CHE 132 Final Exam Study Guide: Kinetics, Colligative Properties, Entropy, Free Energy, Equilibrium, Acid-Base Chemistry, Electrochemistry, and Transition Metals

Kinetics

Reaction Rate and Rate Laws

Chemical kinetics studies the speed at which chemical reactions occur and the factors that affect these rates.

• Reaction Rate: The change in concentration of a reactant or product per unit time.

• Rate Law: An equation that relates the reaction rate to the concentrations of reactants, typically in the form $\text{Rate} = k[A]^m[B]^n$.

• Reaction Order: The power to which the concentration of a reactant is raised in the rate law.

• Initial Rates Method: Used to determine the order of reaction by measuring rates at the beginning of the reaction.

Integrated Rate Laws

Integrated rate laws relate concentrations of reactants to time for zero, first, and second order reactions.

• Zero Order: $[A] = [A]_0 - kt$

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

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

Half-Life

The time required for half of the reactant to be consumed.

• First Order: $t_{1/2} = \frac{0.693}{k}$

• Second Order: $t_{1/2} = \frac{1}{k[A]_0}$

Arrhenius Equation

Describes how reaction rates vary with temperature.

• $k = Ae^{-E_a/RT}$

• Activation Energy ($E_a$): Minimum energy required for a reaction to occur.

Collision Theory

Explains reaction rates based on collisions between molecules.

• Effective collisions require proper orientation and sufficient energy.

Reaction Mechanisms

Stepwise sequence of elementary reactions by which overall chemical change occurs.

• Rate-determining step: Slowest step in the mechanism.

• Reaction coordinate diagrams illustrate energy changes during a reaction.

Colligative Properties

Intermolecular Interactions

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

• Vapor Pressure Depression: Lowering of vapor pressure due to solute.

• Raoult's Law: $P_{solution} = X_{solvent} P^0_{solvent}$

• Osmotic Pressure: $\Pi = MRT$

• Freezing Point Depression: $\Delta T_f = iK_f m$

• Boiling Point Elevation: $\Delta T_b = iK_b m$

Converting Units of Concentration

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

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

• Mass Fraction: $\text{mass fraction} = \frac{\text{mass of component}}{\text{total mass}}$

Entropy

Boltzmann's Definition

Entropy is a measure of disorder or randomness in a system.

• $S = k_B \ln W$

• Microstates: Different possible arrangements of particles.

Second Law of Thermodynamics

• Entropy of the universe increases for spontaneous processes.

Units and Calculations

• Standard entropy change: $\Delta S^\circ$

• Qualitative assessment: More particles, higher temperature, and phase changes increase entropy.

Free Energy

Gibbs Free Energy ($\Delta G$)

Determines spontaneity of a process at constant temperature and pressure.

• $\Delta G = \Delta H - T\Delta S$

• Negative $\Delta G$ indicates a spontaneous process.

Relationship to K

• $\Delta G^\circ = -RT \ln K$

Equilibrium

Equilibrium Constant (K)

Describes the ratio of concentrations of products to reactants at equilibrium.

• $K = \frac{[\text{products}]}{[\text{reactants}]}$

• $K_p$ for gases, $K_c$ for concentrations.

Le Châtelier's Principle

• System shifts to counteract changes in concentration, pressure, or temperature.

Relationship between $K$ and $Q$

• $Q$ is the reaction quotient; compare $Q$ to $K$ to predict direction of shift.

Acid-Base Chemistry

Definitions and Strengths

Acids donate protons; bases accept protons.

• Strong acids/bases: Completely dissociate in water.

• Weak acids/bases: Partially dissociate.

• pH: $pH = -\log[H^+]$

• pOH: $pOH = -\log[OH^-]$

• Relationship: $pH + pOH = 14$

Buffer Solutions

• Resist changes in pH upon addition of small amounts of acid or base.

• Henderson-Hasselbalch equation: $pH = pK_a + \log \left(\frac{[A^-]}{[HA]}\right)$

Titrations

• Used to determine concentration of an acid or base.

• Equivalence point: Moles of acid equal moles of base.

Equilibria of Slightly Soluble Compounds

Solubility Product ($K_{sp}$)

Describes equilibrium between a solid and its ions in solution.

• $K_{sp} = [A^+][B^-]$ for $AB$

• Common ion effect: Addition of a common ion decreases solubility.

Electrochemistry

Redox Reactions and Cells

Electrochemistry studies chemical processes that involve electron transfer.

• Oxidation: Loss of electrons.

• Reduction: Gain of electrons.

• Galvanic (Voltaic) Cell: Converts chemical energy to electrical energy.

• Standard Cell Potential ($E^\circ_{cell}$): $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$

• Nernst Equation: $E_{cell} = E^\circ_{cell} - \frac{0.0592}{n} \log Q$

Transition Metal Chemistry

Electronic Configuration

Transition metals have partially filled d orbitals, leading to unique chemical properties.

• Electronic configuration affects color, magnetism, and reactivity.

Coordination Compounds

• Ligands: Molecules or ions that bind to a central metal atom.

• Coordination Number: Number of ligand attachments to the metal.

• Geometry: Common geometries include octahedral, tetrahedral, and square planar.

Ligand	Type	Example
Monodentate	Binds through one atom	NH3
Bidentate	Binds through two atoms	ethylenediamine
Polydentate	Binds through multiple atoms	EDTA

Additional info: These notes expand on the provided outline to ensure completeness and academic clarity for exam preparation.