Solutions and Their Physical Properties: General Chemistry Study Notes

Solutions and Their Physical Properties

Types of Solutions: Some Terminology

Solutions are homogeneous mixtures composed of two or more substances. The solvent is the component present in the largest amount and determines the physical state of the solution, while solutes are the substances dissolved in the solvent.

• Gaseous solutions: Air (N2, O2, etc.), natural gas (CH4, C2H6, etc.)

• Liquid solutions: Seawater (H2O, NaCl, etc.), vinegar (H2O, CH3COOH), soda pop (H2O, CO2, C12H22O11)

• Solid solutions: Yellow brass (Cu, Zn), palladium-hydrogen (Pd, H2)

Solution Concentration

Concentration expresses the amount of solute present in a given quantity of solvent or solution. Common units include:

• Percent concentration:

  • Mass percent (m/m): $\frac{\text{mass of solute}}{\text{mass of solution}} \times 100$

  • Volume percent (v/v): $\frac{\text{volume of solute}}{\text{volume of solution}} \times 100$

  • Mass/volume percent (m/v): $\frac{\text{mass of solute}}{\text{volume of solution}} \times 100$

• Parts per million (ppm), billion (ppb), trillion (ppt): Used for very dilute solutions.

• Mole fraction (χ): $\chi_i = \frac{\text{moles of component } i}{\text{total moles of all components}}$

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Molality (m): $m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}$

Intermolecular Forces and the Solution Process

Enthalpy of Solution

The process of dissolving involves breaking intermolecular forces in both solute and solvent, and forming new interactions. The overall enthalpy change ($\Delta H_{\text{soln}}$) can be endothermic, exothermic, or zero (ideal solution).

• Ideal solution: Intermolecular forces between all components are similar; $\Delta H_{\text{soln}} = 0$.

• Nonideal solution: If adhesive forces (between different molecules) are stronger than cohesive forces (between like molecules), $\Delta H_{\text{soln}} < 0$ (exothermic).

Formation of Ionic Solutions

Ionic compounds dissolve in polar solvents like water due to ion-dipole interactions. The enthalpy of solution is the sum of lattice energy (endothermic) and hydration energies (exothermic).

• Lattice energy: Energy required to separate ions in a solid.

• Hydration energy: Energy released when ions interact with water molecules.

• Overall: $\Delta H_{\text{soln}} = \Delta H_1 + \Delta H_2 + \Delta H_3$

Solution Formation and Equilibrium

Saturated, Unsaturated, and Supersaturated Solutions

A saturated solution contains the maximum amount of solute at a given temperature. Unsaturated solutions can dissolve more solute, while supersaturated solutions contain more solute than is stable and can precipitate excess solute.

Solubilities of Gases

Temperature and Pressure Effects

Gas solubility in water decreases with increasing temperature but increases with pressure. Henry's Law quantifies the effect of pressure:

• Henry's Law: $C = k \times P_{\text{gas}}$

Vapor Pressures of Solutions

Raoult's Law

The vapor pressure of a solvent is lowered by the presence of a nonvolatile solute. Raoult's Law describes this effect:

• $P_A = \chi_A P_A^\circ$

• Where $P_A$ is the vapor pressure of component A, $\chi_A$ is its mole fraction, and $P_A^\circ$ is the vapor pressure of pure A.

Osmotic Pressure

Osmosis and Osmotic Pressure

Osmosis is the movement of solvent through a semipermeable membrane from a region of lower solute concentration to higher concentration. The osmotic pressure ($\pi$) is given by:

• $\pi V = nRT$ or $\pi = CRT$

• Where $C$ is molarity, $R$ is the gas constant, and $T$ is temperature in Kelvin.

Biological Aspects

Cells in hypertonic, isotonic, or hypotonic solutions experience water flow that can cause crenation (shrinking) or rupture (lysis).

• Hypertonic: Water flows out, cell shrinks.

• Isotonic: No net water flow.

• Hypotonic: Water flows in, cell swells and may burst.

Phase Changes of Nonelectrolyte Solutions

Colligative Properties: Freezing-Point Depression and Boiling-Point Elevation

The presence of a solute lowers the vapor pressure of a solvent, resulting in boiling point elevation and freezing point depression:

• $\Delta T_f = -K_f m$

• $\Delta T_b = K_b m$

• Where $K_f$ and $K_b$ are the freezing and boiling point constants, and $m$ is molality.

Solutions of Electrolytes

Van't Hoff Factor and Colligative Properties

Electrolytes dissociate into ions, increasing the number of solute particles and affecting colligative properties. The van't Hoff factor ($i$) accounts for this effect:

• $\pi = iCRT$

• $\Delta T_f = -iK_f m$

• $\Delta T_b = iK_b m$

• $i = \frac{\text{measured } \Delta T_f}{\text{expected } \Delta T_f}$

Colloidal Mixtures

Properties of Colloids

Colloids are mixtures with particle sizes between 1 and 1000 nm. They can remain suspended indefinitely and exhibit unique properties such as the Tyndall effect (scattering of light).

• Examples: Milk, fog, gels

• Increasing ionic strength can cause coagulation or precipitation of colloidal particles.