AP Chemistry Questions on Colligative Properties and Solutions

📚 Quick Study Guide

• 💧 Colligative Properties: These are properties of solutions that depend on the *number* of solute particles, not their identity. Think boiling point elevation, freezing point depression, osmotic pressure, and vapor pressure lowering.
• 🌡️ Boiling Point Elevation: The boiling point of a solution is *higher* than that of the pure solvent. Formula: $$\Delta T_b = iK_b m$$, where $\Delta T_b$ is the boiling point elevation, $i$ is the van't Hoff factor, $K_b$ is the ebullioscopic constant, and $m$ is the molality.
• 🧊 Freezing Point Depression: The freezing point of a solution is *lower* than that of the pure solvent. Formula: $$\Delta T_f = iK_f m$$, where $\Delta T_f$ is the freezing point depression, $i$ is the van't Hoff factor, $K_f$ is the cryoscopic constant, and $m$ is the molality.
• 🌊 Osmotic Pressure: The pressure required to prevent the flow of solvent across a semipermeable membrane. Formula: $$\Pi = iMRT$$, where $\Pi$ is the osmotic pressure, $i$ is the van't Hoff factor, $M$ is the molarity, $R$ is the ideal gas constant, and $T$ is the temperature in Kelvin.
• 💨 Vapor Pressure Lowering: The vapor pressure of a solution is *lower* than that of the pure solvent. Raoult's Law: $$P_{solution} = X_{solvent}P^0_{solvent}$$, where $P_{solution}$ is the vapor pressure of the solution, $X_{solvent}$ is the mole fraction of the solvent, and $P^0_{solvent}$ is the vapor pressure of the pure solvent.
• ➗ Molality (m): Moles of solute per kilogram of solvent. $$m = \frac{\text{moles of solute}}{\text{kg of solvent}}$$
• ➕ van't Hoff factor (i): The number of particles a solute dissociates into in solution. For example, NaCl dissociates into 2 ions (Na+ and Cl-), so i = 2. For non-electrolytes like glucose, i = 1.

🧪 Practice Quiz

1. What colligative property explains why salt is used to melt ice on roads?
   1. Boiling point elevation
   2. Freezing point depression
   3. Osmotic pressure
   4. Vapor pressure lowering
2. Which of the following solutions will have the highest boiling point?
   1. 1.0 m NaCl
   2. 1.0 m Glucose
   3. 1.0 m $MgCl_2$
   4. 1.0 m $AlCl_3$
3. What is the van't Hoff factor for $K_2SO_4$?
   1. 1
   2. 2
   3. 3
   4. 4
4. If 10.0 g of glucose (molar mass = 180 g/mol) is dissolved in 100.0 g of water, what is the molality of the solution?
   1. 0.18 m
   2. 0.56 m
   3. 1.80 m
   4. 5.56 m
5. Which of the following factors does NOT affect the magnitude of a colligative property?
   1. The identity of the solute
   2. The concentration of the solute
   3. The nature of the solvent
   4. The temperature of the solution
6. A solution of ethanol in water has a vapor pressure of 50.0 torr at 25°C. The vapor pressure of pure water at this temperature is 23.8 torr. Assuming ideal behavior, what is the mole fraction of ethanol in the solution?
   1. 0.47
   2. 0.53
   3. 0.68
   4. 0.32
7. What is the primary reason for using colligative properties in real-world applications?
   1. To change the color of a solution
   2. To modify physical properties of solutions without needing to alter chemical composition
   3. To increase the density of a solution
   4. To measure the pH of a solution