Electron Configurations, Orbital Diagrams, and Coulomb's Law: General Chemistry Study Notes

Periodic Law and the Organization of the Periodic Table

Periodic Law

The Periodic Law states that the properties of elements are periodic functions of their atomic numbers. This law underpins the structure of the modern periodic table.

• Periodic Table: Elements are arranged in order of increasing atomic number, which reveals recurring chemical properties.

• Groups and Periods: Elements in the same group share similar chemical properties due to similar valence electron configurations.

• Trends: The arrangement influences trends in reactivity, atomic structure, and chemical behavior.

Electron Orbital Diagrams

Visual Representation of Electrons in Orbitals

Electron orbital diagrams show how electrons are distributed among atomic orbitals. Each box represents an orbital, and arrows indicate electrons with their spins.

• Degenerate Orbitals: Orbitals with the same energy level (e.g., the three p orbitals).

• Hund's Rule: Electrons fill degenerate orbitals singly first, with parallel spins, before pairing up.

Electron Orbital Diagram Table

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

• Example: An atom with 8 electrons in its set of orbitals would fill the 1s, 2s, and 2p orbitals as follows: 1s: ↑↓ 2s: ↑↓ 2p: ↑ ↑ ↑ ↓

Ground State Electron Configurations

Auf Bau Principle

The Auf Bau Principle states that electrons fill the lowest energy orbitals first before moving to higher energy orbitals.

• Order of Filling: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p, etc.

• Example: Fluorine (Z = 9): $1s^2 2s^2 2p^5$

Condensed Electron Configuration

Shortcut Notation Using Noble Gases

Condensed electron configuration uses the previous noble gas in brackets to simplify the notation for elements with many electrons.

• Steps:

  1. Find the element on the periodic table.

  2. Locate the noble gas that comes before the element and place it in brackets.

  3. Continue the configuration from the noble gas onward.

• Example: Aluminum (Z = 13): [Ne] $3s^2 3p^1$

Electron Orbital Stability

Half-Filled and Fully-Filled Subshells

p and d subshells are most stable when they are half-filled or fully-filled due to symmetrical electron distribution.

• Symmetrical Distribution: Leads to increased stability.

• Example: d5 and d10 configurations are especially stable.

Exceptions to Electron Configurations

Transition Metals and Stability

Starting from chromium (Z = 24), exceptions to the expected electron configurations occur to achieve greater stability.

Element	Expected Configuration	Actual Configuration
Cr (Z = 24)	[Ar] $4s^2 3d^4$	[Ar] $4s^1 3d^5$
Cu (Z = 29)	[Ar] $4s^2 3d^9$	[Ar] $4s^1 3d^{10}$

• Reason: Promotion of an electron from the s orbital to the d orbital creates half-filled or fully-filled d subshells, increasing stability.

Electron Configurations of Ions

Cations and Anions

Electron configurations change when atoms gain or lose electrons to form ions.

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

• Anions: Electrons are added to the lowest available energy orbitals.

• Example (Cation): Titanium (III) ion: Remove electrons from the 4s orbital before the 3d orbital.

• Example (Anion): Nitride ion (N3−): Add three electrons to nitrogen's configuration.

Paramagnetic vs. Diamagnetic Substances

Magnetic Properties Based on Electron Configuration

Magnetism in atoms depends on the presence of unpaired electrons.

• Paramagnetic: Atoms with at least one unpaired electron; attracted to magnetic fields.

• Diamagnetic: All electrons are paired; not attracted to magnetic fields.

Type	s orbital	p orbitals
Paramagnetic	↑	↑ ↑ ↑
Diamagnetic	↑↓	↑↓ ↑↓ ↑↓

Coulomb's Law

Electrostatic Forces Between Charged Particles

Coulomb's Law quantifies the force and energy between two charged particles.

• Formula: $E = e \frac{Q_1 Q_2}{r}$ Where:

  • $E$ = Energy or Force (N, Nm2/C2)

  • $e$ = Permittivity constant

  • $Q_1$, $Q_2$ = Charges of particles (C)

  • $r$ = Distance between centers (m)

• Applications: Used to calculate the potential energy and force between ions in ionic compounds.

• Example: Calculate the force between two ions with known charges and separation distance.

Summary Table: Key Principles and Rules

Principle/Rule	Description	Example
Periodic Law	Properties repeat periodically with atomic number	Trends in reactivity
Hund's Rule	Electrons fill degenerate orbitals singly first	2p: ↑ ↑ ↑
Auf Bau Principle	Electrons fill lowest energy orbitals first	1s before 2s
Condensed Configuration	Uses noble gas shorthand	[Ne] $3s^2 3p^1$
Coulomb's Law	Force between charged particles	$E = e \frac{Q_1 Q_2}{r}$

Additional info:

• Practice problems throughout the material reinforce understanding of electron configurations, orbital diagrams, and periodic trends.

• Exceptions to electron configurations are especially important for transition metals and should be memorized for exams.

• Understanding paramagnetism and diamagnetism is crucial for predicting magnetic properties of elements and compounds.