Periodicity, Electronic Structure, and Ionic Bonding: Study Notes for General Chemistry

Periodicity and the Electronic Structure of Atoms

Periodic Trends in Properties of Elements

The periodic table displays repeating patterns, known as periodicity, in the properties of elements. These patterns are explained by the arrangement of electrons in atoms, which is described by electron configuration.

• Periodicity: The presence of repeating patterns in element properties.

• Electron Configuration: The distribution of electrons in atomic orbitals determines element properties.

The Beginning of Quantum Mechanics

Quantum mechanics revolutionized our understanding of atomic structure by introducing probabilistic models for subatomic particles, replacing deterministic classical physics.

• Classical Physics: Predicts future conditions from current conditions (e.g., Newton's Laws).

• Quantum Mechanics: Describes subatomic phenomena probabilistically.

Wave Properties of Light

Light exhibits both wave and particle properties. Key wave characteristics include wavelength, amplitude, and frequency. The energy of a wave depends on its amplitude and frequency.

• Wavelength (\lambda): Distance between crests.

• Frequency (\nu): Number of crests passing a point per unit time.

• Velocity: $v = \lambda \nu$

• Energy: Proportional to amplitude and frequency.

Electromagnetic Radiation and the Spectrum

Electromagnetic radiation consists of oscillating electric and magnetic fields, traveling through space. The visible spectrum is a small portion of the entire electromagnetic spectrum.

• Speed of Light (c): $c = 2.998 \times 10^8$ m/s

• Relationship: $c = \lambda \nu$

• Continuous Spectrum: White light contains all visible wavelengths.

Properties of Waves: Diffraction and Interference

Light waves can diffract and interfere, producing patterns of bright and dark spots. Diffraction occurs when waves encounter obstacles or openings similar in size to their wavelength.

• Diffraction: Bending of waves around obstacles.

• Interference: Waves in phase reinforce (bright spots); out of phase cancel (dark spots).

The Photoelectric Effect and Quantum Theory

The photoelectric effect demonstrates the particle nature of light. Electrons are ejected from metal surfaces when exposed to light above a threshold frequency, regardless of intensity.

• Threshold Frequency: Minimum frequency required to eject electrons.

• Work Function (\phi): Minimum energy needed to remove an electron.

• Energy of Photon: $E_{\text{photon}} = h\nu = \frac{hc}{\lambda}$

• Kinetic Energy: $KE = h\nu - \phi$

Calculating Energy and Wavelength for Photoelectric Effect

To determine the maximum wavelength that causes the photoelectric effect, convert energy per mole to energy per photon, then use the photon energy to calculate wavelength.

• Energy per photon: $\frac{283\ \text{kJ}}{\text{mol}} \times \frac{1000\ \text{J}}{1\ \text{kJ}} \times \frac{1\ \text{mol}}{6.02 \times 10^{23}\ \text{photons}} = 4.7 \times 10^{-19}\ \text{J/photon}$

• Wavelength: $\lambda = \frac{hc}{E} = \frac{(6.626 \times 10^{-34}\ \text{J s})(3.00 \times 10^8\ \text{m/s})}{4.7 \times 10^{-19}\ \text{J}} = 4.22 \times 10^{-7}\ \text{m} = 422\ \text{nm}$

Wave-Particle Duality

Light exhibits both wave and particle properties, a concept known as wave-particle duality. This duality is also observed in electrons.

• Wave Behavior: Diffraction and interference.

• Particle Behavior: Photoelectric effect and emission spectra.

Bohr Model and Hydrogen Atom Spectra

The Bohr model explains the emission and absorption spectra of hydrogen by quantizing electron orbits. Energy transitions correspond to specific wavelengths.

• Energy Transition: $\Delta E = E_{\text{final}} - E_{\text{initial}} = h\nu$

• Bohr Equation: $\Delta E = -R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$

Quantum Mechanical Model and Quantum Numbers

Quantum mechanics describes electrons as standing waves, characterized by quantum numbers. Each atomic orbital is defined by a set of quantum numbers.

• Principal Quantum Number (n): Specifies size and energy level.

• Angular Momentum Quantum Number (\ell): Specifies shape.

• Magnetic Quantum Number (m_\ell): Specifies orientation.

• Electron Spin Quantum Number (m_s): Specifies spin direction (+½ or -½).

Energy Levels in Hydrogen Atom

For hydrogen, the energy of an orbital depends only on the principal quantum number (n). All subshells with the same n have equal energy.

• Energy Equation: $E = -R_H \left( \frac{1}{n^2} \right)$, where $R_H = 1312\ \text{kJ/mol}$

Electron Configurations and Orbital Diagrams

Electron configurations describe how electrons are distributed in atomic orbitals. The Aufbau principle, Pauli exclusion principle, and Hund's rule guide the filling of orbitals.

• Aufbau Principle: Electrons fill lowest energy orbitals first.

• Pauli Exclusion Principle: Maximum of two electrons per orbital, with opposite spins.

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

Examples of Electron Configurations

Ground state electron configurations for hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, and oxygen illustrate the application of quantum numbers and orbital filling rules.

• Hydrogen: 1s1

• Helium: 1s2

• Lithium: 1s2 2s1

• Beryllium: 1s2 2s2

• Boron: 1s2 2s2 2p1

• Carbon: 1s2 2s2 2p2

• Nitrogen: 1s2 2s2 2p3

• Oxygen: 1s2 2s2 2p4

Condensed Electron Configurations

Condensed electron configurations use noble gas notation to simplify the representation of electron arrangements.

