Chapter 4: Chemical Bonding and Lewis Structures

Summary

This chapter introduces ionic, covalent, and metallic bonding, including Lewis dot symbols, Lewis structures, resonance, formal charge, and exceptions to the octet rule. Students learn to predict bond order, bond length, and bond energy relationships.

Concepts Covered

This chapter covers the following 32 concepts from the learning graph:

Chemical Bonds
Ionic Bonds
Covalent Bonds
Metallic Bonds
Bond Formation Energy
Ionic Compounds
Crystal Lattice
Lattice Energy
Cation Formation
Anion Formation
Polyatomic Ions
Naming Ionic Compounds
Writing Ionic Formulas
Transition Metal Ions
Lewis Dot Symbols
Lewis Structures
Octet Rule
Single Bonds
Double Bonds
Triple Bonds
Lone Pairs
Bonding Pairs
Resonance Structures
Resonance Hybrid
Formal Charge
Formal Charge Calculation
Expanded Octets
Incomplete Octets
Exceptions to Octet Rule
Bond Order
Bond Length
Bond Energy

Prerequisites

This chapter builds on concepts from:

4.1 Why Atoms Bond: The Energy Driving Force

A fundamental question in chemistry is: why do atoms combine at all? The answer lies in energy. Isolated atoms are almost never in their lowest possible energy state when surrounded by other atoms of different types — they can achieve a lower, more stable energy configuration by sharing or transferring electrons to form chemical bonds.

Think of bond formation as analogous to rolling a ball into a valley. The ball (the system of atoms) naturally moves toward lower potential energy. When two hydrogen atoms, each with one electron, approach each other, the electron of each atom begins to feel the attractive pull of both nuclei. This mutual attraction lowers the overall energy of the system below that of the two separated atoms. The amount of energy released when a bond forms — or equivalently, the energy required to break the bond — is called the bond formation energy. This energy is always released during bond formation and must always be supplied to break a bond.

The type of chemical bond that forms depends on the participating atoms' electronegativity values, which reflect how strongly each atom attracts electrons toward itself. Recall from Chapter 3 that electronegativity increases across periods and decreases down groups. Three major categories of bonding emerge from these differences:

Ionic bonds form between atoms with a large electronegativity difference (typically greater than 1.7), usually a metal and a nonmetal. One atom effectively transfers electrons to the other.
Covalent bonds form between atoms with similar electronegativities (difference typically less than 1.7), usually nonmetals. Electrons are shared between atoms.
Metallic bonds form between metal atoms, which pool their valence electrons into a shared "sea" of delocalized electrons.

Understanding which type of bond forms — and predicting the properties that result — is the central skill of this chapter.

4.2 Ionic Bonding: Electron Transfer and Electrostatic Attraction

Ionic bonding arises from the electrostatic attraction between oppositely charged ions. When a metal atom with low ionization energy encounters a nonmetal atom with high electron affinity, the thermodynamically favorable outcome is complete electron transfer: the metal loses one or more valence electrons to become a positively charged cation, and the nonmetal gains those electrons to become a negatively charged anion.

Cation and Anion Formation

Cation formation occurs when a metal atom loses valence electrons. Sodium (Na, Group 1) loses its single 3s electron:

\[ \text{Na} \rightarrow \text{Na}^+ + e^- \]

The resulting Na⁺ ion has the electron configuration of neon — a completely filled outermost shell. This is a key driving force: achieving a noble gas electron configuration by losing or gaining electrons.

Anion formation occurs when a nonmetal gains electrons to fill its outermost shell. Chlorine (Cl, Group 17) gains one electron:

\[ \text{Cl} + e^- \rightarrow \text{Cl}^- \]

The resulting Cl⁻ ion has the electron configuration of argon. The combination of Na⁺ and Cl⁻ produces sodium chloride, common table salt. Note that in the final compound, electrons have not truly been "created" or "destroyed" — the electron lost by sodium is the same electron gained by chlorine.

