Solved Examples of Freezing Point Depression: A Step-by-Step Approach

📚 Quick Study Guide

• 🧊 Freezing Point Depression: A colligative property where the freezing point of a solvent is lowered when a solute is added.
• 🌡️ Formula: $\Delta T_f = K_f \cdot m \cdot i$, where:
  • $\Delta T_f$ is the freezing point depression.
  • $K_f$ is the cryoscopic constant of the solvent.
  • $m$ is the molality of the solution (moles of solute per kg of solvent).
  • $i$ is the van't Hoff factor (number of particles the solute dissociates into).
• ⚖️ Molality (m): $m = \frac{\text{moles of solute}}{\text{kg of solvent}}$
• ➕ Van't Hoff factor (i):
  • For non-electrolytes (like sugar), $i = 1$.
  • For electrolytes (like NaCl, which dissociates into Na+ and Cl-), $i$ is approximately the number of ions formed.
• 📝 Calculating Freezing Point: Freezing Point of Solution = Freezing Point of Pure Solvent - $\Delta T_f$

Practice Quiz

1. What is the freezing point depression ($\Delta T_f$) when 0.1 moles of glucose are dissolved in 100 g of water? ( $K_f$ for water = 1.86 °C kg/mol, i = 1)

   1. 0.186 °C
   2. 1.86 °C
   3. 18.6 °C
   4. 0.0186 °C

2. What is the molality of a solution containing 20 g of NaCl (molar mass = 58.44 g/mol) in 500 g of water?

   1. 0.068 m
   2. 0.68 m
   3. 6.8 m
   4. 0.0068 m

3. If the freezing point of pure water is 0 °C, what is the freezing point of a solution containing 0.2 moles of NaCl in 200 g of water? ($K_f$ for water = 1.86 °C kg/mol, i = 2)

   1. -3.72 °C
   2. 3.72 °C
   3. -1.86 °C
   4. 1.86 °C

4. Which of the following solutions will have the lowest freezing point? (Assume i=1 for all solutes)

   1. 1 m Glucose
   2. 0.5 m Sucrose
   3. 0.2 m NaCl
   4. 0.1 m $CaCl_2$

5. What is the van't Hoff factor for $MgCl_2$ when it completely dissociates in water?

   1. 1
   2. 2
   3. 3
   4. 4

6. A solution containing which of the following solutes will cause the greatest freezing point depression in water, assuming equal molal concentrations?

   1. Glucose
   2. Sucrose
   3. NaCl
   4. $AlCl_3$

7. What mass of ethylene glycol (molar mass = 62.07 g/mol) must be added to 1.0 kg of water to produce a solution that freezes at -5.0 °C? ($K_f$ for water = 1.86 °C kg/mol, i = 1)

   1. 167 g
   2. 1.67 g
   3. 2.68 g
   4. 267 g