Introduction to Colligative Properties
📌 Colligative properties are characteristics of a solution, like boiling point, freezing point, vapor pressure, and osmotic pressure, that depend solely on the amount of dissolved solute particles.
💧 Dissolving a solute in water will increase the boiling point and decrease the freezing point of the solution.
🧊 Pure water freezes at $0^\circ \text{C}$ and boils at $100^\circ \text{C}$ at sea level (1 atmosphere pressure).
🔬 The effect magnitude depends on the number of dissolved particles, not the chemical identity of the solute.

Solute Dissociation and Particle Count
🍬 Polar molecules like sugar dissolve but do not dissociate (1 mole solute $\rightarrow$ 1 mole particles).
⚛️ Ionic compounds (electrolytes) dissociate into ions when dissolved, leading to more particles (e.g., 1 mole of NaCl $\rightarrow$ 2 moles of dissolved particles: $\text{Na}^+$ and $\text{Cl}^-$).
🧪 Potassium sulfide ($\text{K}_2\text{S}$) dissociates into 3 moles of particles (2 moles of $\text{K}^+$ and 1 mole of $\text{S}^{2-}$), resulting in the greatest effect on boiling/freezing point change compared to 1 mole of sugar or 1 mole of NaCl.

Calculating Boiling Point Elevation
📈 The change in boiling point ($\Delta T_b$) is calculated using the formula: $\Delta T_b = K_b \cdot m \cdot i$.
- $K_b$ is the boiling point constant for the solvent (for water, $0.512^\circ \text{C}/m$).
- $m$ is the molality of the solution.
- $i$ is the van't Hoff factor (number of particles the substance dissociates into).
লবণ For a $1.5 \text{m}$ $\text{NaCl}$ solution ($i=2$), the $\Delta T_b$ is $0.512 \cdot 1.5 \cdot 2 = 1.536^\circ \text{C}$, leading to a new boiling point of $100^\circ \text{C} + 1.536^\circ \text{C} \approx 101.5^\circ \text{C}$.
🧪 For a $1.5 \text{m}$ $\text{CaCl}_2$ solution ($i=3$), the $\Delta T_b$ is $0.512 \cdot 1.5 \cdot 3 = 2.304^\circ \text{C}$, resulting in a boiling point of $102.3^\circ \text{C}$.

Calculating Freezing Point Depression
📉 The change in freezing point ($\Delta T_f$) is calculated using the formula: $\Delta T_f = K_f \cdot m \cdot i$.
- $K_f$ is the freezing point constant for water, which is $1.86^\circ \text{C}/m$.
- Freezing point depression means the resulting freezing point must be subtracted from the solvent's freezing point ($0^\circ \text{C}$ for water).
🧂 Salt is effective for icy roads because its dissociation ($i=2$) lowers the freezing point more significantly than sugar ($i=1$); a $0.5 \text{m}$ salt solution freezes at $-1.86^\circ \text{C}$, while a $0.5 \text{m}$ sugar solution freezes at $-0.93^\circ \text{C}$.

Key Points & Insights
➡️ Colligative properties are determined by the quantity of dissolved particles, independent of the solute's chemical identity.
➡️ Ionic compounds increase the boiling point and decrease the freezing point more profoundly than molecular compounds at the same molality due to dissociation into multiple ions.
➡️ The van't Hoff factor ($i$) is crucial for calculating changes for electrolytes, representing the number of particles formed upon dissociation.
➡️ Salt is used on icy roads because it causes a greater freezing point depression compared to non-electrolytes like sugar.

📸 Video summarized with SummaryTube.com on Nov 30, 2025, 12:49 UTC