Solutions and Colligative Properties: General Chemistry Study Notes

Solutions and Colligative Properties

Introduction

Solutions are homogeneous mixtures composed of two or more substances. Understanding the properties of solutions, how they form, and how their physical properties change with solute concentration is fundamental in general chemistry. This study guide covers solubility, energetics of solution formation, solution equilibrium, concentration units, vapor pressure, and colligative properties such as boiling point elevation and freezing point depression.

Solubility

Definition and Factors Affecting Solubility

• Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature.

• Factors affecting solubility include the nature of the solute and solvent ("like dissolves like"), temperature, and pressure (for gases).

• Polar solutes dissolve best in polar solvents; nonpolar solutes dissolve best in nonpolar solvents.

Example: Benzene (nonpolar) is most soluble in CCl4 (nonpolar), while CFCl3 (polar) is most soluble in polar solvents.

Types of Intermolecular Forces in Solutions

• Dispersion forces: Present in all molecules, especially nonpolar ones.

• Dipole-dipole interactions: Occur between polar molecules.

• Hydrogen bonding: Strong dipole-dipole interaction involving H bonded to N, O, or F.

Example: Water and ethanol mix due to hydrogen bonding; benzene and hexane mix due to dispersion forces.

Energetics of Solution Formation

Enthalpy Changes in Solution Formation

• Solution formation involves three steps: breaking solute-solute interactions, breaking solvent-solvent interactions, and forming solute-solvent interactions.

• The overall enthalpy change ($\Delta H_{solution}$) can be exothermic or endothermic.

• Exothermic process: Energy released when solute and solvent interact is greater than energy required to separate them.

• Endothermic process: Energy required to separate solute and solvent is greater than energy released upon mixing.

Example: Hydration of ions is usually exothermic. For LiCl, $\Delta H_{hydration} = -871$ kJ/mol; for NaCl, $\Delta H_{hydration} = -765$ kJ/mol.

Solution Equilibrium and Saturation

Saturated, Unsaturated, and Supersaturated Solutions

• Saturated solution: Contains the maximum amount of solute at equilibrium.

• Unsaturated solution: Contains less solute than the equilibrium amount.

• Supersaturated solution: Contains more solute than can theoretically dissolve at a given temperature; unstable.

Example: At 60°C, a solution with 38 g KCl per 100 g water is unsaturated if the solubility is 45 g/100 g water. At 0°C, if solubility is 28 g/100 g water, then 12 g KCl will precipitate from a 40 g/100 g solution.

Concentration of Solutions

Common Units of Concentration

• Molarity (M): Moles of solute per liter of solution.

• Molality (m): Moles of solute per kilogram of solvent.

• Percent by mass: (Mass of solute / Mass of solution) × 100%

• Parts per million (ppm): (Mass of solute / Mass of solution) × 106

Example: To prepare a 0.1 M NaNO3 solution, dissolve 1.06 g NaNO3 in water and dilute to 125 mL.

Sample Calculations

• To find the molarity after dilution: $M_1V_1 = M_2V_2$

• To prepare a solution: Weigh the required mass of solute, dissolve in a portion of solvent, and dilute to the desired volume.

Example: Dissolving 1.05 g NaNO3 in 124 g water and diluting to 125 mL yields a specific molarity.

Vapor Pressure of Solutions

Raoult's Law and Deviations

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

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

• Solutions with non-volatile solutes have lower vapor pressure than pure solvents.

• Deviations from Raoult's Law occur when solute-solvent interactions differ from solvent-solvent or solute-solute interactions.

Example: A solution with a mole fraction of C6H14 ($X_{C_6H_{14}}$) = 0.391 will have a vapor pressure lower than pure C6H14.

Colligative Properties

Freezing Point Depression and Boiling Point Elevation

• Colligative properties depend on the number of solute particles, not their identity.

• Freezing point depression: The freezing point of a solution is lower than that of the pure solvent.

• Boiling point elevation: The boiling point of a solution is higher than that of the pure solvent.

• Formulas:

  • Freezing point depression: $\Delta T_f = i K_f m$

  • Boiling point elevation: $\Delta T_b = i K_b m$

  where $i$ is the van't Hoff factor, $K_f$ and $K_b$ are constants, and $m$ is molality.

Example: Adding a solute to water lowers its freezing point (e.g., $\Delta T_f = -11.8^\circ$C) and raises its boiling point (e.g., $\Delta T_b = 103.26^\circ$C).

Sample Table: Colligative Properties Calculations

Property	Formula	Example Value
Freezing Point Depression	$\Delta T_f = i K_f m$	$\Delta T_f = -11.8^\circ$C
Boiling Point Elevation	$\Delta T_b = i K_b m$	$\Delta T_b = 3.26^\circ$C
Vapor Pressure Lowering	$P_{solution} = X_{solvent} P^0_{solvent}$	$P_{solution} = 133$ torr

Summary and Study Tips

• Practice problems on solution preparation, concentration calculations, and colligative properties.

• Understand the conceptual basis for why colligative properties depend on the number of particles.

• Review key equations and know how to apply them to different scenarios.

• Check answers only after attempting problems independently to reinforce learning.

Additional info: For further practice, refer to end-of-chapter problems and self-assessment quizzes in your textbook.