Common patterns for main-group ion formation:

Group 1 metals form 1+ cations (e.g., Li⁺, Na⁺, K⁺)
Group 2 metals form 2+ cations (e.g., Mg²⁺, Ca²⁺, Ba²⁺)
Group 13 metals/metalloids form 3+ cations (e.g., Al³⁺)
Group 15 nonmetals form 3− anions (e.g., N³⁻, P³⁻)
Group 16 nonmetals form 2− anions (e.g., O²⁻, S²⁻)
Group 17 nonmetals form 1− anions (e.g., F⁻, Cl⁻, Br⁻, I⁻)

Transition Metal Ions

Transition metal ions are more complex because d-block elements can lose different numbers of electrons depending on conditions, giving rise to multiple possible oxidation states. When transition metals form cations, they lose their outermost s electrons first, then d electrons. Iron (Fe, [Ar] 4s² 3d⁶), for example, can form:

Fe²⁺: loses the two 4s electrons, giving [Ar] 3d⁶
Fe³⁺: loses both 4s electrons and one 3d electron, giving [Ar] 3d⁵

The 3d⁵ half-filled configuration of Fe³⁺ is particularly stable (all five d orbitals singly occupied, Hund's Rule), which is why both Fe²⁺ and Fe³⁺ are commonly encountered. Other transition metals with variable oxidation states include copper (Cu⁺ and Cu²⁺), manganese (Mn²⁺ through Mn⁷⁺), and chromium (Cr²⁺ and Cr³⁺). Because the charge is not predictable from group number alone, transition metal ion names must always include a Roman numeral indicating the charge.

Crystal Lattice and Lattice Energy

Ionic compounds do not exist as simple pairs of ions. Instead, large numbers of cations and anions arrange themselves into a highly ordered three-dimensional structure called a crystal lattice. In sodium chloride, for example, each Na⁺ ion is surrounded by six Cl⁻ ions in an octahedral arrangement, and each Cl⁻ is surrounded by six Na⁺ ions. This extended three-dimensional alternating pattern maximizes attractive interactions (between opposite charges) while minimizing repulsive interactions (between like charges).

The stability of an ionic crystal lattice is quantified by the lattice energy — the energy released when one mole of an ionic compound forms from its gaseous ions, or equivalently, the energy required to completely separate one mole of the ionic solid into isolated gaseous ions. Lattice energy is always a large positive value when defined as the energy of separation (endothermic process).

The magnitude of lattice energy is governed by Coulomb's Law. The electrostatic potential energy between two ions is:

\[ E \propto \frac{Q_1 \times Q_2}{r} \]

where \(Q_1\) and \(Q_2\) are the ion charges and \(r\) is the distance between ion centers (approximately the sum of their ionic radii). This relationship has two critical implications:

Higher ionic charges increase lattice energy. MgO (Mg²⁺ and O²⁻, charges of +2 and −2) has a much higher lattice energy (~3800 kJ/mol) than NaF (Na⁺ and F⁻, charges of +1 and −1, ~923 kJ/mol), even though the ion sizes are similar.
Smaller ion sizes increase lattice energy. LiF has a higher lattice energy than CsF because Li⁺ is much smaller than Cs⁺, placing the charges closer together.

High lattice energies translate directly into macroscopic properties: high melting points, high hardness, and low volatility. NaCl melts at 801°C; MgO melts at 2852°C.

Diagram: Ionic Crystal Lattice Structure

NaCl Crystal Lattice Interactive Visualizer (p5.js MicroSim)

Type: MicroSim sim-id: ionic-lattice-visualizer
Library: p5.js
Status: Specified

Canvas size: 800x450px, responsive to window resize. Background color: dark navy (#0d1117). The simulation renders an interactive 3D-perspective view of an ionic crystal lattice.

Layout: Left control panel (220px wide) with controls; right visualization area fills remaining space.

Controls panel (top to bottom): - Dropdown labeled "Compound": options NaCl, MgO, CaF₂, CsCl (default: NaCl) - Slider labeled "Grid Size": range 2×2×2 to 4×4×4, default 3×3×3 - Button labeled "Rotate" (toggle auto-rotation on/off) - Checkbox "Show Ion Labels" (default: checked) - Color legend: cation color (blue sphere), anion color (red sphere) - Text box showing "Lattice Energy: [value] kJ/mol" updated per compound selection

Visualization: Renders a perspective projection of the selected ionic lattice. Cations displayed as blue spheres, anions as red spheres, sized proportionally to their ionic radii from a lookup table. Spheres are connected by thin gray lines to nearest neighbors to indicate the lattice geometry. The view rotates continuously when rotation is enabled; user can also click and drag to rotate manually. When "Show Ion Labels" is on, hovering over a sphere shows a tooltip with ion name, charge, and ionic radius.

A small inset panel in the bottom-right corner shows the unit cell in isolation with labeled ion positions.

