General Chemistry Study Guide: Quantum Mechanics, Periodic Properties, and Chemical Bonding

Chapter 8 – The Quantum-Mechanical Model of the Atom

Electromagnetic Radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space. It includes visible light, ultraviolet, infrared, X-rays, gamma rays, microwaves, and radio waves.

• Wavelength (\( \lambda \)): The distance between two consecutive peaks of a wave (measured in meters).

• Frequency (\( \nu \)): The number of wave cycles that pass a given point per second (measured in Hz).

• Energy (E): Related to frequency and wavelength by the following equations:

$E = h\nu$

$E = \dfrac{hc}{\lambda}$

Where:

• \( h \) = Planck's constant (\( 6.626 \times 10^{-34} \) J·s)

• \( c \) = speed of light (\( 3.00 \times 10^8 \) m/s)

• Different regions of the electromagnetic spectrum have different energies and wavelengths. For example, gamma rays have the shortest wavelength and highest energy, while radio waves have the longest wavelength and lowest energy.

Quantum Theory and the Bohr Atom

Quantum theory describes the behavior of matter and energy at the atomic and subatomic levels.

• Planck's Equation: Energy is quantized and can be emitted or absorbed in discrete units called quanta.

• Bohr Model: Electrons orbit the nucleus in specific, quantized energy levels. Transitions between levels result in absorption or emission of photons.

• Line Spectra: Atoms emit light at specific wavelengths, producing a line spectrum unique to each element.

• Emission Spectra: Produced when electrons fall from higher to lower energy levels, emitting photons.

Contributions of de Broglie and Heisenberg

• de Broglie Hypothesis: Particles such as electrons have wave-like properties. The wavelength of a particle is given by:

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

• Heisenberg Uncertainty Principle: It is impossible to simultaneously know both the exact position and momentum of an electron.

$\Delta x \cdot \Delta p \geq \dfrac{h}{4\pi}$

Quantum Numbers and Atomic Orbitals

Quantum numbers describe the properties of atomic orbitals and the properties of electrons in orbitals.

• Principal quantum number (n): Indicates the main energy level (shell).

• Angular momentum quantum number (l): Indicates the shape of the orbital (s, p, d, f).

• Magnetic quantum number (ml): Indicates the orientation of the orbital.

• Spin quantum number (ms): Indicates the spin direction of the electron (+1/2 or -1/2).

Atomic orbitals have characteristic shapes (spherical for s, dumbbell for p, etc.) and represent regions of high probability for finding an electron.

Chapter 9 – Periodic Properties of the Elements

Electron Configurations

Electron configuration describes the arrangement of electrons in an atom or ion.

• Ground State: The lowest energy arrangement of electrons.

• Excited State: An electron has absorbed energy and moved to a higher energy orbital.

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

• Aufbau Principle: Electrons fill orbitals starting with the lowest energy first.

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

Effective Nuclear Charge and Coulomb’s Law

• Effective Nuclear Charge (Zeff): The net positive charge experienced by valence electrons. Increases across a period and decreases down a group.

• Coulomb’s Law: Describes the force between two charged particles:

$F = k \dfrac{q_1 q_2}{r^2}$

Periodic Trends

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

• Ionic Radius: Cations are smaller, anions are larger than their parent atoms. In an isoelectronic series, higher nuclear charge means smaller ion.

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

• Electron Affinity: Energy change when an electron is added. More negative values indicate a greater tendency to gain electrons.

• Metallic Properties: Metals are typically malleable, ductile, and good conductors. Metallic character increases down a group and decreases across a period.

Periodic Table and Chemical Behavior

• Valence Electrons: Electrons in the outermost shell, determine chemical reactivity.

• Alkali Metals: Highly reactive, form +1 ions.

• Halogens: Very reactive nonmetals, form -1 ions.

• Noble Gases: Inert, have full valence shells.

Chapter 10 – Chemical Bonding I: The Lewis Model

Types of Chemical Bonds

• Ionic Bonds: Formed by transfer of electrons from metals to nonmetals.

• Covalent Bonds: Formed by sharing of electrons between nonmetals.

Lewis Dot Symbols and Structures

• Lewis Dot Symbols: Represent valence electrons as dots around the element symbol.

• Lewis Structures: Show bonding and nonbonding electrons in molecules and ions.

Lattice Energy and the Born-Haber Cycle

• Lattice Energy: The energy required to separate one mole of an ionic solid into gaseous ions.

• Born-Haber Cycle: A thermochemical cycle used to calculate lattice energy using enthalpy changes.

