Multiple Choice
Which aqueous solution will have the lowest freezing point, assuming all solutes behave ideally and each solution has the same molal concentration?
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14. Solutions
Freezing Point Depression
Multiple Choice
Calculate the mass of KCl used to prepare a solution in 3.00 L of water with a freezing point of –1.20 °C. Assume that the density of water = 1.00 g/mL.
A
0.276 g
B
0.829 g
C
20.6 g
D
72.1 g
E
144 g
Verified step by step guidance1
Identify the freezing point depression formula: ΔT_f = i * K_f * m, where ΔT_f is the change in freezing point, i is the van't Hoff factor, K_f is the cryoscopic constant, and m is the molality of the solution.
Calculate the change in freezing point (ΔT_f) by subtracting the solution's freezing point from the pure solvent's freezing point (0 °C for water). Here, ΔT_f = 0 °C - (-1.20 °C) = 1.20 °C.
Determine the van't Hoff factor (i) for KCl. Since KCl dissociates into K⁺ and Cl⁻ ions, i = 2.
Use the given cryoscopic constant for water, K_f = 1.86 °C kg/mol, and rearrange the freezing point depression formula to solve for molality (m): m = ΔT_f / (i * K_f).
Calculate the moles of KCl using the molality and the mass of the solvent (water). Convert the volume of water to kilograms (3.00 L = 3.00 kg, since the density is 1.00 g/mL), then use the formula: moles of KCl = m * mass of water (in kg). Finally, convert moles of KCl to grams using the molar mass of KCl (74.55 g/mol).
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