Atomic Structure, Electron Configuration, and Periodic Trends: General Chemistry Study Notes

Atomic Structure and Energy

Endothermic and Exothermic Reactions

Endothermic and exothermic reactions describe the flow of energy during chemical processes.

• Endothermic reactions: Absorb energy from the surroundings (ΔH > 0).

• Exothermic reactions: Release energy to the surroundings (ΔH < 0).

• Example: Combustion of methane is exothermic; photosynthesis is endothermic.

Calorimetry and Hess's Law

Calorimetry measures heat changes in chemical reactions, while Hess's Law allows calculation of enthalpy changes for reactions by combining known reactions.

• Calorimetry equation: $q = m c_s \Delta T$

• Hess's Law: The total enthalpy change for a reaction is the sum of enthalpy changes for individual steps.

• Example: Calculating the enthalpy change for the formation of water from hydrogen and oxygen using known enthalpies of formation.

Enthalpy of Formation (ΔHf)

The enthalpy change when one mole of a compound forms from its elements in their standard states.

• Standard enthalpy of formation: $\Delta H_f^\circ$

• Application: Used to calculate reaction enthalpies via Hess's Law.

Atomic Spectra and Quantum Theory

Wavelength, Frequency, and Energy

Light exhibits both wave and particle properties. The relationship between wavelength (λ), frequency (ν), and energy (E) is fundamental in atomic theory.

• Relationship: $c = \lambda \nu$ (where c is the speed of light)

• Energy of a photon: $E = h \nu$ (where h is Planck's constant)

• Example: Calculating the energy of a photon with a given wavelength.

Rydberg Equation and Atomic Transitions

The Rydberg equation predicts the wavelength of light emitted or absorbed during electron transitions in a hydrogen atom.

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

• Application: Used to calculate the wavelength for electronic transitions.

• Example: Calculating the wavelength of light emitted when an electron falls from n=3 to n=2 in hydrogen.

Bohr Model and Quantum Numbers

The Bohr model describes electrons in quantized orbits around the nucleus. Quantum numbers specify the properties of atomic orbitals and electrons.

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

• Angular momentum quantum number (l): Indicates orbital shape.

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

• Spin quantum number (ms): Indicates electron spin direction.

• Example: For n=2, l can be 0 or 1; ml can be -1, 0, or 1.

Electron Configuration and Orbital Diagrams

Quantum Numbers to Orbitals

Quantum numbers are used to assign electrons to specific orbitals in an atom.

• Electron configuration: The arrangement of electrons in an atom's orbitals.

• Orbital diagrams: Visual representations using arrows to show electron spins in orbitals.

• Example: The electron configuration of oxygen: 1s2 2s2 2p4.

Electron Configurations (Short Hand and Arrows)

Electron configurations can be written in full, in shorthand (using noble gas core), or as orbital diagrams with arrows.

• Shorthand notation: Uses the previous noble gas to represent core electrons. Example: [Ne] 3s2 3p5 for chlorine.

• Orbital diagrams: Use arrows (↑, ↓) to represent electron spins in boxes for each orbital.

Periodic Trends and Atomic Properties

Sizes of Atoms and Ions

Atomic and ionic sizes vary across periods and down groups in the periodic table.

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

• Cation size: Smaller than parent atom; Anion size: Larger than parent atom.

Effective Nuclear Charge (Zeff)

The net positive charge experienced by valence electrons.

• Formula: $Z_{eff} = Z - S$ (Z = atomic number, S = shielding constant)

• Trend: Increases across a period, slightly increases down a group.

Ionization Energy and Electron Affinity

Ionization energy is the energy required to remove an electron; electron affinity is the energy change when an electron is added.

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

• Electron affinity: Generally becomes more negative across a period.

Electron Configurations of Ions

When atoms form ions, electrons are added or removed according to specific rules.

• Cations: Electrons are removed from the highest principal quantum number (n) orbital first.

• Anions: Electrons are added to the next available orbital.

• Example: Na: 1s2 2s2 2p6 3s1; Na+: 1s2 2s2 2p6

Periodic Table Trends

Trends in the periodic table help predict chemical and physical properties of elements.

• Atomic radius, ionization energy, electron affinity, and metallic character all show predictable trends across periods and groups.

Lattice Energy and Born-Haber Cycle

Lattice Energy

Lattice energy is the energy released when gaseous ions form an ionic solid.

• Formula (Born-Landé equation): $U = -\frac{N_A M z^+ z^- e^2}{4 \pi \epsilon_0 r_0} \left(1 - \frac{1}{n}\right)$

• Application: Explains the stability of ionic compounds.

Born-Haber Cycle

The Born-Haber cycle is a thermochemical cycle used to analyze the steps in the formation of an ionic compound from its elements.

• Steps include: Sublimation, ionization, dissociation, electron affinity, and lattice energy.

• Application: Used to calculate lattice energies indirectly.