Study Guide: Thermochemistry, Quantum Mechanics, and Periodic Trends (Chapters 7–9)

Chapter 7: Thermochemical Aspects of Chemical Reactions

Types of Energy

Energy is the capacity to do work or transfer heat. In chemistry, energy is often discussed in terms of its different forms and how it changes during chemical reactions.

• Kinetic Energy: Energy due to motion. For a particle of mass m and velocity v:

$E_{\text{kinetic}} = \frac{1}{2}mv^2$

• Potential Energy: Energy due to position or composition (e.g., chemical bonds).

• Thermal Energy: Associated with the temperature of a system; a form of kinetic energy.

• Chemical Energy: Stored within the bonds of chemical substances.

First Law of Thermodynamics

The first law states that energy cannot be created or destroyed, only transferred or transformed.

• Internal Energy (U): The total energy contained within a system.

• Mathematical Statement:

$\Delta U = q + w$

• Where q is heat and w is work.

System and Surroundings

Chemical reactions occur in a system, which is separated from the surroundings.

• System: The part of the universe being studied (e.g., reactants and products).

• Surroundings: Everything else outside the system.

• Open, Closed, and Isolated Systems: Classification based on exchange of matter and energy.

Free Energy Diagrams

These diagrams show the energy changes during a chemical reaction, indicating reactants, products, and the activation energy barrier.

• Exergonic Reaction: Releases free energy; products have lower energy than reactants.

• Endergonic Reaction: Absorbs free energy; products have higher energy than reactants.

Work and Heat

• Work (w): Energy transfer due to a force acting over a distance. In chemistry, often pressure-volume work:

$w = -P_{\text{ext}} \Delta V$

• Heat (q): Energy transfer due to temperature difference.

Enthalpy (H)

Enthalpy is the heat content of a system at constant pressure.

• Change in Enthalpy:

$\Delta H = \Delta U + P\Delta V$

• At constant pressure, $\Delta H = q_p$ (heat at constant pressure).

Stoichiometry with Enthalpy

Relates the enthalpy change to the amount of reactants or products in a chemical equation.

• Use $\Delta H$ as a conversion factor in mole calculations.

Calorimetry

Calorimetry measures the heat exchanged in a chemical or physical process.

• Specific Heat Capacity (c): Amount of heat required to raise the temperature of 1 g of a substance by 1°C.

• Equation:

$q = mc\Delta T$

• Where m is mass, c is specific heat, and $\Delta T$ is temperature change.

Hess' Law

States that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in.

• Allows calculation of $\Delta H$ for a reaction by adding $\Delta H$ values for individual steps.

Heat of Reaction and Heat of Formation

• Heat of Reaction ($\Delta H_{rxn}$): Enthalpy change for a chemical reaction.

• Standard Heat of Formation ($\Delta H_f^\circ$): Enthalpy change when 1 mole of a compound forms from its elements in their standard states.

• Calculation:

$\Delta H_{rxn} = \sum n \Delta H_f^\circ (\text{products}) - \sum n \Delta H_f^\circ (\text{reactants})$

Chapter 8: Quantum Mechanics, Electron Configurations, and Periodic Trends

Properties of Waves

Light and electrons exhibit wave-like properties, described by wavelength, frequency, and amplitude.

• Wavelength (λ): Distance between two consecutive peaks.

• Frequency (ν): Number of cycles per second (Hz).

• Relationship:

$c = \lambda \nu$

• Where c is the speed of light ($3.00 \times 10^8$ m/s).

Relationship Between Energy, Wavelength, and Frequency

• Photon Energy:

$E = h\nu = \frac{hc}{\lambda}$

• Where h is Planck's constant ($6.626 \times 10^{-34}$ J·s).

Photoelectric Effect

When light of sufficient frequency strikes a metal surface, electrons are ejected. Demonstrates the particle nature of light.

• Threshold Frequency: Minimum frequency needed to eject electrons.

• Equation:

$E_{\text{photon}} = \phi + KE_{\text{electron}}$

• Where $\phi$ is the work function of the metal.

de Broglie Equation for the Wavelength of Matter

All matter has wave-like properties, especially significant for small particles like electrons.

