Lewis Theory and Covalent Bonding: Octet Rule, Electron Counting, and Resonance

Octet Rule and Bonding Foundations

• Covalent bonding and the octet rule: most atoms achieve stability by surrounding themselves with eight valence electrons (an octet). Hydrogen is an exception: it follows a duet (2 electrons).
• Incomplete octets and expanded octets: some atoms can have fewer than eight electrons (e.g., the third-row elements like sulfur and phosphorus can exceed eight, while boron and beryllium can have incomplete octets).
• Lewis theory aims to predict molecular structure by counting valence electrons and arranging atoms so that octet/duet rules are satisfied as much as possible.
• The idea of “directionality” in bonding: electrons between two atoms give bonds a direction and help determine a three-dimensional structure.
• Covalent bonds and the ownership concept: in covalent compounds, the atoms involved share electrons and effectively “own” the bonding electrons within the bond; the molecule overall is held together by these covalent bonds.
• Example idea: methane (CH extsubscript{4}) has a carbon atom bonded to four hydrogens; the carbon atom effectively owns the four hydrogens through bonding.
• Contrast with ionic compounds: ionic species involve electrostatic attraction between cations and anions rather than covalent sharing.

Covalent Bonding: Bonding and Lone Pairs

• A bond is a shared pair of electrons; a sigma bond involves end-to-end overlap, while a pi bond involves side-by-side overlap.
• Bond representation: use a straight line to represent a bond; lone pairs are drawn as pairs of dots (but often not drawn when focusing on the bonding framework).
• Two electrons per bond: every covalent bond consists of two electrons, whether sigma or pi.
• Bonding electrons vs nonbonding electrons: bonding electrons are those shared in bonds; nonbonding electrons (lone pairs) sit on atoms and are not part of a bond.
• How electrons contribute to stability: the shared electrons are attracted to both nuclei, stabilizing the molecule.

Simple Bonding Examples: H extsubscript{2} and H–F

• Hydrogen molecule H extsubscript{2}:
  • Each hydrogen has one valence electron; to satisfy the duet, two electrons are shared between the two H atoms.
  • The H–H bond is represented by a single line; each H ends up with a duet (2 electrons around it).
  • Hydrogen does not reach an octet; it reaches a duet of two electrons.
• Hydrogen fluoride HF:
  • H has 1 valence electron; F has 7 valence electrons.
  • They share one pair of electrons to form one covalent bond (H–F).
  • Hydrogen ends with a duet; fluorine ends with an octet (two electrons in bonds plus six nonbonding electrons as lone pairs).
  • Pattern: hydrogen contributes one electron to the bond; fluorine contributes one electron to the bond; each atom’s unpaired electrons determine the number of bonds formed.
• Unpaired electrons concept: before bonding, atoms have unpaired electrons that participate in bond formation; after bonding, those unpaired electrons are paired within the bond.

Counting Valence Electrons and Building a Simple Lewis Structure: CH extsubscript{4}

• Start with the simplest atoms; count valence electrons: carbon has $4$ valence electrons, hydrogen has $1$ each.
• Total valence electrons for CH extsubscript{4}: $4 + 4 imes1 = 8$. In general, total valence electrons for a molecule is the sum of valence electrons of all atoms.
• Carbon’s octet: carbon has no lone pairs and forms four bonds (four C–H bonds). Each bond contributes $2$ electrons, so carbon’s bonding electrons total is $4 imes2 = 8$, satisfying the octet:
  • Carbon: nonbonding electrons = 0; bonding electrons = $8$; octet is satisfied with a total of $8$ around C.
• Methane structure: a tetrahedral arrangement with four C–H bonds; the carbon “owns” the four hydrogens via covalent bonding.

Bonding Patterns and the Octet Rule in Common Atoms

• General pattern for atoms without charge:
  • Hydrogen: $1$ bond, $0$ lone pairs
  • Boron: $3$ bonds, $0$ lone pairs
  • Carbon: $4$ bonds, $0$ lone pairs
  • Oxygen: typically $2$ bonds, $2$ lone pairs
  • Halogens (e.g., F, Cl): $1$ bond, $3$ lone pairs
• The number of unpaired electrons on an atom often matches the number of bonds it forms in neutral, common cases (e.g., H has 1 unpaired electron and forms 1 bond; C typically forms 4 bonds and has 0 lone pairs).
• Lone pairs are sites of reactivity in many organic molecules; if you see an atom that should have lone pairs but none are drawn, you should add them to reflect likely reactivity.
• Nitrogen example (neutral, no charge): typically has three bonds and one lone pair (e.g., in NH extsubscript{3}). This corresponds to a formal neutral nitrogen in many common neutral compounds.
• Oxygen example (neutral, no charge): typically has two bonds and two lone pairs (e.g., in H extsubscript{2}O design).
• If an atom has no charge, its typical bonding pattern follows these rules; you can use the pattern to infer the number of lone pairs.