Learning objective: Students will be able to (Understanding — Bloom's level 2) describe the three-dimensional arrangement of ions in an ionic crystal lattice and (Analyzing — Bloom's level 4) explain how ion charge and size affect lattice energy by comparing two compounds side by side.

4.3 Naming Ionic Compounds and Writing Formulas

The systematic nomenclature and formula-writing conventions for ionic compounds follow well-defined rules that AP Chemistry students must master fluently.

Naming Ionic Compounds

For ionic compounds formed from main-group elements, the naming convention is:

Name the cation first, using the element name unchanged (e.g., sodium, calcium).
Name the anion second, changing the ending of the element name to -ide (e.g., chloride, oxide, sulfide).

For transition metal cations, the charge must be specified with a Roman numeral in parentheses immediately after the element name, because these metals can have variable charges. Iron(II) chloride (FeCl₂) and iron(III) chloride (FeCl₃) are distinct compounds with different properties.

Polyatomic Ions

Polyatomic ions are groups of atoms covalently bonded together that carry an overall charge. They behave as a unit in ionic compounds. Some common polyatomic ions that must be memorized for AP Chemistry:

Polyatomic Ion	Formula	Charge
Ammonium	NH₄⁺	+1
Hydroxide	OH⁻	−1
Nitrate	NO₃⁻	−1
Nitrite	NO₂⁻	−1
Sulfate	SO₄²⁻	−2
Sulfite	SO₃²⁻	−2
Carbonate	CO₃²⁻	−2
Bicarbonate	HCO₃⁻	−1
Phosphate	PO₄³⁻	−3
Acetate	CH₃COO⁻	−1
Permanganate	MnO₄⁻	−1
Dichromate	Cr₂O₇²⁻	−2

When a polyatomic ion appears more than once in a formula, it is enclosed in parentheses with a subscript. For example, calcium phosphate is Ca₃(PO₄)₂, where the parentheses make clear that the subscript 2 applies to the entire PO₄³⁻ unit, not just the oxygen.

Writing Ionic Formulas

Writing ionic formulas requires that the overall compound be electrically neutral — the total positive charge from cations must exactly cancel the total negative charge from anions. The "criss-cross" method provides a systematic approach: take the charge of the cation as the subscript of the anion, and the charge of the anion (as an absolute value) as the subscript of the cation, then reduce to the lowest whole-number ratio.

For example, aluminum (Al³⁺) and sulfate (SO₄²⁻):

The 3 from Al³⁺ becomes the subscript on SO₄, and the 2 from SO₄²⁻ becomes the subscript on Al.
This gives Al₂(SO₄)₃.
Checking: 2 × (+3) + 3 × (−2) = +6 − 6 = 0. Confirmed neutral.

When two atoms with similar electronegativities approach each other — as happens between two nonmetal atoms — neither atom has sufficient energy advantage to completely strip electrons from the other. Instead, both atoms achieve a more stable configuration by sharing electrons. This sharing constitutes a covalent bond.

Lewis Dot Symbols

The first step in visualizing covalent bonding uses a notation developed by G. N. Lewis in the early twentieth century. Lewis dot symbols represent an atom's valence electrons as dots placed around the element's symbol, one dot per valence electron, up to a maximum of eight (one on each of four sides before pairing begins).

The number of dots equals the number of valence electrons, which for main-group elements equals the group number:

Hydrogen (Group 1): 1 dot · H ·
Carbon (Group 14): 4 dots (one on each side) · Ċ ·
Nitrogen (Group 15): 5 dots (one pair plus three singles) : Ṅ ·
Oxygen (Group 16): 6 dots (two pairs plus two singles) : Ȯ :
Chlorine (Group 17): 7 dots (three pairs plus one single) : Cl ·
Argon (Group 18): 8 dots (four pairs) : Ar :

Lewis dot symbols reveal at a glance how many bonds an atom is likely to form: each unpaired dot represents one bond, because each bond requires one electron from each participating atom. Hydrogen (1 unpaired dot) forms 1 bond; carbon (4 unpaired dots) forms 4 bonds; nitrogen (3 unpaired dots) forms 3 bonds; oxygen (2 unpaired dots) forms 2 bonds.

4.5 Drawing Lewis Structures: A Step-by-Step Procedure

A Lewis structure is a two-dimensional diagram showing how all atoms in a molecule or polyatomic ion are connected, including all bonding pairs and lone pairs of electrons. Mastering Lewis structures is fundamental to predicting molecular geometry (Chapter 5), polarity, and reactivity.

