Periodic Trends and Electron Configurations: General Chemistry Study Notes

Chapter 4: Periodic Trends of the Elements

Development of the Periodic Table

The periodic table is a foundational tool in chemistry, organizing elements according to recurring chemical properties. Its development involved several key historical figures and concepts.

• Law of Octaves: In 1864, John Newlands observed that when elements are arranged by atomic number, every eighth element shares similar properties. This pattern was called the law of octaves.

• Periodicity: In 1869, Dmitri Mendeleev and Lothar Meyer independently proposed the idea of periodicity, grouping elements by properties and predicting the existence and properties of undiscovered elements.

• Atomic Number: In 1913, Henry Moseley discovered the correlation between atomic number (number of protons) and X-ray frequency, leading to the modern arrangement of elements by atomic number rather than atomic mass.

Modern periodic tables include atomic number, symbol, and are arranged according to electron configuration.

Periodic Trends in Properties

Periodic trends describe how certain properties of elements change across periods and groups in the periodic table.

• Atomic Radius: The distance from the nucleus to the outermost electron shell. Increases down a group and decreases across a period.

• Ionization Energy: The energy required to remove an electron from an atom in the gas phase. Increases across a period and decreases down a group.

• Electron Affinity: The energy change when an atom gains an electron. Generally increases across a period.

• Metallic Character: Refers to how closely an element's properties match those of metals. Increases down a group and decreases across a period.

Electron Configurations

Atomic Orbitals and Principles

Electron configuration describes the distribution of electrons in atomic orbitals. Several principles govern how electrons fill these orbitals:

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

• Aufbau Principle: Electrons fill the lowest energy orbitals first before occupying higher energy levels.

• Hund’s Rule: Electrons will occupy degenerate orbitals singly before pairing up, maximizing the number of electrons with the same spin.

Example: The ground state electron configuration of carbon (Z = 6) is $1s^2 2s^2 2p^2$.

Writing Electron Configurations

General rules for writing electron configurations:

• Electrons occupy the lowest available energy orbitals.

• Each orbital holds a maximum of two electrons.

• Electrons do not pair in degenerate orbitals if an empty orbital is available.

• Orbitals fill in the order indicated by the Aufbau diagram.

Example: Calcium (Z = 20): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2$

Noble Gas Core Notation

Electron configurations can be abbreviated using the noble gas core:

• Potassium (Z = 19): [Ar]$4s^1$

• Arsenic (Z = 33): [Ar]$4s^2 3d^{10} 4p^3$

Exceptions in Transition Metals

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

• Chromium (Z = 24): [Ar]$4s^1 3d^5$

• Copper (Z = 29): [Ar]$4s^1 3d^{10}$

Additional info: These exceptions arise because half-filled and fully filled d subshells are energetically favorable.

Classification of Elements

Main Group, Transition Metals, and Inner Transition Metals

Elements are classified based on their position and electron configuration:

• Main Group Elements: Groups 1, 2, and 13–17 (also called representative elements).

• Noble Gases: Group 18, with completely filled p subshells.

• Transition Metals: Groups 3–11, with partially filled d subshells.

• Inner Transition Metals: Lanthanides and actinides (f-block elements).

Valence Electrons

Valence electrons are the outermost electrons of an atom and are involved in chemical bonding. Electron configurations help predict chemical properties.

• Group 1A: [noble gas]$ns^1$

• Group 2A: [noble gas]$ns^2$

• Group 7A: [noble gas]$ns^2 np^5$

Effective Nuclear Charge ($Z_{eff}$)

Definition and Calculation

Effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom, accounting for both attraction to the nucleus and repulsion by other electrons.

• Formula: $Z_{eff} = Z - ext{S}$

• $Z$ is the atomic number (number of protons).

• $ext{S}$ is the shielding constant (approximate number of inner shell electrons).

• $Z_{eff}$ increases across a period and changes little down a group.

