Multiple Choice
What is the freezing point of a solution that contains 50.0 g of FeBr₃ in 200.0 g of water, given that the freezing point depression constant (Kf) for water is 1.86 °C/m?
14. Solutions
Freezing Point Depression
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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)
A
100.0 g
B
250.0 g
C
198.5 g
D
150.0 g
Verified step by step guidance1
Identify the formula for freezing point depression: ΔT_f = i * K_f * m, where ΔT_f is the change in freezing point, i is the van't Hoff factor (which is 1 for CH₃OH as it does not dissociate in solution), K_f is the cryoscopic constant, and m is the molality of the solution.
Rearrange the formula to solve for molality (m): m = ΔT_f / (i * K_f). Substitute the given values: ΔT_f = 12.0 °C, i = 1, and K_f = 1.86 °C/m.
Calculate the molality of the solution using the rearranged formula. This will give you the moles of CH₃OH per kilogram of water.
Convert the mass of water from grams to kilograms by dividing by 1000. Use this value to calculate the moles of CH₃OH needed using the molality obtained in the previous step.
Finally, convert the moles of CH₃OH to grams using the molar mass (MM = 32.04 g/mol) by multiplying the moles by the molar mass. This will give you the mass of CH₃OH required to achieve the desired freezing point depression.
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