The octet rule is the foundational principle: most second-period main-group atoms tend to form bonds until they are surrounded by eight electrons (four pairs). This mimics the electron configuration of the nearest noble gas and represents a stable, filled valence shell. Hydrogen is the main exception — it needs only two electrons (duet rule) to mimic helium.

The Six-Step Procedure for Lewis Structures

Follow these steps systematically to draw a correct Lewis structure:

Count total valence electrons. Sum the valence electrons from all atoms. For anions, add one electron per negative charge; for cations, subtract one electron per positive charge.
Identify the central atom. The central atom is usually the least electronegative atom in the molecule (not hydrogen, which always goes on the outside). If there is a unique atom, it is typically central.
Connect atoms with single bonds. Draw a single bond (one pair of electrons, represented as a line) between the central atom and each surrounding (terminal) atom. Each bond uses 2 electrons from the total count.
Complete the octets of terminal atoms. Place remaining electrons as lone pairs on surrounding atoms until each has 8 electrons (or 2 for hydrogen).
Place any remaining electrons on the central atom. After filling terminal atoms, place leftover electrons on the central atom.
Check the central atom's octet. If the central atom has fewer than 8 electrons, convert lone pairs from terminal atoms into double or triple bonds until the central atom has a full octet.

Types of Bonds

The number of electron pairs shared between two atoms determines the bond type:

Single bonds consist of one shared pair of electrons (2 electrons total), represented by a single line (—). Examples: H–H, H–Cl, C–H.
Double bonds consist of two shared pairs of electrons (4 electrons total), represented by a double line (=). Examples: C=O in carbon dioxide, C=C in ethylene.
Triple bonds consist of three shared pairs of electrons (6 electrons total), represented by a triple line (≡). Examples: N≡N in nitrogen gas, C≡O in carbon monoxide.

Within any Lewis structure, electrons exist as either bonding pairs (shared between two atoms, forming a bond) or lone pairs (also called nonbonding pairs — electrons associated with only one atom, not involved in bonding). Lone pairs occupy space and influence molecular geometry, as explored in Chapter 5.

Worked Example: Carbon Dioxide (CO₂)

Total valence electrons: C contributes 4, each O contributes 6. Total = 4 + 6 + 6 = 16 electrons.
Central atom: C (less electronegative than O).
Single bonds: O–C–O uses 4 electrons; 12 remain.
Complete O octets: each O needs 6 more electrons as lone pairs; 6 + 6 = 12 electrons used. 0 remain.
No electrons left for central atom. Check C: only 4 electrons (2 bonds × 2 e⁻ each). C needs 8.
Convert lone pairs to double bonds: move one lone pair from each O to form double bonds. Result: O=C=O. Each atom now has 8 electrons.

Diagram: Interactive Lewis Structure Builder

Lewis Structure Builder (p5.js MicroSim)

Type: MicroSim sim-id: lewis-structure-builder
Library: p5.js
Status: Specified

Canvas size: 800x450px, responsive to window resize. Background: light gray (#f5f5f5). The simulation guides students through building a Lewis structure step by step using the six-step procedure.

Layout: Top bar shows molecule selector; left panel (200px) shows the six-step checklist with current step highlighted; main canvas (center) shows the developing Lewis structure; right panel (180px) shows an electron count tracker.

Controls: - Dropdown "Select Molecule": options H₂O, NH₃, CO₂, SO₂, PCl₃, CH₄, HCN (default: H₂O) - Button "Next Step" advances through the six steps - Button "Reset" returns to step 1 - Toggle "Show Electron Counts" overlays electron count badges on each atom

Main canvas behavior per step: - Step 1: Displays atom symbols; right panel shows valence electron count per atom and running total; total valence electrons highlighted in green once correctly tallied. - Step 2: Central atom is highlighted with a blue ring; a tooltip explains why it is central. - Step 3: Single bond lines appear animating from central to each terminal atom; electron count decrements from total. - Step 4: Lone pairs appear as paired dots on terminal atoms in yellow; electron count decrements. - Step 5: Remaining lone pairs placed on central atom (shown in orange). - Step 6: If central atom is deficient, red arrows animate from a terminal lone pair to a new bond line; bond type upgrades from single to double or triple with animation.