Periodic Trends in Properties

Atomic Radius

Atomic radius is the distance from the nucleus to the outermost electron shell. It varies depending on the type of element:

• Metallic Radius: Half the distance between nuclei of two identical metal atoms.

• Covalent Radius: Half the distance between nuclei of two identical nonmetal atoms bonded together.

Trend: Increases down a group (due to increasing n), decreases across a period (due to increasing $Z_{eff}$).

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in the gas phase.

• First Ionization Energy ($IE_1$): $Na(g) \rightarrow Na^+(g) + e^-$

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

• Subsequent ionizations require more energy, especially when removing core electrons.

Example: $IE_1(Na) = 496 \text{ kJ/mol}$, $IE_2(Na) = 4562 \text{ kJ/mol}$

Electron Affinity

Electron affinity is the energy change when an atom in the gas phase accepts an electron.

• Formula: $X(g) + e^- \rightarrow X^-(g)$

• Trend: Generally increases across a period as $Z_{eff}$ increases.

• It is easier to add an electron to an s orbital than to a p orbital of the same principal quantum number.

Example: $EA_1(O) = 141 \text{ kJ/mol}$, $EA_2(O) = -741 \text{ kJ/mol}$

Additional info: First electron affinities can be positive, but subsequent additions are always negative due to repulsion.

Metallic Character

Metallic character describes how closely an element's properties match those of metals.

• Metals: Shiny, malleable, ductile, good conductors, low ionization energies, tend to form cations.

• Nonmetals: Dull, brittle, poor conductors, high ionization energies, tend to form anions.

• Metalloids: Intermediate properties between metals and nonmetals.

Coulomb’s Law and Periodic Trends

Coulomb’s law explains the force between charged particles:

• Formula: $F \propto \frac{Q_1 Q_2}{d^2}$

• Attractive force increases with charge and decreases with distance squared.

Example: Comparing the attractive force between the nucleus and a valence electron in carbon and nitrogen using $Z_{eff}$ and atomic radius.

Electron Configurations of Ions

Main Group Ions

To write the electron configuration of an ion:

1. Write the configuration for the atom.

2. Add or remove the appropriate number of electrons.

Example:

• Na: $1s^2 2s^2 2p^6 3s^1$ → Na+: $1s^2 2s^2 2p^6$ (isoelectronic with Ne)

• Cl: $1s^2 2s^2 2p^6 3s^2 3p^5$ → Cl-: $1s^2 2s^2 2p^6 3s^2 3p^6$ (isoelectronic with Ar)

d-Block Ions

For d-block elements, electrons are removed first from the subshell with the highest principal quantum number.

• Fe: [Ar]$4s^2 3d^6$ → Fe2+: [Ar]$3d^6$

• Fe3+: [Ar]$3d^5$

Ionic Radius and Isoelectronic Series

Ionic Radius

Ionic radius is the radius of a cation or anion. When an atom loses electrons to become a cation, its radius decreases due to reduced electron-electron repulsion. Significant decreases occur when all valence electrons are removed.

Isoelectronic Series

An isoelectronic series consists of species with identical electron configurations but different nuclear charges.

• Example: $K^+$, $Ar$, $Cl^-$, $S^{2-}$, $P^{3-}$ (all have 18 electrons)

• Within an isoelectronic series, ionic radius decreases as nuclear charge increases.

Summary Table: Periodic Trends

Property	Trend Across Period	Trend Down Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Increases	Varies (less clear)
Metallic Character	Decreases	Increases

Chapter Summary: Key Points

• Development of the Periodic Table

• Electron Configurations

• Energies of Atomic Orbitals in Many-Electron Systems

• Pauli Exclusion Principle

• Aufbau Principle

• Hund’s Rule

• Writing Electron Configurations

• Electron Configurations and the Periodic Table

• Classification of Elements

• Valence Configuration

• Effective Nuclear Charge

• Atomic Radius

• Ionization Energy

• Electron Affinity

• Metallic Character

• Ions of Main Group Elements

• Ions of d-Block Elements

• Ionic Radius

• Isoelectronic Series