# Lecture 11: Chemical Bonding II: Lewis Structures and Resonance

## General Chemistry I

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## Learning Objectives

By the end of this lecture, students will be able to:

1. Draw Lewis dot symbols for atoms and ions
2. Follow a systematic procedure to draw Lewis structures for molecules and polyatomic ions
3. Assign formal charges to atoms in Lewis structures
4. Identify resonance structures and describe the concept of resonance hybrids
5. Recognize exceptions to the octet rule and draw structures for electron-deficient, expanded octet, and odd-electron species

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## Lecture Content

### I. Lewis Dot Symbols

A Lewis dot symbol consists of an element's chemical symbol surrounded by dots representing its valence electrons. For main-group elements, the number of valence electrons equals the group number. Dots are placed on four sides of the symbol, one per side before any pairing occurs. Sodium has 1 dot, carbon has 4, nitrogen has 5, oxygen has 6, fluorine has 7, and neon has 8. These symbols provide a visual starting point for understanding bonding: atoms share or transfer dots to reach an octet.

### II. The Octet Rule

Main-group atoms tend to form bonds until they are surrounded by 8 valence electrons. Hydrogen is the principal exception, seeking only 2 electrons (the duet rule). A bonding pair is a pair of electrons shared between two atoms, shown as a line in structural formulas. A lone pair belongs to a single atom and is not shared, shown as two dots.

### III. Drawing Lewis Structures -- Systematic Procedure

Drawing a correct Lewis structure follows a five-step procedure. First, determine the total number of valence electrons by summing the valence electrons of all atoms. For anions, add electrons equal to the negative charge; for cations, subtract electrons equal to the positive charge. Second, write the skeletal structure by placing the least electronegative atom at the center (hydrogen and fluorine are always terminal) and connecting atoms with single bonds, each of which uses 2 electrons. Third, distribute the remaining electrons by placing lone pairs on terminal atoms first to satisfy their octets, then placing any leftover electrons on the central atom. Fourth, check octets: if the central atom has fewer than 8 electrons, convert lone pairs from adjacent atoms into bonding pairs to form double or triple bonds. For elements in Period 3 and beyond, expanded octets are permitted if needed. Fifth, verify that the total number of electrons in the finished structure matches the count from step one.

### IV. Worked Examples

Consider water (H2O). The total valence electron count is 2(1) + 6 = 8. Oxygen serves as the central atom, bonded to two hydrogen atoms by single bonds (using 4 electrons). The 4 remaining electrons form two lone pairs on oxygen. Oxygen has 8 electrons (2 bonds plus 2 lone pairs) and each hydrogen has 2 -- all octets and duets are satisfied.

For carbon dioxide (CO2), the count is 4 + 2(6) = 16 valence electrons. Carbon is the central atom, initially connected to each oxygen by a single bond (4 electrons used). Distributing the remaining 12 electrons as lone pairs on the oxygens (6 each) satisfies their octets but leaves carbon with only 4 electrons. Converting one lone pair from each oxygen into a bonding pair creates two double bonds (O=C=O). Now carbon has 8 electrons, each oxygen has 8, and the total is 16.

### V. Formal Charge

Formal charge is a bookkeeping tool used to evaluate and compare Lewis structures. It is calculated as: FC = (valence electrons of the free atom) - (lone pair electrons) - (1/2 bonding electrons), or equivalently, FC = valence electrons - dots - lines. Three guidelines help select the best Lewis structure: the structure with formal charges closest to zero on all atoms is preferred; negative formal charges should reside on the more electronegative atoms; and adjacent atoms should not both carry formal charges of the same sign. The sum of all formal charges must equal the overall charge of the species (zero for neutral molecules).

<image>A comparison of two possible Lewis structures for carbon dioxide with formal charge analysis. Structure A (O=C=O): each atom's formal charge calculation is shown step-by-step below it. O: FC = 6 - 4 - 2 = 0; C: FC = 4 - 0 - 4 = 0; O: FC = 6 - 4 - 2 = 0. All formal charges are zero -- labeled "PREFERRED." Structure B (O-C≡O): formal charges calculated as O: FC = 6 - 6 - 1 = -1; C: FC = 4 - 0 - 4 = 0; O: FC = 6 - 2 - 3 = +1. Has non-zero formal charges and positive charge on more electronegative O -- labeled "LESS FAVORED." Both structures are shown with all lone pairs drawn explicitly.</image>

### VI. Resonance Structures

In some cases, more than one valid Lewis structure can be drawn for a molecule. These alternative structures, called resonance structures, differ only in the placement of electrons (not atoms) and are connected by double-headed arrows (<->). The actual molecule is not accurately represented by any single resonance structure. Instead, it is a resonance hybrid -- a weighted average of all contributing structures -- in which electrons are delocalized (spread over multiple atoms) rather than confined to specific bonds.

