A solution is prepared by dissolving 5.00 g of calcium chloride dihydrate (CaCl_{2}\cdot2H_{2}O, M = 147.0 g·mol^{-1}) in 200.0 g of water. Assuming complete dissociation into three ions, calculate the freezing point depression of the solution. Use the cryoscopic constant of water K_{f}=1.86\;\text{K·kg·mol^{-1}}.
Answer
\Delta T_{f}=0.95\;\text{K}
The correct answer is \Delta T_{f}=0.95\;\text{K} — Apply the freezing point depression formula: \Delta T_{f}= i\,K_{f}\,m = 3 \times 1.86\;\text{K·kg·mol^{-1}} \times 0.170\;\text{mol·kg^{-1}} = 0.95\;\text{K}.
Step-by-step solution
- Calculate moles of solute: n = 5.00 g / 147.0 g·= 0.0340 mol.
- Determine the molality: m = n / mass of solvent (kg) = 0.0340 mol / 0.200 kg = 0.170\;\text{mol·kg^{-1}}.
- Identify the van 't Hoff factor for (i = 3) because it yields and .
- Apply the freezing point depression formula: \Delta T_{f}= i\,K_{f}\,m = 3 \times 1.86\;\text{K·kg·mol^{-1}} \times 0.170\;\text{mol·kg^{-1}} = 0.95\;\text{K}.
Common mistake: Neglecting the dissociation factor i or using the total mass of solution instead of the mass of solvent for molality
Concept tested: Freezing point depression with van 't Hoff factor
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