• de Broglie Wavelength:

$\lambda = \frac{h}{mv}$

• Where m is mass and v is velocity.

Wave/Particle Duality Experiments

Experiments such as electron diffraction and the photoelectric effect demonstrate that electrons and photons exhibit both wave-like and particle-like properties.

Bohr Model

Early model of the atom where electrons orbit the nucleus in quantized energy levels.

• Energy Levels: Electrons can only occupy certain orbits with fixed energies.

• Limitations: Explains hydrogen atom spectra but not multi-electron atoms.

Rydberg Equation

Predicts the wavelengths of light emitted by hydrogen atoms.

$\frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$

• Where $R_H$ is the Rydberg constant ($1.097 \times 10^7$ m-1), $n_1$ and $n_2$ are integers with $n_2 > n_1$.

Quantum Numbers

Describe the properties of atomic orbitals and the properties of electrons in orbitals.

• Principal Quantum Number (n): Energy level (n = 1, 2, 3, ...).

• Angular Momentum Quantum Number (l): Shape of orbital (l = 0 to n-1).

• Magnetic Quantum Number (ml): Orientation of orbital (ml = -l to +l).

• Spin Quantum Number (ms): Electron spin (+1/2 or -1/2).

Orbital Designations

Orbitals are labeled by their quantum numbers (e.g., 1s, 2p, 3d).

• s-orbital: l = 0

• p-orbital: l = 1

• d-orbital: l = 2

• f-orbital: l = 3

Chapter 9: Electron Configurations and Periodic Trends

Relative Energy of Orbitals in Multi-Electron Atoms

In atoms with more than one electron, orbitals of the same principal quantum number (n) have different energies due to electron-electron repulsions and shielding.

• Order of increasing energy: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s ...

Filling Orbital Diagrams

Electrons fill orbitals in order of increasing energy, following the Aufbau principle, Pauli exclusion principle, and Hund's rule.

• Aufbau Principle: Electrons occupy the lowest energy orbitals first.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

• Hund's Rule: Electrons fill degenerate orbitals singly before pairing.

Electron Configuration of Atoms, Ions, and Transition Metals

Electron configuration shows the distribution of electrons among orbitals.

• Atoms: Fill according to the order of orbital energies.

• Ions: For cations, remove electrons from the highest n value first; for anions, add electrons to the next available orbital.

• Transition Metals: Often lose s electrons before d electrons when forming cations.

Electron Configuration Using Noble Gas Notation

Shorthand notation uses the previous noble gas to represent core electrons.

• Example: Sodium (Na): [Ne] 3s1

Valence and Core Electrons

• Valence Electrons: Electrons in the outermost shell; involved in chemical bonding.

• Core Electrons: Inner electrons not involved in bonding.

Exceptions to the Aufbau Principle for Transition Elements

Some transition metals have electron configurations that differ from the expected order due to increased stability of half-filled or fully filled d subshells.

• Example: Chromium (Cr): [Ar] 4s1 3d5 (instead of [Ar] 4s2 3d4)

• Example: Copper (Cu): [Ar] 4s1 3d10

Periodic Trends

Properties of elements show periodic variation with atomic number.

• Effective Nuclear Charge (Zeff): The net positive charge experienced by valence electrons.

• Atomic Radius: Decreases across a period, increases down a group.

• Ionic Radius: Cations are smaller, anions are larger than their parent atoms.

• Ionization Energy: Energy required to remove an electron; increases across a period, decreases down a group.

• Electron Affinity: Energy change when an atom gains an electron; generally becomes more negative across a period.

Summary Table: Periodic Trends

Property	Across a Period (Left to Right)	Down a Group (Top to Bottom)
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Becomes more negative	Becomes less negative
Zeff	Increases	Slightly increases

Example: Sodium (Na) has a larger atomic radius than chlorine (Cl), but a lower ionization energy.

Additional info: These notes are based on the exam coverage list and expand on the key topics for Chapters 7, 8, and 9, omitting sections 8.1, 9.1, and 9.2 as specified.