Final structure is displayed with bond lines (single = 1 line, double = 2 lines, triple = 3 lines) and lone pair dots. Each atom shows a small electron count badge (green if octet satisfied, red if not).

Learning objective: Students will be able to (Applying — Bloom's level 3) construct correct Lewis structures for molecules and polyatomic ions by following the six-step procedure, and (Evaluating — Bloom's level 5) assess whether the octet rule is satisfied for each atom in the structure.

4.6 Resonance Structures and the Resonance Hybrid

For many molecules and polyatomic ions, a single Lewis structure does not adequately represent the true electron distribution. Consider ozone (O₃). Following the Lewis structure procedure yields a structure with a single bond on one side of the central oxygen and a double bond on the other. But experimental evidence shows that both O–O bonds in ozone are identical in length — intermediate between a typical single bond and a typical double bond. Neither Lewis structure alone is correct.

The solution is the concept of resonance. When two or more valid Lewis structures can be drawn for a molecule by moving only electrons (not atoms) between equivalent positions, the real molecule is not any single one of those structures. Instead, the molecule is best described as a resonance hybrid — a weighted average of all contributing resonance structures.

Drawing Resonance Structures

Resonance structures are drawn by moving lone pairs or double bonds to equivalent positions while keeping the atomic skeleton unchanged. The structures are connected by a double-headed arrow (↔), never a regular single-headed equilibrium arrow.

For ozone (O₃), the two resonance structures can be described as:

Structure A: left O–O single bond, right O=O double bond, lone pair on central O
Structure B: left O=O double bond, right O–O single bond, lone pair on central O (mirror of A)

The resonance hybrid has both bonds at an intermediate bond order of 1.5. The true ozone molecule has partial double-bond character in both O–O bonds simultaneously, not a molecule that "flips" between the two structures.

Key rules for drawing resonance structures:

Only electrons move between resonance structures — never atoms
All resonance structures must have the same atomic connectivity
All resonance structures must have the same total number of electrons
All resonance structures must be valid Lewis structures (with octets satisfied where possible)
Structures that contribute more to the resonance hybrid are those with lower formal charges on atoms and negative formal charges on more electronegative atoms

Diagram: Resonance Structures Comparison Infographic

Resonance Structures Infographic (Static Diagram Specification)

Type: Infographic sim-id: resonance-structures-infographic
Library: p5.js
Status: Specified

Canvas size: 800x420px, white background. The infographic shows three molecules side-by-side demonstrating resonance: ozone (O₃), nitrate ion (NO₃⁻), and benzene (C₆H₆).

For each molecule, display: - Column 1 (200px wide): Lewis structure A labeled "Structure 1" - Column 2 (40px): Double-headed resonance arrow (↔) in bold blue - Column 3 (200px): Lewis structure B labeled "Structure 2" (and Structure 3 for nitrate) - Column 4 (200px): "Resonance Hybrid" showing the average structure with dashed bonds where bond order is fractional

Bond rendering conventions: - Single bonds: solid thin line (#333) - Double bonds: solid double line (#333) - Partial bonds (hybrid): dashed lines (#0077cc, medium thickness) - Lone pairs: paired dots in red (#cc0000) - Formal charges: small superscript labels in green (#009900) for negative, red (#cc0000) for positive

A footer text area explains: "The resonance hybrid is the single true structure; individual resonance structures are tools for bookkeeping, not real alternating forms."

Color-coded legend at top right: - Blue dashed = partial bond (fractional bond order) - Red dots = lone pairs - Green/red superscripts = formal charge

Learning objective: Students will be able to (Understanding — Bloom's level 2) explain what resonance structures represent and distinguish them from the resonance hybrid, and (Analyzing — Bloom's level 4) identify which resonance structures contribute more to the hybrid based on formal charge minimization.

4.7 Formal Charge: Choosing the Best Structure

When multiple valid Lewis structures exist — either as resonance contributors or as genuinely different possible arrangements — formal charge provides a quantitative tool for determining which structure best represents the actual electron distribution.

Formal charge is defined as the charge an atom would have if all bonding electrons were shared equally between the bonded atoms, regardless of actual electronegativity. It is calculated using:

\[ FC = V - N - \frac{B}{2} \]

where:

\(FC\) = formal charge on the atom
\(V\) = number of valence electrons in the neutral free atom (the atom's group number for main-group elements)
\(N\) = number of nonbonding (lone pair) electrons on the atom in the Lewis structure
\(B\) = number of bonding electrons shared by the atom (total electrons in all bonds to that atom)

Formal Charge Calculation

The formal charge calculation is straightforward once you identify N and B directly from the Lewis structure.

