Final answer:
The mass of iron (III) chloride hexahydrate needed to prepare a 0.5 dm³ of a 0.40 M solution is 54 grams, calculated using the molar mass and dimensional analysis.
Step-by-step explanation:
To calculate the mass of iron (III) chloride hexahydrate, FeCl3·6H2O, required to prepare a 0.5 dm³ (which is equivalent to 500 mL) of a 0.40 M solution, we first need to determine the molar mass (molecular weight) of FeCl3·6H2O. By adding the atomic masses of all atoms in the formula, we find the molar mass to be approximately 270.3 g/mol.
Next, we use dimensional analysis to convert from the desired molarity and volume to the mass of the solute needed:
(0.40 mol/dm³) × (0.5 dm³) × (270.3 g/mol) = mass of FeCl3·6H2O needed
Performing the multiplication:
(0.40 mol/dm³) × (0.5 dm³) × (270.3 g/mol) = 54 g
Therefore, the mass of iron (III) chloride hexahydrate needed is 54 grams, which matches option D.