Multiple Choice
What is the freezing point of a solution that contains 50.0 g of NaNO₃ in 200.0 g of water, given that the molal 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 NaCl needs to be added to 2.5 kg of water in order to create a solution with a freezing point of -5.4 °C? The freezing point depression constant of water is 1.86 °C/m.
A
72.1 grams
B
90.0 grams
C
58.5 grams
D
45.0 grams
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, K_f is the freezing point depression constant, and m is the molality of the solution.
Calculate the change in freezing point, ΔT_f, by subtracting the freezing point of the solution (-5.4 °C) from the normal freezing point of water (0 °C).
Determine the van't Hoff factor, i, for NaCl. Since NaCl dissociates into two ions (Na^+ and Cl^-), i = 2.
Rearrange the formula to solve for molality, m: m = ΔT_f / (i * K_f). Substitute the known values: ΔT_f, i, and K_f (1.86 °C/m) into the equation to find m.
Use the definition of molality, m = moles of solute / kg of solvent, to find the moles of NaCl. Then, convert moles of NaCl to grams using the molar mass of NaCl (58.44 g/mol).
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