Octet Rule Exceptions: Expanded and Incomplete Octets

• BeH extsubscript{2} (beryllium hydride): Be in the center with two hydrogens; results in an incomplete octet for Be, which is allowed for Be and does not violate the octet rule in this case. This is an example of an incomplete octet.
• BF extsubscript{3} (boron trifluoride): central boron bonded to three fluorines; boron ends up with only six valence electrons around it (incomplete octet), which makes BF extsubscript{3} a Lewis acid because boron can accept electron density from a Lewis base.
• Third-row elements sulfur (S) and phosphorus (P) can have expanded octets: they can accommodate 10, 12, or more valence electrons around them in some compounds (e.g., SF extsubscript{6} with sulfur using more than eight electrons). This does not violate the octet rule for these heavier elements.

Valence Electron Counting, Electron Groups, and Formal Charge

• Valence electron counting approaches used in Lewis structures:
  • Octet count: ensure each atom (except H) has a total of eight electrons around it (or the appropriate duet for H).
  • Charge count: accounts for overall molecular charge and adjusts electron counts to reflect charged species.
  • Electron group count: considers regions of electron density (bonds and lone pairs) around a atom.
• Formal charge (FC) is a crucial concept to assess the distribution of electrons in a Lewis structure and to compare resonance forms:
  • General formula: FC = V - ig(N + rac{B}{2}ig) where
  • $V$ = number of valence electrons for the neutral atom
  • $N$ = number of nonbonding electrons on the atom
  • $B$ = number of electrons in bonds (bonding electrons around the atom)
  • For a neutral carbon with four bonds (e.g., in CH extsubscript{4}): $V=4,\, N=0,\, B=8 \Rightarrow FC = 4 - (0 + 8/2) = 0.$
  • For ammonia NH extsubscript{3}: $V=5,\, N=2 \text{(one lone pair)},\ B=6 \Rightarrow FC = 5 - (2 + 6/2) = 5 - (2 + 3) = 0.$
• Important note from the lecture: if a formal charge is written, you may encounter examples where a lone pair is drawn implicitly and a resonance form may shift the location of the negative charge (e.g., a resonance structure with negative charge on N vs. on O). In many cases, the major resonance contributor places negative charge on the more electronegative atom (e.g., O over N). The resonance forms themselves are not real; the real structure is a resonance hybrid (weighted average of all contributors).

Resonance Structures and the Resonance Hybrid

• Resonance structures illustrate the same connectivity of atoms but differ in the placement of lone pairs and double bonds.
• Key notation:
  • Use double-headed arrows (↔) to denote resonance structures and resonance hybridisation rather than a single, static structure.
  • The major contributor is the resonance form with the most favorable distribution of formal charges (often minimizing charges) and placing negative charges on the more electronegative atoms.
• Example discussed in the lecture (amide-like scenario):
  • Structure A places the negative charge on nitrogen.
  • Structure B places the negative charge on oxygen.
  • The real structure is the resonance hybrid, in which the negative charge is delocalized between oxygen and nitrogen, weighted toward the more electronegative atom (oxygen).
• Practical takeaway:
  • Different resonance forms can imply different local charge distributions and reactive hotspots, but only the resonance hybrid describes the actual electron distribution.
  • When solving problems, use resonance to explain bond lengths, bond orders, and reactive sites, and remember that resonance forms are not separate real molecules.

Practical Implications and Problem-Solving Tips

• Lone pairs as reactive sites: identify lone pairs to predict areas of reactivity in organic chemistry.
• Always check for completeness of octets on second-row elements; be aware of exceptions (Be, B) and third-row expansions (S, P).
• Use patterns for quick counting: for neutral atoms, unpaired electrons often indicate the typical bonding pattern (e.g., H:1 bond; C:4 bonds; O:2 bonds; halogens: 1 bond).
• When in doubt about the Lewis structure, go step by step: count valence electrons, determine central atoms (usually the least electronegative unless following typical bonding patterns), place bonds first, then fill lone pairs, and finally assign formal charges to assess stability.

Quick Reference: Key Formulas and Numbers

• Octet rule target: $8$ valence electrons around most second-row atoms; duet for hydrogen: $2$ electrons around H.
• Two electrons per bond: $2$ electrons constitute one covalent bond.
• Valence electron total for a molecule: sum of the valence electrons of all atoms.
• Formal charge: FC = V - ig(N + rac{B}{2}ig).
• Bond order intuition: the number of bonds between two atoms corresponds to the bond order (e.g., single bond = 1, double bond = 2, triple bond = 3) with a corresponding count of shared electron pairs.
• Expanded octet exception: third-row elements (e.g., S, P) can have more than eight electrons around them.
• Incomplete octet exception: Be and B can have fewer than eight electrons around them in some stable molecules (e.g., BeH extsubscript{2}, BF extsubscript{3}).
• Resonance: a set of valid Lewis structures for the same molecule; the real structure is the resonance hybrid; use two-headed arrows to denote resonance.