Orbital Filling Order and Periodic Table

The periodic table structure reflects the order of orbital filling, which follows the sequence: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p, etc.

Valence Electrons and Noble Gas Notation

Valence electrons are those in the highest principal energy shell. Noble gas notation uses the electron configuration of the preceding noble gas as a core.

• Valence Electrons: Determine chemical reactivity and periodic properties.

• Noble Gas Notation: [He], [Ne], [Ar], [Kr], [Xe], [Rn]

Transition Metals and Electron Configuration Anomalies

Transition metals often exhibit exceptions to the expected order of orbital filling, due to extra stability from half-filled or fully-filled d subshells.

• Example: Chromium (Cr) and Copper (Cu) have anomalous configurations.

Periodic Trends: Atomic Radii

Atomic radius decreases across a period (left to right) and increases down a group (top to bottom). Cations are smaller than their neutral atoms, while anions are larger.

• Trend: Decrease across period, increase down group.

• Cations: Smaller due to loss of electrons.

• Anions: Larger due to gain of electrons.

Ionic Compounds: Periodic Trends and Bonding Theory

Ionic Bonding and Classification of Elements

Ionic bonds form between metals and nonmetals, involving the transfer of electrons from the metal to the nonmetal. Elements are classified as main group metals, transition metals, metalloids, and nonmetals.

Electronic Configurations of Ions

Ion formation involves removing electrons for cations and adding electrons for anions, often resulting in a noble gas configuration.

• Isoelectronic: Ions with the same number of electrons as a noble gas.

• Transition Metal Cations: ns electrons are lost first.

Paramagnetism and Diamagnetism

Atoms with unpaired electrons are paramagnetic (attracted to magnetic fields), while those with all paired electrons are diamagnetic (repelled by magnetic fields).

Periodic Trends: Ionization Energy and Electron Affinity

Ionization energy is the energy required to remove an electron from a gas-phase atom. Electron affinity is the energy change when an electron is added to a gas-phase atom.

• Ionization Energy: Increases across a period, decreases down a group.

• Electron Affinity: Usually negative (favorable), increases across a period.

The Octet Rule and Stoichiometry of Ionic Compounds

Main group elements tend to gain or lose electrons to achieve eight valence electrons (octet rule), predicting ionic charges and chemical formulas.

• Examples: NaCl, Na2S, CaCl2, Al2O3

Energy in Ionic Compound Formation and Crystal Lattice

Ionic compounds form stable crystal lattices, releasing large amounts of energy. The Born-Haber cycle is used to calculate lattice energies.

• Lattice Energy (U): Energy required to break up an ionic solid into gaseous ions.

• Coulomb's Law: $U = k \frac{z_1 z_2}{d}$

• Trend: Larger ion size decreases lattice energy; higher ion charge increases lattice energy.

Covalent Bonding and Electron-Dot Structures

Lewis Bonding Theory

Lewis theory explains bonding by emphasizing valence electrons. Lewis dot structures model the arrangement of electrons in molecules.

• Bond Types: Ionic (transfer), covalent (sharing), metallic (pooling).

Properties of Covalent Bonds

Covalent bonds involve shared electron pairs. Bond length and strength depend on the number of shared electrons and atomic size.

• Bond Length: Shorter bonds are stronger; multiple bonds are shorter than single bonds.

• Bond Energy: Energy required to break a bond; stronger bonds have higher bond energies.

Bond Polarity and Electronegativity

Bond polarity arises from unequal sharing of electrons. Electronegativity measures an atom's ability to attract shared electrons.

• Electronegativity Trend: Increases across a period, decreases down a group.

• Dipole Moment: $\mu = q r$

Electron Dot Structures and the Octet Rule

Electron dot structures show valence electrons as dots. The octet rule guides the formation of stable covalent bonds.

• Single, Double, Triple Bonds: Atoms share one, two, or three pairs of electrons.

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

Table: Types of Chemical Bonds

Types of Atoms	Type of Bond	Characteristic
Metal and nonmetal	Ionic	Electrons transferred
Nonmetal and nonmetal	Covalent	Electrons shared
Metal and metal	Metallic	Electrons pooled

Table: Maximum Number of Electrons in Subshells

Subshell	Number of Orbitals	Maximum Electrons
s	1	2
p	3	6
d	5	10
f	7	14

Table: Lattice Energy Trends for Metal Chlorides

Metal Ion	Lattice Energy (kJ/mol)
Li+	834
Na+	788
K+	701
Cs+	657

Table: Effect of Ionic Charge on Lattice Energy

Anion	Na+	Mg2+	Al3+
OH-	900	3006	5627
O2-	2481	3791	15916

Table: Expanded and Condensed Electron Configurations

Element	Expanded	Condensed
H	1s1	1s1
He	1s2	1s2
Li	1s22s1	1s22s1
Be	1s22s2	1s22s2
B	1s22s22p1	1s22s22p1
C	1s22s22p2	1s22s22p2
N	1s22s22p3	1s22s22p3
O	1s22s22p4	1s22s22p4
F	1s22s22p5	1s22s22p5
Ne	1s22s22p6	1s22s22p6

Example:

• Bond Energy Calculation: For CH4 + 2 O2 → CO2 + 2 H2O, sum the energies of bonds broken and formed to estimate ΔE.

Additional info: Academic context was added to clarify quantum numbers, periodic trends, and the Born-Haber cycle for lattice energy calculation.