Worked example: Calculate the formal charge on each atom in carbon dioxide (O=C=O).

For each doubly bonded oxygen in CO₂: - \(V = 6\) (oxygen has 6 valence electrons) - \(N = 4\) (two lone pairs = 4 nonbonding electrons) - \(B = 4\) (one double bond = 4 bonding electrons) - \(FC = 6 - 4 - \frac{4}{2} = 6 - 4 - 2 = 0\)

For carbon in CO₂: - \(V = 4\) (carbon has 4 valence electrons) - \(N = 0\) (no lone pairs on carbon in this structure) - \(B = 8\) (two double bonds, each contributing 4 bonding electrons) - \(FC = 4 - 0 - \frac{8}{2} = 4 - 0 - 4 = 0\)

All formal charges are zero in the O=C=O structure, which signals it is the best representation. The sum of all formal charges in a neutral molecule must equal zero; in an ion, the sum must equal the ion's charge.

Guidelines for Using Formal Charge

The preferred Lewis structure is the one that minimizes formal charges according to these rules, listed in order of importance:

Structures where all formal charges are zero are preferred over structures where atoms carry charges.
If formal charges are unavoidable, they should be as small as possible.
Any negative formal charges should reside on the most electronegative atoms.
Adjacent atoms should not both carry formal charges of the same sign.

Consider the two possible Lewis structures for carbon monoxide (CO):

Structure A: :C≡O: gives C a formal charge of −1 and O a formal charge of +1.
Structure B: :C=O: gives C a formal charge of −2 and O a formal charge of 0.

Structure A is preferred despite the counterintuitive result that carbon carries the negative charge — because the formal charges are smaller in magnitude in Structure A, satisfying rule 2. This example illustrates that formal charge is a bookkeeping tool, not a statement about actual charge distribution, which is better described by partial charges derived from electronegativity differences.

Diagram: Formal Charge Calculator Infographic

Formal Charge Step-by-Step Diagram

Type: Diagram sim-id: formal-charge-diagram
Library: p5.js
Status: Specified

Canvas size: 800x400px, white background (#ffffff). The diagram walks through a formal charge calculation visually for two molecules side by side: NH₃ (nitrogen atom) and SO₄²⁻ (sulfur atom).

Layout: Two equal columns (380px each) with a thin vertical divider. Each column contains:

Row 1 (80px): The Lewis structure of the molecule/ion drawn with atoms as labeled circles (radius 24px), bonds as lines between circles, and lone pairs as paired dots. Bonds and lone pairs in contrasting colors.

Row 2 (120px): Three labeled boxes stacked vertically: - Box 1 (blue background): "V = valence electrons = [number]" with the periodic table group noted - Box 2 (yellow background): "N = lone pair electrons = [number]" with the lone pairs circled on the structure above - Box 3 (green background): "B = bonding electrons = [number]" with the bonds highlighted on the structure above

Row 3 (80px): Equation display: FC = V − N − B/2 = [V] − [N] − [B/2] = [result], rendered in large, clear font with each substituted number color-coded to match the boxes above.

Row 4 (40px): Result badge showing "Formal Charge = [value]" with green background if 0, yellow if ±1, red if ±2 or larger.

Footer (40px): Caption reads "Always verify: sum of all formal charges = molecular charge."

Learning objective: Students will be able to (Applying — Bloom's level 3) calculate formal charges on individual atoms in a Lewis structure using the formula FC = V − N − B/2 and (Evaluating — Bloom's level 5) use formal charge analysis to identify the most accurate Lewis structure for a molecule or ion.

4.8 Exceptions to the Octet Rule

The octet rule is a powerful and reliable guiding principle, but it has genuine exceptions that AP Chemistry students must recognize and explain.

Incomplete Octets (Electron-Deficient Compounds)

Some atoms are stable with fewer than eight electrons in their valence shell. These incomplete octets occur most commonly in compounds of beryllium and boron.

Beryllium (Group 2, 2 valence electrons) commonly forms compounds like BeCl₂ with only 4 electrons around Be — a "duet" of bonds.
Boron (Group 13, 3 valence electrons) commonly forms compounds like BF₃ with only 6 electrons around B — three bonds and no lone pairs.

