General Chemistry Study Guide: Thermodynamics, Electrochemistry, Nuclear Chemistry, and Crystalline Solids

Thermodynamics and Free Energy

Key Terms

• Spontaneous Process: A process that occurs without outside intervention.

• Entropy (S): A measure of the disorder or randomness in a system.

• Second Law of Thermodynamics: States that the entropy of the universe increases for a spontaneous process.

• Reversible Process: A process that can be reversed by infinitesimal changes in a variable.

• Gibbs Free Energy (G): A thermodynamic quantity used to predict spontaneity; $G = H - TS$.

• Standard Entropy Change for a Reaction: The change in entropy when reactants are converted to products under standard conditions.

• Standard Molar Entropies: The entropy content of one mole of a substance under standard conditions.

• Third Law of Thermodynamics: The entropy of a perfect crystal at absolute zero is zero.

• Standard Change in Free Energy: The change in Gibbs free energy under standard conditions.

• Free Energy Change of a Reaction Under Nonstandard Conditions: The change in Gibbs free energy when conditions differ from standard state.

Concepts

• Spontaneous vs. Nonspontaneous Processes: Spontaneous processes occur naturally; nonspontaneous require energy input.

• Thermodynamics: The study of energy changes and transfers in chemical and physical processes.

• Difference from Kinetics: Thermodynamics predicts if a process can occur; kinetics describes how fast it occurs.

• Entropy Change in Universe: For spontaneous processes, the entropy of the universe increases.

• Energetically Equivalent Arrangements: More arrangements (microstates) mean higher entropy.

• Units of Entropy: Joules per kelvin ($J/K$).

• Entropy and State Changes: Entropy increases with melting, vaporization, and mixing.

• Reversible Change in State: $\Delta S = \frac{q_{rev}}{T}$

• Spontaneity and Entropy Decrease: A process can be spontaneous if the surroundings' entropy increases more than the system's decreases.

• Enthalpy and Surroundings' Entropy: If $\Delta H$ is negative, surroundings' entropy increases.

• Temperature and Surroundings' Entropy: $\Delta S_{surroundings} = -\frac{\Delta H_{system}}{T}$

• Negative $\Delta G$: Indicates a spontaneous process.

• Positive $\Delta G$: Indicates a nonspontaneous process.

• Calculating $\Delta G$: $\Delta G = \Delta H - T\Delta S$

• Hess's Law and Entropy: Standard entropy change for a reaction can be calculated using Hess's Law.

• Factors Affecting Microstates: Temperature, volume, and number of particles.

• Calculating Standard Free Energy: (1) From $\Delta G^\circ_f$ values, (2) From $\Delta H^\circ$ and $\Delta S^\circ$, (3) From equilibrium constant $K$.

• Magnitude of $\Delta G^\circ_{rxn}$: Large negative value means more energy available to do work.

• Real vs. Standard Conditions: Real conditions often differ from standard; use the Nernst equation for corrections.

• Free Energy and Equilibrium Constant: $\Delta G^\circ = -RT \ln K$

Equations and Relationships

• Definition of Entropy: $S = k \ln W$

• Change in Entropy: $\Delta S = S_{final} - S_{initial}$

• Change in Entropy of Universe: $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings}$

• Change in Gibbs Free Energy: $\Delta G = \Delta H - T\Delta S$

$\Delta H$	$\Delta S$	Low Temperature	High Temperature
+	+	Nonspontaneous	Spontaneous
-	-	Spontaneous	Nonspontaneous
+	-	Nonspontaneous	Nonspontaneous
-	+	Spontaneous	Spontaneous

• Standard Change in Entropy: $\Delta S^\circ_{rxn} = \sum S^\circ_{products} - \sum S^\circ_{reactants}$

• Methods for Calculating Free Energy of Formation: (1) From tabulated $\Delta G^\circ_f$ values, (2) From $\Delta H^\circ$ and $\Delta S^\circ$, (3) From $K$.