$\Delta H_{\text{lattice}} = \Delta H_{\text{f}} - (\text{sum of other enthalpy changes})$

• Lattice energy increases with higher ion charge and smaller ion size.

Bond Order, Length, and Energy

• Single, Double, Triple Bonds: More shared pairs mean higher bond order, shorter bond length, and higher bond energy.

• Bonding and Nonbonding Electrons: Bonding electrons are shared; nonbonding (lone pairs) are not involved in bonding.

Electronegativity and Bond Polarity

• Electronegativity: The ability of an atom to attract electrons in a bond. Increases across a period, decreases down a group.

• Bond Polarity: Difference in electronegativity leads to polar covalent bonds.

• Dipole Moment: A measure of bond polarity.

• Percent Ionic Character: Indicates the degree to which a bond is ionic.

Formal Charge and Resonance

• Formal Charge: Calculated to determine the most stable Lewis structure.

• Resonance: Some molecules have multiple valid Lewis structures; the actual structure is a hybrid.

Octet Rule and Exceptions

• Octet Rule: Atoms tend to have eight electrons in their valence shell.

• Exceptions: Incomplete octet (e.g., Be, B), expanded octet (elements in period 3 or higher).

Bond Dissociation Energy and Enthalpy Calculations

• Bond Dissociation Energy (BDE): Energy required to break a bond.

• Enthalpy Change (\( \Delta H \)): Can be estimated using bond energies:

$\Delta H = \sum \text{(BDE of bonds broken)} - \sum \text{(BDE of bonds formed)}$

Chapter 11 – Chemical Bonding II: Molecular Shapes, VSEPR, and MO Theory

VSEPR Model and Molecular Geometry

The Valence Shell Electron Pair Repulsion (VSEPR) model predicts the shapes of molecules based on repulsion between electron groups.

• Electron Groups: Include bonding pairs and lone pairs.

• Electron Geometry: Arrangement of all electron groups.

• Molecular Geometry: Arrangement of only the atoms (ignoring lone pairs).

• Lone pairs occupy more space and affect bond angles.

Molecular Shape and Polarity

• Polar Molecules: Have an uneven distribution of charge (net dipole moment).

• Nonpolar Molecules: Symmetrical charge distribution; dipoles cancel.

Valence Bond Theory and Hybridization

• Valence Bond Theory: Chemical bonds form by overlap of atomic orbitals.

• Hybridization: Mixing of atomic orbitals to form new, equivalent hybrid orbitals (sp3, sp2, sp).

• Sigma (\( \sigma \)) Bonds: Head-on overlap of orbitals.

• Pi (\( \pi \)) Bonds: Side-by-side overlap of p orbitals.

Molecular Orbital (MO) Theory

• MO Theory: Atomic orbitals combine to form molecular orbitals that are delocalized over the molecule.

• Bonding and Antibonding Orbitals: Bonding orbitals are lower in energy; antibonding are higher.

• Bond Order: Indicates bond strength and stability:

$\text{Bond Order} = \dfrac{\text{number of bonding electrons} - \text{number of antibonding electrons}}{2}$

• Paramagnetism: Molecules with unpaired electrons are attracted to a magnetic field.

• Diamagnetism: Molecules with all electrons paired are weakly repelled by a magnetic field.

Laboratory Experiments

Spectrophotometry (Experiment 4 and 5)

Spectrophotometry is a technique used to measure the amount of light absorbed by a solution at a specific wavelength. It is commonly used to determine the concentration of a solute in solution using Beer's Law:

$A = \varepsilon b c$

• \( A \): Absorbance (no units)

• \( \varepsilon \): Molar absorptivity (L·mol-1·cm-1)

• \( b \): Path length of the cell (cm)

• \( c \): Concentration of the solution (mol/L)

Additional Problems on Lattice Energy

Sample Lattice Energy Calculations

Lattice energy can be calculated using the Born-Haber cycle, which involves several steps including ionization energy, electron affinity, sublimation, and enthalpy of formation.

Step	MgCl2 (kJ/mol)	Fe2O3 (kJ/mol)
First ionization energy	738	+759
Second ionization energy	1451	+1561
Third ionization energy	—	+2957
Heat/Enthalpy of sublimation	146	+415
Electron affinity (first)	-348.7	-141
Electron affinity (second)	—	+844
Enthalpy of formation	-641.6	-826
Lattice energy (calculated)	-2522	-15,066

Note: The negative sign indicates energy is released when the lattice forms.

Example: To calculate the lattice energy, sum all the steps except the lattice energy and enthalpy of formation, then solve for lattice energy using the enthalpy of formation value.

Additional info: For more practice, refer to the suggested textbook problems and quizzes listed for each chapter.