BF₃ is electron deficient: boron has only 6 electrons in its valence shell. This makes BF₃ a powerful Lewis acid (electron-pair acceptor), which is why it reacts readily with molecules like NH₃ that have a lone pair to donate.

Expanded Octets (Hypervalent Compounds)

On the other side of the octet rule, some atoms can accommodate more than eight electrons in their valence shell. These expanded octets are possible only for atoms in the third period and beyond, because these atoms have access to empty d orbitals that can participate in bonding.

Common examples of exceptions to the octet rule involving expanded octets include:

Molecule	Central Atom	Electron Groups	Total Electrons on Central Atom
PCl₅	P (Period 3)	5 bonds	10 electrons
SF₆	S (Period 3)	6 bonds	12 electrons
ClF₃	Cl (Period 3)	3 bonds + 2 lone pairs	10 electrons
XeF₄	Xe (Period 5)	4 bonds + 2 lone pairs	12 electrons
IF₅	I (Period 5)	5 bonds + 1 lone pair	12 electrons

Second-period elements (C, N, O, F) can never have expanded octets because they have no available d orbitals. When drawing Lewis structures for compounds containing third-period or heavier central atoms, expanded octets are often the correct choice if they result in lower formal charges.

Consider SO₄²⁻ (sulfate ion). A structure with all single bonds gives S a formal charge of +2 and each O a formal charge of −1 (total: +2 − 4 = −2, correct). An alternative structure using two double bonds and two single bonds gives S a formal charge of 0 and reduces formal charges on oxygen. The expanded-octet structure with lower formal charges is generally considered a better representation, although the AP Chemistry exam typically accepts either valid structure.

Odd-Electron Species

A final exception involves molecules with an odd number of valence electrons, making it impossible to pair all electrons. Examples include nitric oxide (NO, 11 valence electrons) and nitrogen dioxide (NO₂, 17 valence electrons). These radical species contain an unpaired electron and cannot satisfy the octet rule for every atom. They are highly reactive as a result.

Key summary of octet rule exceptions:

Incomplete octets: Be (4 e⁻), B (6 e⁻) — atoms are electron deficient
Expanded octets: third-period and heavier elements (P, S, Cl, Xe, I) — enabled by available d orbitals
Odd-electron radicals: NO, NO₂, ClO₂ — unpaired electron unavoidable

4.9 Bond Order, Bond Length, and Bond Energy

Three interconnected properties describe the character and strength of any covalent bond: bond order, bond length, and bond energy. Understanding the relationships among these three quantities allows chemists to predict molecular stability and reactivity.

Bond Order

Bond order is defined as the number of bonding electron pairs shared between two atoms. For simple cases, bond order equals the number of lines in the Lewis structure:

Single bond (C–C): bond order = 1
Double bond (C=C): bond order = 2
Triple bond (C≡C): bond order = 3

For resonance structures, the bond order is the average over all equivalent bonds. In ozone (O₃), where the Lewis structures show one single bond and one double bond, the average bond order for each O–O bond is:

\[ \text{Bond Order} = \frac{1 + 2}{2} = 1.5 \]

In benzene (C₆H₆), all six C–C bonds are equivalent, each with a bond order of 1.5.

Bond Length and Bond Energy Relationships

The three bond properties are related through two fundamental trends, supported by extensive experimental data:

Trend 1: As bond order increases, bond length decreases.

Sharing more electron pairs pulls the nuclei closer together because the electrons between the nuclei create a stronger attractive force. The bond length trend for carbon-carbon bonds illustrates this clearly:

Bond Type	Bond Order	Bond Length (pm)	Bond Energy (kJ/mol)
C–C (single)	1	154	347
C=C (double)	2	134	614
C≡C (triple)	3	120	839
N–N (single)	1	145	163
N=N (double)	2	123	418
N≡N (triple)	3	110	945

Trend 2: As bond order increases, bond energy increases.

More shared electron pairs mean a stronger bond, requiring more energy to break. The dramatic increase from N–N (163 kJ/mol) to N≡N (945 kJ/mol) explains why nitrogen gas (N₂, with a triple bond) is so unreactive at room temperature — an enormous amount of energy is needed to break that bond and make the nitrogen atoms available for other reactions.

The relationship between bond order, length, and energy can be summarized:

\[ \text{Bond Order} \uparrow \quad \Rightarrow \quad \text{Bond Length} \downarrow \quad \text{and} \quad \text{Bond Energy} \uparrow \]

These trends also apply across different elements. Comparing bonds between the same two elements at different bond orders always follows this pattern. When comparing bonds between different elements, the atomic sizes must also be considered — bonds involving larger atoms are longer and often weaker.

