

• A. 4.5 g
• B. 7.5 g
• C. 2.0 g
• D. 2.7 g

Answer: (D)

Verified step by step guidance

1. Identify the compound given: calcium chloride dihydrate, which is \(\mathrm{CaCl_2 \cdot 9H_2O}\), meaning one formula unit contains one CaCl2 and nine water molecules of hydration.
2. Calculate the molar mass of \(\mathrm{CaCl_2 \cdot 9H_2O}\) by summing the atomic masses: \(\mathrm{Ca}\), \(\mathrm{Cl}\), \(\mathrm{H}\), and \(\mathrm{O}\). Use atomic masses approximately: Ca = 40.08 g/mol, Cl = 35.45 g/mol, H = 1.008 g/mol, O = 16.00 g/mol.
3. Calculate the molar mass of pure \(\mathrm{CaCl_2}\) alone by summing the atomic masses of one Ca and two Cl atoms.
4. Determine the mass fraction of \(\mathrm{CaCl_2}\) in \(\mathrm{CaCl_2 \cdot 9H_2O}\) using the formula: \(\text{mass fraction} = \frac{\text{molar mass of } \mathrm{CaCl_2}}{\text{molar mass of } \mathrm{CaCl_2 \cdot 9H_2O}}\).
5. Multiply the given sample mass (7.5 g) by the mass fraction calculated to find the grams of pure \(\mathrm{CaCl_2}\) present: \(\text{grams of } \mathrm{CaCl_2} = 7.5 \text{ g} \times \text{mass fraction}\).