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Chapter 10: Problem 80

From the following: pure water solution of \(\mathbf{C}_{12} \mathbf{H}_{22} \mathbf{O}_{11}(m=0.01)\) in water solution of \(\mathrm{NaCl}(m=0.01)\) in water solution of \(\mathrm{CaCl}_{2}(m=0.01)\) in water Choose the one with the a. highest freezing point. b. lowest freezing point. c. highest boiling point. d. lowest boiling point. e. highest osmotic pressure.

Short Answer

Expert verified
a. Highest freezing point: C12H22O11 solution b. Lowest freezing point: CaCl2 solution c. Highest boiling point: CaCl2 solution d. Lowest boiling point: C12H22O11 solution e. Highest osmotic pressure: CaCl2 solution

Step by step solution

01

Identify the solutions given

The given solutions are: 1. Pure water solution of C12H22O11 (sucrose) with a molality (m) of 0.01 2. Solution of NaCl with a molality (m) of 0.01 3. Solution of CaCl2 with a molality (m) of 0.01
02

Determine the Van't Hoff factor for each solute

The Van't Hoff factor, i, is the number of ions that a solute dissociates into when dissolved in solution. We have: 1. For sucrose (C12H22O11), i = 1, as it doesn't dissociate into ions. 2. For NaCl, i = 2, as it dissociates into Na+ and Cl-. 3. For CaCl2, i = 3, as it dissociates into Ca2+ and two Cl- ions.
03

Apply the formulas for colligative properties

We'll use the formulas for freezing point depression, boiling point elevation, and osmotic pressure. Here, we assume that all three solution properties are related to the total number of solute particles. 1. Freezing point depression: \(\Delta T_f = K_f \cdot m \cdot i\) 2. Boiling point elevation: \(\Delta T_b = K_b \cdot m \cdot i\) 3. Osmotic pressure: \(\Pi = i \cdot M \cdot R \cdot T\) where K_f and K_b are the molal freezing-point depression and boiling-point elevation constants, respectively; m is the molality; i is the Van't Hoff factor; M is the molar concentration, which can be considered equivalent to molality in this case; R is the ideal gas constant; and T is the temperature in Kelvin.
04

Compare freezing points

The solution with the highest freezing point will have the lowest freezing point depression. Using the formula and the data we have for all three solutions, we can order them as follows: C12H22O11 - Lowest Freezing Point Depression NaCl - Intermediate Freezing Point Depression CaCl2 - Highest Freezing Point Depression Hence, the solution of C12H22O11 in water has the highest freezing point. The solution with the lowest freezing point is CaCl2. a. Highest freezing point: C12H22O11 solution b. Lowest freezing point: CaCl2 solution
05

Compare boiling points

The solution with the highest boiling point will have the highest boiling point elevation. Using the formula and the available data for all three solutions, we can order them as follows: C12H22O11 - Lowest Boiling Point Elevation NaCl - Intermediate Boiling Point Elevation CaCl2 - Highest Boiling Point Elevation Hence, the solution of CaCl2 in water has the highest boiling point. The solution with the lowest boiling point is C12H22O11. c. Highest boiling point: CaCl2 solution d. Lowest boiling point: C12H22O11 solution
06

Compare osmotic pressure

The solution with the highest osmotic pressure will have the highest concentration of solute particles. Using the formula and the available data for all three solutions, we can order them as follows: C12H22O11 - Lowest Number of Solute Particles NaCl - Intermediate Number of Solute Particles CaCl2 - Highest Number of Solute Particles Hence, the solution of CaCl2 in water has the highest osmotic pressure. e. Highest osmotic pressure: CaCl2 solution

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Most popular questions from this chapter

How does \(\Delta H_{\text {soln }}\) relate to deviations from Raoult's law? Explain.

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