Bond energies are directly useful in estimating the enthalpy change (\(\Delta H\)) of a chemical reaction using Hess's Law applied to bond breaking and forming:

\[ \Delta H_{rxn} \approx \sum (\text{Bond Energies Broken}) - \sum (\text{Bond Energies Formed}) \]

Bonds broken absorb energy (endothermic); bonds formed release energy (exothermic). This calculation gives an estimate, not an exact value, because bond energies are average values over many different molecules.

4.10 Metallic Bonding: The Electron Sea Model

The final type of bonding addresses metals. Pure metals are not ionic (no distinct anions and cations), and they are not covalently bonded (they are not nonmetals sharing electron pairs between pairs of atoms). Instead, metallic bonds arise from a completely different arrangement: the electron sea model.

In a metallic solid, the metal atoms release their valence electrons into a delocalized "sea" or "cloud" that is shared by all atoms in the solid simultaneously. The positively charged metal cations (the nuclei plus core electrons) are arranged in a regular lattice, held together by their attraction to the surrounding sea of mobile valence electrons. No individual electron belongs to any specific atom or pair of atoms — all the valence electrons move freely throughout the entire metal.

This model elegantly explains the characteristic physical properties of metals:

Electrical conductivity: The free electrons are mobile and can carry electric current in response to an applied voltage.
Thermal conductivity: Free electrons also carry kinetic energy efficiently throughout the structure, spreading heat rapidly.
Malleability and ductility: When a force deforms the metal and shifts layers of cations relative to one another, the electron sea adjusts instantly to the new positions. Unlike ionic crystals (which fracture because repulsive ion layers are brought into contact), metals simply deform without breaking.
Metallic luster: Free electrons absorb and re-emit photons across a broad range of wavelengths, giving metals their characteristic shiny appearance.

The strength of metallic bonding varies with the number of valence electrons contributed and the size of the metal cation. Metals with more valence electrons and smaller cations (higher charge density) have stronger metallic bonds — reflected in higher melting points. Tungsten (W), with six valence electrons in a compact lattice, has one of the highest melting points of any element (3422°C), while mercury (Hg), with a filled d subshell contributing poorly to metallic bonding, is a liquid at room temperature.

A comparison of metallic bonding properties:

More valence electrons contributed → stronger metallic bond → higher melting point
Smaller atomic radius → more charge density → stronger metallic bonding
Metallic bonds are non-directional (unlike covalent bonds), giving metals their characteristic plasticity

4.11 Chapter Summary and Concept Connections

This chapter has developed a comprehensive framework for understanding how and why atoms bond, tracing from the fundamental energy driving force through three distinct bonding types and the electron-pair bookkeeping tools that chemists use to predict molecular structure.

The key conceptual threads connecting the 32 concepts:

Chemical bonds form because bonded states have lower energy than separated atoms; the electronegativity difference between atoms determines which type of bond forms.
Ionic bonding involves electron transfer creating cations and anions that organize into crystal lattices stabilized by lattice energy; Coulomb's Law governs lattice energy through ion charge and size.
Ionic compound nomenclature and formula writing follow systematic rules, complicated for transition metals by variable oxidation states and extended to polyatomic ions.
Covalent bonding involves electron sharing; Lewis dot symbols and the six-step Lewis structure procedure translate this sharing into a diagrammatic language of bonding pairs and lone pairs, single bonds, double bonds, and triple bonds, all governed by the octet rule.
Resonance structures and the resonance hybrid handle cases where a single Lewis structure is inadequate; formal charge calculation identifies which structures best represent reality.
Exceptions to the octet rule — incomplete octets, expanded octets, and odd-electron species — define the boundaries of the octet rule and connect to reactivity.
Bond order, bond length, and bond energy are mutually interdependent: higher bond order means shorter, stronger bonds, with direct quantitative consequences for thermochemistry.
Metallic bonding completes the picture, explaining the unique properties of metals through the electron sea model.

These concepts lay the essential foundation for Chapter 5, where molecular geometry is predicted using VSEPR theory — a direct extension of the Lewis structure electron-pair counting done here.

Chapter 4 — Chemical Bonding and Lewis Structures | AP Chemistry

References

See Annotated References