Multiple Choice
Which of the following solutes, when dissolved in 1 kg of water, will lower the freezing point to -3.72 b0C? (Assume complete dissociation and use K_f = 1.86 b0C kg/mol for water.)
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14. Solutions
Freezing Point Depression
Multiple Choice
Which of the following aqueous solutions has the lowest freezing point?
A
0.10 molal KNO_3
B
0.10 molal C_6H_{12}O_6 (glucose)
C
0.10 molal NaCl
D
0.10 molal CaCl_2
Verified step by step guidance1
Recall that the freezing point depression of a solution depends on the molality (m) of the solute, the van't Hoff factor (i), and the freezing point depression constant (K_f) of the solvent. The formula is: \[\Delta T_f = i \times K_f \times m\]
Identify the van't Hoff factor (i) for each solute, which represents the number of particles the solute dissociates into in solution:
- For KNO_3, which dissociates into K^+ and NO_3^-, \[i = 2\]
- For glucose (C_6H_{12}O_6), a non-electrolyte, \[i = 1\]
- For NaCl, which dissociates into Na^+ and Cl^-, \[i = 2\]
- For CaCl_2, which dissociates into Ca^{2+} and 2 Cl^-, \[i = 3\]
Since all solutions have the same molality (0.10 molal) and the same solvent (water, so K_f is constant), the freezing point depression depends directly on the van't Hoff factor. Calculate the effective concentration of particles as \[i \times m\] for each solution.
Compare the values of \[i \times m\] for each solution. The solution with the highest value will have the greatest freezing point depression and thus the lowest freezing point.
Conclude that 0.10 molal CaCl_2, with the highest van't Hoff factor (i = 3), produces the greatest freezing point depression and therefore has the lowest freezing point among the given solutions.
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