• Relationship Between $\Delta G^\circ_{rxn}$ and $\Delta G_{rxn}$: $\Delta G_{rxn} = \Delta G^\circ_{rxn} + RT \ln Q$

• Relationship Between $\Delta G^\circ_{rxn}$ and $K$: $\Delta G^\circ_{rxn} = -RT \ln K$

• Temperature Dependence of $K$: $K$ changes with temperature according to van 't Hoff equation.

Outcome
Identify spontaneous and nonspontaneous processes
Analyze systems of particles and reactions in terms of entropy change
Calculate the entropy change for a change in state
Calculate entropy changes in the system, the surroundings, and the universe
Analyze reaction spontaneity using Gibbs free energy change, enthalpy, and entropy
Calculate the standard entropy change for a reaction
Analyze reaction spontaneity using standard Gibbs free energy, standard enthalpy, and standard entropy
Calculate standard Gibbs free energy for a reaction using free energies of formation
Calculate standard Gibbs free energy for a stepwise reaction
Calculate Gibbs free energy for a reaction under nonstandard conditions
Perform standard Gibbs free energy calculations using equilibrium constants

Electrochemistry

Key Terms

• Electrical Current: Flow of electric charge.

• Electrochemical Cell: Device that generates electrical energy from chemical reactions or vice versa.

• Voltaic (Galvanic) Cell: Electrochemical cell that produces electricity from spontaneous redox reactions.

• Electrolytic Cell: Cell that uses electrical energy to drive nonspontaneous chemical reactions.

• Half-Cell: Part of an electrochemical cell where either oxidation or reduction occurs.

• Electrode: Conductor through which electrons enter or leave the cell.

• Potential Difference: Voltage between two points.

• Electromotive Force (emf): The cell potential; the driving force for electron flow.

• Cell Potential ($E_{cell}$): The voltage produced by an electrochemical cell.

• Standard Cell Potential ($E^\circ_{cell}$): Cell potential under standard conditions.

• Cathode: Electrode where reduction occurs.

• Salt Bridge: Device that maintains electrical neutrality by allowing ion flow.

• Standard Electrode Potential: Electrode potential measured under standard conditions.

• Standard Hydrogen Electrode: Reference electrode with $E^\circ = 0$ V.

• Faraday's Constant ($F$): Charge of one mole of electrons, $F = 96,485$ C/mol.

• Nernst Equation: Equation relating cell potential to concentrations.

• Dry-Cell Battery, Alkaline Battery, Lead-Acid Storage Battery, Nickel-Cadmium Battery, Lithium Ion Battery, Fuel Cell: Types of batteries and cells with different chemistries.

• Electrolysis: Chemical decomposition by passing electric current.

• Corrosion: Deterioration of metals due to redox reactions.

Concepts

• Oxidation-Reduction Reaction: Chemical reaction involving electron transfer.

• Fuel Cell: Device that converts chemical energy directly into electrical energy.

• Oxidation: Loss of electrons; increase in oxidation state.

• Reduction: Gain of electrons; decrease in oxidation state.

• Balancing Redox Reactions: Use half-reactions; balance electrons and charges.

• Voltaic Cell Design: Two half-cells connected by a salt bridge; electrons flow from anode to cathode.

• Electron Flow: From anode (oxidation) to cathode (reduction).

• Units: Electron flow: ampere (A); cell potential: volt (V).

• Salt Bridge: Maintains charge balance by allowing ion migration.

• Cell Diagram: Notation representing cell components and reactions.

• Electrode Potentials: Measured relative to standard hydrogen electrode.

• Positive $E^\circ$: Species is easily reduced.

• Negative $E^\circ$: Species is easily oxidized.

• Spontaneous Reaction: $E^\circ_{cell} > 0$

• Nonspontaneous Reaction: $E^\circ_{cell} < 0$

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

• Rechargeable Batteries: Dry-cell, lead-acid, nickel-cadmium, lithium ion.

