Multiple Choice
What mass in grams of CH₃OH (MM = 32.04 g/mol) would need to be added to 270.1 g of water in order to lower the freezing point of water by 12.0 °C? (Kf for water is 1.86 °C/m)
14. Solutions
Freezing Point Depression
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What is the freezing point of a solution made by dissolving 59.5 g of CaCl2 into 100 g of H2O, given that the van't Hoff factor (i) for CaCl2 is 3 and the freezing point depression constant (Kf) for water is 1.86 °C/m?
A
-3.72 °C
B
-1.86 °C
C
-5.58 °C
D
0 °C
Verified step by step guidance1
First, calculate the molar mass of CaCl2. The molar mass is the sum of the atomic masses of calcium (Ca) and chlorine (Cl). Use the periodic table to find these values: Ca = 40.08 g/mol, Cl = 35.45 g/mol. Therefore, the molar mass of CaCl2 is: g/mol.
Next, calculate the number of moles of CaCl2 using the formula: . Substitute the mass of CaCl2 (59.5 g) and the molar mass calculated in the previous step.
Determine the molality of the solution. Molality (m) is calculated using the formula: . Convert the mass of water (100 g) to kilograms and use the moles of CaCl2 calculated earlier.
Apply the freezing point depression formula: , where is the van't Hoff factor, is the freezing point depression constant, and is the molality. Substitute the values: = 3, = 1.86 °C/m, and the molality calculated.
Finally, calculate the new freezing point of the solution by subtracting the freezing point depression () from the normal freezing point of water (0 °C).
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