Answer:
The correct answer is D) 2.50
Explanation:
The freezing-point depression (ΔTf) of a liquid solvent caused by the addition of a solute can be expressed by the following equation:
ΔTf= Kf x m x i
Where Kf is a cryoscopic constant (it depends on the solvent), m is the molality of the solution (moles of solute per kg of solvent) and i is the van't Hoff factor (it indicates in how many particles is dissociated the solute in the solution).
As the freezing point of C₆H₁₂O₂ and CaCl₂ solutions are the same and both have the same solvent in the same amount, the expressions are equal:
ΔTf (CaCl₂) = ΔTf (C₆H₁₂O₆)
Kf x m x i(CaCl₂)= Kf x m x i(C₆H₁₂O₆)
Kf is the same of both solution, because the solvent is the same (water), so we can eliminate this term and replace m for moles of solute (because we have the same solvent in the same amount). Furthermore, iC₆H₁₂O₆= 1 because C₆H₁₂O₆ is glucose and it is a non ionic solute. Thus,
0.2 mol x i(CaCl) = 0.5 mol x 1
i(CaCl2)= 0.5 mol/0.2 mol
i(CaCl2)= 2.50
Notice that the result is consistent with the number of ions in which CaCl2 dissociates in water (Ca⁺ + 2 Cl⁻= 3). Remember that for most ionic solutes, the actual van't Hoff factor is lower than the predicted by the number of ions in which it dissociates.
