General Chemistry II: Study Guide for Chapters 11–14

Liquids and Phase Changes

Intermolecular Forces and States of Matter

Understanding the relative strengths of intermolecular forces is essential for predicting the properties of solids, liquids, and gases.

• Solids have the strongest intermolecular forces, followed by liquids, and then gases with the weakest.

• Principal forces include hydrogen bonding, dipole-dipole interactions, and London dispersion forces.

• Example: Water (H2O) exhibits strong hydrogen bonding, resulting in high boiling and melting points compared to similar-sized molecules.

Vapor Pressure and Boiling Point

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature.

• Boiling point is the temperature at which vapor pressure equals external pressure.

• Boiling point decreases as external pressure decreases.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation relates vapor pressure and temperature, allowing calculation of enthalpy of vaporization.

• Two-point form: $\ln \frac{P_{\text{vap,2}}}{P_{\text{vap,1}}} = -\frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)$

• The slope of a plot of $\ln P_{\text{vap}}$ vs. $1/T$ is $-\Delta H_{\text{vap}}/R$.

• Use $R$ in units of J/(K·mol).

Phase Changes and Thermodynamic Quantities

Phase changes involve enthalpy ($\Delta H$) and entropy ($\Delta S$) changes.

• Fusion (melting): solid to liquid

• Freezing: liquid to solid

• Vaporization: liquid to gas

• Condensation: gas to liquid

• Sublimation: solid to gas

• Deposition: gas to solid

• Signs: $\Delta H$ and $\Delta S$ are positive for melting, vaporization, and sublimation; negative for freezing, condensation, and deposition.

• Entropy: $S_{\text{solid}} < S_{\text{liquid}} < S_{\text{gas}}$

Gibbs Free Energy ($\Delta G$)

Gibbs free energy determines spontaneity of processes.

• $\Delta G = \Delta H - T\Delta S$

• $\Delta G < 0$ for spontaneous processes, $\Delta G > 0$ for nonspontaneous, $\Delta G = 0$ at equilibrium.

Phase Diagrams

Phase diagrams show the state of a substance at various temperatures and pressures.

• Can determine which phase is present at given conditions.

• Solid-liquid coexistence curve slope indicates whether freezing point increases or decreases with pressure (water is unusual: freezing point decreases with pressure).

• Triple point: all three phases coexist.

• Critical point: marks the end of the liquid-gas boundary.

Solids and Solid-State Materials

Types of Solids

Solids are classified based on their structure and bonding.

• Crystalline solids: have ordered, repeating structures.

• Amorphous solids: lack long-range order.

• Ionic solids: composed of cations and anions.

• Molecular solids: held together by intermolecular forces.

• Network covalent solids: atoms connected by covalent bonds (e.g., diamond).

• Metallic solids: metal atoms with delocalized electrons.

X-ray Crystallography and Bragg's Law

X-ray crystallography is used to determine crystal structures. Bragg's law relates the angle of X-ray diffraction to the spacing between crystal planes.

• Bragg's law: $d = \frac{n\lambda}{2\sin\theta}$

Unit Cells and Packing

The unit cell is the smallest repeating unit in a crystal.

• Simple cubic (scp): 1 atom per unit cell

• Body-centered cubic (bcc): 2 atoms per unit cell

• Face-centered cubic (fcc or ccp): 4 atoms per unit cell

• Atoms at center contribute 1, face 1/2, edge 1/4, corner 1/8 to the unit cell.

• ccp has the highest packing efficiency.

Ionic Solids and Crystal Structures

Ionic solids have alternating cations and anions. The formula can be determined by counting ions in the unit cell.

• Oxidation numbers can be deduced from the arrangement.

Carbon Allotropes

Graphite, diamond, and fullerene (C60) are important carbon structures.

• Graphite: layers of hexagonal carbon rings

• Diamond: 3D network of covalent bonds

• Fullerene: spherical structure of 60 carbon atoms

Metallic Bonding and Band Theory

Metallic bonding involves delocalized electrons ('electron sea' model), explaining malleability, ductility, and conductivity.

• Band theory: molecular orbitals form bands; population of bands determines conductivity.

• Transition metals: d electron count affects bonding strength and melting point.

Semiconductors and Superconductors

Semiconductors have a band gap between valence and conduction bands; conductivity increases with temperature.

• n-type: extra electrons

• p-type: holes (missing electrons)

• Doping increases conductivity.

• Diodes use p-n junctions.

• "3-5 semiconductors" (e.g., GaAs) combine group 3 and 5 elements.