• Electrolytic vs. Voltaic Cell: Electrolytic requires energy input; voltaic generates energy.

• Electrolysis Calculations: Use Faraday's laws to relate charge, current, and amount of substance.

• Corrosion Prevention: Use sacrificial electrodes or coatings.

Equations and Relationships

• Definition of Ampere: $1\ \text{A} = 1\ \text{C}/\text{s}$

• Definition of Volt: $1\ \text{V} = 1\ \text{J}/\text{C}$

• Standard Hydrogen Electrode: $E^\circ = 0$ V

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

• Relating $\Delta G^\circ$ and $E^\circ_{cell}$: $\Delta G^\circ = -nFE^\circ_{cell}$

• Relating $K$ and $E^\circ_{cell}$: $E^\circ_{cell} = \frac{0.0592}{n} \log K$

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

Outcome
Identify the parts of a voltaic cell
Represent electrochemical cells using cell diagram notation
Calculate standard cell potentials for electrochemical cells
Predict the spontaneity of redox reactions
Identify solutions that can selectively oxidize metals and metal ions
Calculate standard free energy changes for electrochemical reactions from standard cell potentials
Perform calculations involving $\Delta G^\circ$, $E^\circ_{cell}$, and $K$
Analyze cell potentials under nonstandard conditions
Analyze batteries in terms of mass components, redox reactions, and standard cell potentials
Analyze electrolysis cells in terms of components parts, voltages, and direction of electron flow
Analyze molten-salt electrolysis reactions in terms of products and half-reactions
Analyze aqueous-solution electrolysis reactions in terms of products and half-reactions
Perform stoichiometric calculations for electrolysis reactions
Predict metals that act as sacrificial electrodes for iron

Nuclear Chemistry

Key Terms

• Radioactivity: Spontaneous emission of particles or energy from unstable nuclei.

• Nuclide: A specific isotope of an element.

• Alpha Decay: Emission of an alpha particle ($^4_2He$).

• Beta Decay: Emission of a beta particle (electron or positron).

• Gamma Emission: Emission of high-energy photons.

• Positron Emission: Emission of a positron ($^0_{+1}e$).

• Electron Capture: Nucleus captures an inner electron.

• Strong Force: Force holding nucleons together.

• Nucleons: Protons and neutrons in the nucleus.

• Magic Numbers: Numbers of nucleons that confer extra stability.

• Radiometric Dating: Determining age using radioactive isotopes.

• Nuclear Fission: Splitting of a heavy nucleus into lighter nuclei.

• Nuclear Fusion: Combining light nuclei to form a heavier nucleus.

• Mass Defect: Difference between mass of nucleus and sum of nucleons.

• Nuclear Binding Energy: Energy required to break a nucleus into its nucleons.

• Transmutation: Conversion of one element into another.

• Linear Accelerator: Device to accelerate charged particles.

Concepts

• Radioactivity: Unstable nuclei emit radiation to become more stable.

• Medical Uses: Radioisotopes for imaging and treatment.

• Types of Natural Radioactivity: Alpha, beta, gamma, positron emission.

• Alpha Radiation: Emission of $^4_2He$ nucleus; low penetration, high ionization.

• Beta Particles: Electrons ($^0_{-1}e$) or positrons ($^0_{+1}e$); moderate penetration.

• Gamma Rays: High-energy photons; high penetration, low ionization.

• Electron Capture: Nucleus absorbs an electron, converting a proton to a neutron.

• Nuclear vs. Chemical Equations: Nuclear equations balance mass and atomic numbers; chemical equations balance atoms.

• Ionizing vs. Penetrating Power: Alpha: high ionizing, low penetrating; gamma: low ionizing, high penetrating.

• Nuclear Stability: Determined by neutron/proton ratio and magic numbers.

• Radiation Detectors: Measure intensity and type of radiation.

• Radioactive Decay Rate: First-order kinetics; $N = N_0 e^{-kt}$

• Fission vs. Fusion: Fission splits nuclei; fusion combines nuclei.

