Colligative Properties
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Topic Summary & Highlights
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Core Concept
Colligative Properties are physical properties of solutions that change when a solute is added to a solvent. These properties depend solely on the number of solute particles in a solution, not their identity. The main colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.
Boiling Point Elevation: $\Delta T_b = i \cdot K_b \cdot m$
Freezing Point Depression: $\Delta T_f = i \cdot K_f \cdot m$
Osmotic Pressure: $\pi = i \cdot M \cdot R \cdot T$
Vapor Pressure Lowering: $\Delta P = X_{\text{solute}} \cdot P^0_{\text{solvent}}$
Practice Tips
Colligative properties depend only on the quantity (number of particles) of solute, not the type of solute, and include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.
Focus on particle effect: Colligative properties are influenced by the number of dissolved particles (ions or molecules), not their identity. Ionic compounds dissociate into multiple particles, multiplying the effect.
Account for van 't Hoff factor (i): For ionic solutes, i represents the number of particles the solute dissociates into (e.g., NaCl → 2 particles; CaCl₂ → 3 particles).
Recognize the role of molality (m): Colligative properties are often expressed using molality, which is independent of temperature since it is mass-based, not volume-based.
Know the assumptions for ideal solutions: Colligative properties assume dilute solutions and no significant solute-solvent interactions beyond dissolution.
Key Colligative Properties
Vapor Pressure Lowering:
Adding a non-volatile solute (one that doesn’t evaporate) to a solvent decreases the solution’s vapor pressure.
Raoult’s Law describes this relationship: $P_{\text{solution}} = X_{\text{solvent}} \times P^{\circ}_{\text{solvent}}$
Where:
$P_{\text{solution}}$: Vapor pressure of the solution
$X_{\text{solvent}}$: Mole fraction of the solvent
$P^{\circ}_{\text{solvent}}$: Vapor pressure of the pure solvent
As solute particles occupy space at the surface, fewer solvent molecules can escape into the gas phase, resulting in lower vapor pressure.
Boiling Point Elevation:
When a solute is added, the boiling point of the solution becomes higher than that of the pure solvent.
Boiling Point Elevation Formula: $\Delta T_b = i \cdot K_b \cdot m$
Where:
ΔTb: Boiling point elevation
i: Van’t Hoff factor (number of particles the solute dissociates into)
Kb: Boiling point elevation constant (unique to each solvent)
m: Molality of the solution (moles of solute per kilogram of solvent)
This occurs because the addition of solute particles reduces the solvent’s ability to enter the vapor phase, requiring a higher temperature to reach the boiling point.
Freezing Point Depression:
Adding a solute lowers the freezing point of the solution relative to the pure solvent.
Freezing Point Depression Formula: $\Delta T_f = i \cdot K_f \cdot m$
Where:
$\Delta T_f$: Freezing point depression
i: Van’t Hoff factor
$K_f$: Freezing point depression constant (specific to each solvent)
m: Molality of the solution
Solute particles disrupt the formation of the orderly solid structure, so a lower temperature is required for the solution to freeze.
Osmotic Pressure:
Osmotic pressure is the pressure required to stop the flow of solvent into a solution through a semipermeable membrane.
Osmotic Pressure Formula: Π = i ⋅ M ⋅ R ⋅ T
Where:
Π: Osmotic pressure
i: Van’t Hoff factor
M: Molarity of the solution
R: Ideal gas constant ($0.0821 \, \text{L} \cdot \text{atm} \, \text{mol}^{-1} \, \text{K}^{-1}$)
T: Temperature in Kelvin
Osmosis occurs when solvent molecules move through a semipermeable membrane to equalize concentration. Adding solute to one side increases osmotic pressure.
Key Colligative Properties
Vapor Pressure Lowering:
Adding a non-volatile solute (one that doesn’t evaporate) to a solvent decreases the solution’s vapor pressure.
Raoult’s Law describes this relationship: $P_{\text{solution}} = X_{\text{solvent}} \times P^{\circ}_{\text{solvent}}$
Where:
$P_{\text{solution}}$: Vapor pressure of the solution
$X_{\text{solvent}}$: Mole fraction of the solvent
$P^{\circ}_{\text{solvent}}$: Vapor pressure of the pure solvent
As solute particles occupy space at the surface, fewer solvent molecules can escape into the gas phase, resulting in lower vapor pressure.
Boiling Point Elevation:
When a solute is added, the boiling point of the solution becomes higher than that of the pure solvent.
Boiling Point Elevation Formula: $\Delta T_b = i \cdot K_b \cdot m$
Where:
ΔTb: Boiling point elevation
i: Van’t Hoff factor (number of particles the solute dissociates into)
Kb: Boiling point elevation constant (unique to each solvent)
m: Molality of the solution (moles of solute per kilogram of solvent)
This occurs because the addition of solute particles reduces the solvent’s ability to enter the vapor phase, requiring a higher temperature to reach the boiling point.
Freezing Point Depression:
Adding a solute lowers the freezing point of the solution relative to the pure solvent.
Freezing Point Depression Formula: $\Delta T_f = i \cdot K_f \cdot m$
Where:
$\Delta T_f$: Freezing point depression
i: Van’t Hoff factor
$K_f$: Freezing point depression constant (specific to each solvent)
m: Molality of the solution
Solute particles disrupt the formation of the orderly solid structure, so a lower temperature is required for the solution to freeze.
Osmotic Pressure:
Osmotic pressure is the pressure required to stop the flow of solvent into a solution through a semipermeable membrane.
Osmotic Pressure Formula: Π = i ⋅ M ⋅ R ⋅ T
Where:
Π: Osmotic pressure
i: Van’t Hoff factor
M: Molarity of the solution
R: Ideal gas constant ($0.0821 \, \text{L} \cdot \text{atm} \, \text{mol}^{-1} \, \text{K}^{-1}$)
T: Temperature in Kelvin
Osmosis occurs when solvent molecules move through a semipermeable membrane to equalize concentration. Adding solute to one side increases osmotic pressure.