#### A. Example: Ozone (O3)

Ozone has 3(6) = 18 valence electrons. Two equivalent resonance structures can be drawn: O=O-O and O-O=O. In the resonance hybrid, both O-O bonds are equivalent with a bond order of 1.5, and the formal charge is shared equally by both terminal oxygens.

#### B. Example: Carbonate Ion (CO3^2-)

The carbonate ion has 4 + 3(6) + 2 = 24 valence electrons. Three equivalent resonance structures can be drawn, each placing the double bond on a different oxygen. In the hybrid, all three C-O bonds are equivalent with a bond order of 4/3, and the 2- charge is delocalized equally across all three oxygen atoms.

<image>The three resonance structures of the carbonate ion (CO3^2-) shown side by side, connected by double-headed arrows. In Structure 1, the double bond is between C and the top O, with single bonds to the left and right O atoms (which bear formal charges of -1). In Structure 2, the double bond shifts to the left O. In Structure 3, the double bond is on the right O. Below, the resonance hybrid is shown: a central C connected to three O atoms with dashed bonds (indicating bond order of 1.33), and the 2- charge distributed equally, with -2/3 partial charge on each O. Bond length data is shown: all three C-O bonds are 129 pm (between a typical C-O single bond at 143 pm and a C=O double bond at 122 pm).</image>

### VII. Exceptions to the Octet Rule

#### A. Electron-Deficient Compounds (Incomplete Octets)

Some compounds have a central atom with fewer than 8 electrons. This is most common for beryllium (4 electrons) and boron (6 electrons). In BF3, boron forms three single bonds to fluorine and has only 6 electrons around it. While resonance structures with a B=F double bond can be drawn, fluorine's high electronegativity makes it reluctant to share electrons in this way. These electron-deficient compounds are characteristically strong Lewis acids (electron-pair acceptors).

#### B. Odd-Electron Species (Free Radicals)

Molecules with an odd total number of valence electrons cannot satisfy all octets, because at least one atom must carry an unpaired electron. Examples include NO (11 electrons), NO2 (17 electrons), and ClO (13 electrons). Free radicals are typically highly reactive because of their unpaired electron and play important roles in biology, where reactive oxygen species (ROS) contribute to cellular damage.

#### C. Expanded Octets (Hypervalent Compounds)

Elements in Period 3 and beyond can accommodate more than 8 electrons in their valence shell because they have accessible d orbitals. These hypervalent compounds may have 10, 12, or even more electrons around the central atom. PCl5 places 10 electrons around phosphorus (5 bonds), SF6 places 12 around sulfur (6 bonds), XeF2 has 10 around xenon (2 bonds and 3 lone pairs), and ICl4- has 12 around iodine (4 bonds and 2 lone pairs). Expanded octets should only be invoked when necessary -- when the octet rule alone cannot be satisfied, or when doing so minimizes formal charges.

### VIII. Lewis Structures of Polyatomic Ions

Polyatomic ions follow the same procedure as neutral molecules, with the total valence electron count adjusted for the charge. The finished structure is enclosed in brackets with the charge shown as a superscript. For NH4+, the count is 5 + 4(1) - 1 = 8 electrons; nitrogen is surrounded by four N-H bonds with no lone pairs. For SO4^2-, the count is 6 + 4(6) + 2 = 32 electrons, with sulfur bonded to four oxygen atoms.

### IX. Bond Order from Lewis Structures

Bond order is the number of bonding pairs between two atoms. In molecules described by resonance, the bond order is calculated as the total number of bonds between two atoms across all resonance structures divided by the number of structures. A higher bond order predicts a shorter bond length and a higher bond energy. Being able to predict relative bond lengths and strengths from Lewis structures is a key skill in general chemistry.