• Mass Defect: $\Delta m = Zm_p + Nm_n - m_{nucleus}$

• Binding Energy: $E = \Delta m c^2$

• Fusion Drawbacks: Requires high temperature and pressure.

• Transuranium Elements: Created by neutron capture and nuclear reactions.

• Linear Accelerator vs. Cyclotron: Linear accelerates in straight line; cyclotron in circular path.

Equations and Relationships

• Alpha Decay: $^A_ZX \rightarrow ^{A-4}_{Z-2}Y + ^4_2He$

• Beta Decay: $^A_ZX \rightarrow ^A_{Z+1}Y + ^0_{-1}e$

• Gamma Emission: $^A_ZX^* \rightarrow ^A_ZX + \gamma$

• Positron Decay: $^A_ZX \rightarrow ^A_{Z-1}Y + ^0_{+1}e$

• Electron Capture: $^A_ZX + ^0_{-1}e \rightarrow ^A_{Z-1}Y$

• First-Order Rate Law: $N = N_0 e^{-kt}$

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

• Integrated Rate Law: $\ln \frac{N_0}{N} = kt$

• Einstein's Energy-Mass Equation: $E = mc^2$

Outcome
Write nuclear equations for alpha decay
Write nuclear equations for beta decay, gamma emission, positron decay, and electron capture
Predict the products of nuclear decay
Perform radiometric carbon dating calculations
Perform radiometric uranium/lead dating calculations
Predict the products of neutron-induced fission reactions
Perform mass-energy calculations for nuclear fission
Perform mass-energy calculations for nuclear fusion
Determine the amount of energy absorbed from the decay of radioactive material

Crystalline Solids

Key Terms

• Crystalline Lattice: Ordered, repeating arrangement of atoms, ions, or molecules.

• Unit Cell: Smallest repeating unit in a crystal lattice.

• Simple Cubic, Body-Centered Cubic, Face-Centered Cubic: Types of cubic unit cells.

• Coordination Number: Number of nearest neighbors to a particle in a crystal.

• Packing Efficiency: Fraction of volume occupied by particles.

• Hexagonal Closest Packing, Cubic Closest Packing: Highly efficient packing arrangements.

• Molecular Solids: Solids composed of molecules held by intermolecular forces.

• Ionic Solids: Solids composed of ions held by electrostatic forces.

• Atomic Solids: Solids composed of atoms.

• Nonbonding Atomic Solids: Atoms held by weak forces (e.g., noble gases).

• Metallic Atomic Solids: Atoms held by metallic bonding.

• Network Covalent Atomic Solids: Atoms held by covalent bonds in a network.

• Graphite, Diamond, Fullerenes, Nanotubes, Silicates, Silica: Examples of network covalent solids.

Concepts

• Crystal Lattice Representation: Shown by unit cells and lattice points.

• Three Basic Cubic Unit Cells: Simple cubic, body-centered cubic, face-centered cubic.

• Closest-Packed Structures: Arrangements with maximum packing efficiency.

• Three Types of Crystal Solids: Molecular, ionic, atomic.

• Nonbonded Atomic Solid: Atoms held by weak London forces.

• Network Covalent Atomic Solid: Atoms connected by covalent bonds in a continuous network.

• Charges on Unit Cells in Ionic Solids: Determined by the ions present and their stoichiometry.

• Anion/Cation Size Differences: Affect packing and unit cell structure.

• Unit Cells for Ionic Compounds: Often based on closest packing of anions with cations in interstitial sites.

• Network Covalent Solids Composition: Extended networks of covalently bonded atoms.

Outcome
Analyze crystalline solids in terms of unit cell type, coordination number, and packing efficiency
Relate unit cell volume, edge length, and atomic radius
Solve problems involving the density of crystalline solids
Classify crystalline solids by type (molecular, ionic, or atomic)
Predict relative melting points of crystalline solids
Analyze atomic solids in terms of structure and properties