General Chemistry Study Guide: Atomic Structure, Periodicity, and Ionic Bonding

Atomic Structure and Quantum Numbers

Atomic Orbitals and Quantum Numbers

Atomic orbitals are regions in space where electrons are likely to be found. Each orbital is defined by a set of quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms).

• Principal quantum number (n): Indicates the energy level and size of the orbital (n = 1, 2, 3, ...).

• Azimuthal quantum number (l): Defines the shape of the orbital (l = 0 for s, 1 for p, 2 for d, 3 for f).

• Magnetic quantum number (ml): Specifies the orientation of the orbital (-l to +l).

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

Example: For n = 3, l = 2, ml = -2, -1, 0, 1, 2, ms = ±1/2, corresponding to five 3d orbitals.

Additional info: The total number of orbitals for a given n is n2.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals. The Aufbau principle, Pauli exclusion principle, and Hund's rule govern the filling order.

• Aufbau principle: Electrons fill orbitals from lowest to highest energy.

• Pauli exclusion principle: No two electrons in an atom can have the same set of quantum numbers.

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

Example: The ground-state electron configuration of sulfur (Z = 16) is 1s2 2s2 2p6 3s2 3p4.

Excited State Configurations

Excited states occur when electrons are promoted to higher energy orbitals. For example, sulfur in an excited state may have the configuration 1s2 2s2 2p6 3s1 3p5.

Periodic Properties

Ionization Energy

Ionization energy is the energy required to remove an electron from a gaseous atom or ion.

• First ionization energy: Energy to remove the first electron.

• Successive ionization energies increase as electrons are removed.

• Trends: Increases across a period, decreases down a group.

Example: The first ionization energy of Na is lower than that of Mg.

Electron Affinity

Electron affinity is the energy change when an atom gains an electron to form a negative ion.

• Generally becomes more negative across a period.

• Halogens have the highest (most negative) electron affinities.

Atomic and Ionic Radii

Atomic radius is the distance from the nucleus to the outermost electron shell. Ionic radius refers to the size of an ion.

• Atomic radius decreases across a period and increases down a group.

• Cations are smaller than their parent atoms; anions are larger.

Example: Na+ is smaller than Na; Cl- is larger than Cl.

Classification of Elements

Elements are classified as metals, nonmetals, and metalloids based on their properties.

• Metals: Good conductors, malleable, ductile.

• Nonmetals: Poor conductors, brittle.

• Metalloids: Properties intermediate between metals and nonmetals.

Chemical Reactions and Stoichiometry

Types of Chemical Changes

Chemical changes involve the transformation of substances into new products. Physical changes do not alter chemical identity.

• Examples of chemical changes: Rusting of iron, burning of wood, reaction of vinegar with baking soda.

• Examples of physical changes: Melting of ice, boiling of water.

Stoichiometry and Limiting Reactant

Stoichiometry involves calculating the quantities of reactants and products in chemical reactions.

• Limiting reactant: The reactant that is completely consumed first, limiting the amount of product formed.

• Excess reactant: The reactant that remains after the reaction is complete.

Example: In the reaction of potassium with chlorine to form potassium chloride, calculate the mass of product and identify the limiting reactant.

Sample Stoichiometry Calculation

Given: 1.446 g of potassium reacts with 1.811 g of chlorine.

• Calculate moles of each reactant.

• Determine limiting reactant.

• Calculate mass of KCl formed using molar mass.

Atomic Theory and Electronic Structure

Electronic Configuration Notation

Electronic configuration is written using the notation: nlx, where n is the principal quantum number, l is the subshell type, and x is the number of electrons.

• Example: 1s2 2s2 2p6 3s2 3p4 for sulfur.

Quantum Numbers for Differentiating Electrons

Each electron in an atom is described by a unique set of quantum numbers.

• For two differentiating electrons: n, l, ml, ms

• Example: n = 4, l = 1, ml = 0, ms = +1/2

Ionic and Metallic Bonding

Classification of Compounds

Compounds are classified as ionic, metallic, or covalent based on the nature of bonding.

• Ionic compounds: Formed by transfer of electrons (e.g., NaCl, CaCl2).

• Metallic compounds: Consist of metal atoms sharing a 'sea' of electrons (e.g., Cu, Fe).

• Covalent compounds: Formed by sharing of electrons (e.g., H2O, CO2).

Lattice Energy

Lattice energy is the energy released when ions combine to form an ionic solid. It is a measure of the strength of the ionic bond.

• Formula: $\Delta H_{\text{lattice}} = k \dfrac{Q_1 Q_2}{r}$

• Where $Q_1$ and $Q_2$ are the charges of the ions, $r$ is the distance between ion centers, and $k$ is a proportionality constant.

Example: Lattice energy of CaO is higher than that of NaCl due to higher charges on Ca2+ and O2-.

Electron Affinity and Ionization Energy Calculations

Electron affinity and ionization energy can be determined from experimental data.

• Electron affinity: $\text{A} + e^- \rightarrow \text{A}^-$

• Ionization energy: $\text{A} \rightarrow \text{A}^+ + e^-$

Role of Lattice Energy in Ionic Stability

Lattice energy contributes to the stability of ionic compounds. Higher lattice energy means greater stability.

Compound	Lattice Energy (kJ/mol)
NaF	914
CsI	632
PbF2	988
PbCl2	660

Additional info: Lattice energy increases with higher ionic charges and smaller ionic radii.

Classification of Matter and Mixtures

Pure Substances vs. Mixtures

Matter can be classified as pure substances (elements and compounds) or mixtures (homogeneous and heterogeneous).

• Pure substances: Fixed composition, e.g., oxygen gas, petroleum.

• Mixtures: Variable composition, e.g., smoke (heterogeneous), clean fresh air (homogeneous).

Additional Practice and Application

Sample Calculations and Conceptual Questions

• Calculate the number of atoms in a given mass of an element using Avogadro's number: $\text{Number of atoms} = \dfrac{\text{mass}}{\text{molar mass}} \times N_A$

• Determine the limiting reactant in a chemical reaction by comparing mole ratios.

• Predict the electron configuration for ions and excited states.

• Classify compounds as ionic, covalent, or metallic based on their properties.

Summary Table: Periodic Trends

Property	Trend Across Period	Trend Down Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Becomes more negative	Becomes less negative
Metallic Character	Decreases	Increases

Additional info: These trends are explained by changes in effective nuclear charge and electron shielding as you move across periods and down groups.