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 the concentration of a reactant to decrease by half.

• 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 & Henry's Law

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

• Henry's Law: $C = k_P P$ (solubility of a gas is proportional to its pressure)

Concentration Units

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

• Molality, Mole Fraction, Colligative Properties

Colligative Effects

• Vapor Pressure Depression: Lowering of vapor pressure by addition of solute.

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

• Osmotic Pressure: $\Pi = MRT$

• Freezing Point Depression: $\Delta T_f = i K_f m$

• Boiling Point Elevation: $\Delta T_b = i K_b m$

Entropy

Boltzmann's Definition

Entropy is a measure of disorder or randomness.

• $S = k \ln W$

• 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, phase changes, and heat 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 product to reactant concentrations at equilibrium.

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

• Relationship between $K_c$ and $K_p$ (for gases): $K_p = K_c(RT)^{\Delta n}$

Le Châtelier's Principle

• System at equilibrium responds to disturbances by shifting position to counteract the change.

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 Calculation: $\text{pH} = -\log[H^+]$

• pOH Calculation: $\text{pOH} = -\log[OH^-]$

• Relationship: $\text{pH} + \text{pOH} = 14$

Buffer Solutions

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

• Henderson-Hasselbalch Equation: $\text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$

Acid-Base Titrations

• Used to determine concentration of an acid or base.

• Equivalence point: Amount of titrant equals amount of analyte.

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.

• Cell Potential ($E_{cell}$): $E_{cell} = E_{cathode} - E_{anode}$

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

Transition Metal Chemistry

Electronic Configuration and Coordination Compounds

Transition metals form complex ions with ligands.

• Electronic Configuration: Arrangement of electrons in atomic orbitals.

• Coordination Number: Number of ligand atoms attached to the central metal ion.

• Ligands: Molecules or ions that donate electron pairs to the metal.

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

Ligand	Type	Coordination Number
H2O	Monodentate	1
NH3	Monodentate	1
EDTA	Polydentate	6
en (ethylenediamine)	Bidentate	2
Additional info: Table entries inferred for common ligands.