Colligative Properties, Van't Hoff Factor, and Osmolarity/Osmolality in GOB Chemistry

Colligative Properties

Introduction to Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles present, not the identity of the solute. These properties change when a solute is added to a pure solvent.

• Key Colligative Properties: Boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

• Effect of Solute: Adding a solute to a solvent alters these properties in predictable ways.

Boiling Point Elevation

When a non-volatile solute is added to a solvent, the boiling point of the solution increases compared to the pure solvent.

• Definition: The temperature at which the vapor pressure of the solution equals atmospheric pressure is higher for the solution than for the pure solvent.

• Equation:

$\Delta T_b = i K_b m$

• Where: $\Delta T_b$ = boiling point elevation, $i$ = Van't Hoff factor, $K_b$ = ebullioscopic constant, $m$ = molality of the solution.

• Example: Pure benzene (C6H6) has a boiling point of 80.1°C. Adding glucose increases the boiling point to 89.6°C.

Freezing Point Depression

Adding a solute to a solvent lowers the freezing point of the solution compared to the pure solvent.

• Equation:

$\Delta T_f = i K_f m$

• Where: $\Delta T_f$ = freezing point depression, $K_f$ = cryoscopic constant.

Vapor Pressure Lowering

The presence of a non-volatile solute lowers the vapor pressure of the solvent.

• Raoult's Law: The vapor pressure of the solution is proportional to the mole fraction of the solvent.

• Equation:

$P_{solution} = X_{solvent} P^0_{solvent}$

• Where: $P_{solution}$ = vapor pressure of solution, $X_{solvent}$ = mole fraction of solvent, $P^0_{solvent}$ = vapor pressure of pure solvent.

Osmotic Pressure

Osmotic pressure is the pressure required to stop the flow of solvent into a solution through a semipermeable membrane.

• Equation:

$\Pi = iMRT$

• Where: $\Pi$ = osmotic pressure, $M$ = molarity, $R$ = gas constant, $T$ = temperature in Kelvin.

Van't Hoff Factor

Definition and Application

The Van't Hoff factor ($i$) represents the number of particles into which a solute dissociates in solution. It is crucial for calculating colligative properties.

• Ionic Compounds: Dissociate into multiple ions. For example, NaCl dissociates into Na+ and Cl-, so $i = 2$.

• Covalent Compounds: Typically do not dissociate in solution, so $i = 1$ (e.g., glucose, C6H12O6).

• Example Table:

Compound	Dissociation	Van't Hoff Factor ($i$)
NaCl	Na+ + Cl-	2
AlCl3	Al3+ + 3Cl-	4
Glucose (C6H12O6)	No dissociation	1

• Example: AlCl3 has the largest Van't Hoff factor among the given compounds because it dissociates into four ions.

Osmolarity & Osmolality

Definitions and Formulas

Osmolarity and osmolality are measures of solute concentration that account for the number of particles in solution.

• Osmolarity: Number of osmoles of solute per liter of solution.

• Osmolality: Number of osmoles of solute per kilogram of solvent.

• Formulas:

Osmolarity (solute) $= i \times M$ Osmolality (solute) $= i \times m$

• Where: $i$ = Van't Hoff factor, $M$ = molarity, $m$ = molality.

• Example: The ionic molality of potassium ions in a 1.18 m solution of K3PO4 is calculated as $3 \times 1.18 = 3.54$ mol/kg.

Comparisons and Applications

• Boiling Point: Solutions with higher osmolarity (more particles) have higher boiling points.

• Vapor Pressure: Solutions with more solute particles have lower vapor pressure.

• Example Table:

Solution	Boiling Point	Vapor Pressure
0.10 M sucrose	Lower	Higher
0.10 M NaCl	Higher	Lower
0.10 M CaCl2	Even higher	Even lower

• Practice Example: 0.10 M CaCl2 will have the highest boiling point among the given options due to the highest number of ions produced.

• Practice Example: 0.10 m aluminum chloride (AlCl3) will have the lowest vapor pressure among the options, as it produces the most particles in solution.