• Superconductors have zero resistance below critical temperature (Tc).

Solutions and Their Properties

Definitions and Types

A solution is a homogeneous mixture of solute and solvent.

• Types: solid-liquid, liquid-liquid, gas-gas, etc.

• Solubility: maximum amount of solute that can dissolve.

• Saturated solution: contains maximum solute.

• Supersaturated solution: contains more solute than equilibrium allows.

Thermodynamics of Solution Formation

Enthalpy and entropy changes determine whether solution formation is exothermic or endothermic.

• $\Delta H_{\text{soln}} = \Delta H_{\text{solute-solute}} + \Delta H_{\text{solvent-solvent}} + \Delta H_{\text{solute-solvent}}$

• $\Delta S_{\text{soln}}$ is usually positive.

• Exothermic: $\Delta H_{\text{soln}} < 0$, $\Delta G_{\text{soln}} < 0$

• Endothermic: $\Delta G_{\text{soln}}$ depends on $\Delta H_{\text{soln}}$ and $T\Delta S_{\text{soln}}$

Solubility Rules and Concentration Units

"Like dissolves like" predicts solubility based on polarity.

• Molarity (M): $\frac{\text{mol solute}}{\text{L solution}}$

• Molality (m): $\frac{\text{mol solute}}{\text{kg solvent}}$

• Mole fraction (X): $X_B = \frac{n_B}{n_{A,B}}$

Temperature Effects and Henry's Law

Solubility of solids generally increases with temperature; gases decrease.

• Henry's law: $C = kP$

Colligative Properties

Colligative properties depend on the number of solute particles.

• Raoult's law: $P_{\text{solution}} = P_{\text{solvent}} X_{\text{solvent}}$

• Boiling point elevation: $\Delta T_{\text{bp}} = K_b m i$

• Freezing point depression: $\Delta T_{\text{fp}} = -K_f m i$

• van't Hoff factor ($i$): number of particles formed from dissociation

• Osmotic pressure: $\Pi = MRTi$

• Use $R$ in (L·atm)/(K·mol) for osmotic pressure.

Applications

• Salts with higher $i$ are more effective for freezing point depression (e.g., CaCl2 vs. NaCl).

• Osmotic pressure can determine molar mass of proteins.

Chemical Kinetics

Reaction Rates and Rate Laws

Chemical kinetics studies the speed of reactions and factors affecting them.

• Spontaneous reactions ($\Delta G < 0$) may not be fast.

• Reaction rate: change in concentration per unit time (M/s).

• For $aA + bB \rightarrow xX + yY$, $r = -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = -\frac{1}{b} \frac{\Delta [B]}{\Delta t} = \frac{1}{x} \frac{\Delta [X]}{\Delta t} = \frac{1}{y} \frac{\Delta [Y]}{\Delta t}$

• Instantaneous rate: rate at a specific moment.

• Differential rate law: relates rate to concentrations.

• Order of reaction: exponent of concentration in rate law.

• Units of rate constant ($k$): vary with order (first-order: s-1, second-order: M-1s-1).

Determining Rate Laws

Initial rates method and integrated rate laws are used to determine reaction order and rate constants.

• First-order: $\ln [A] = -kt + \ln [A]_0$

• Half-life: $t_{1/2} = \frac{0.693}{k}$

• Second-order: $\frac{1}{[A]} = kt + \frac{1}{[A]_0}$

• For first-order, half-life is independent of initial concentration.

Temperature and Activation Energy

Reaction rates increase with temperature due to higher collision frequency and energy.

• Arrhenius equation: $k = Ae^{-E_a/(RT)}$

• Arrhenius plot: $\ln k$ vs. $1/T$; slope $-E_a/R$, intercept $\ln A$

• Use $R$ in J/(K·mol).

Reaction Mechanisms and Catalysis

Mechanisms describe the sequence of elementary steps in a reaction.

• Elementary step: single transition state.

• Unimolecular and bimolecular steps are common; termolecular rare.

• Rate-determining step: slowest step controls overall rate.

• Intermediates: formed and consumed during mechanism.

• Catalysts: increase rate, not consumed; distinguish from intermediates.

• Homogeneous catalysts: same phase as reactants; heterogeneous: different phase.

• Enzymes: biological catalysts.

Appendix: Periodic Table of the Elements

The periodic table is a fundamental reference for chemical properties, atomic structure, and classification of elements. It is essential for understanding trends in bonding, reactivity, and material properties discussed throughout general chemistry.