Octet rule and exceptions Knowledge-Based Study

Study notes

1. The Basis of the Octet Rule

   In chemical bonding, the octet rule states that main-group atoms tend to bond in such a way that each atom attains eight valence electrons, achieving a stable electron configuration identical to that of a noble gas (typically $ns^2 np^6$).

   Hydrogen is a notable basic exception that adheres instead to the duet rule, requiring only two electrons to fill its $1s$ valence shell, mimicking helium.

   Sharing Electrons in Covalent Bonds

   In covalent molecules, atoms achieve this stable configuration by sharing electron pairs:

   • Bonding pairs: Electrons shared between bonded atoms, contributing simultaneously to the valence shell of each partner.
   • Lone pairs: Non-bonding valence electrons localized on a single atom.

   For example, in a water molecule ($\text{H}_2\text{O}$), oxygen shares two single bonds with hydrogen atoms and retains two lone pairs, resulting in a completed octet of eight valence electrons around oxygen and a duet for each hydrogen.

   Molecules with Fewer Than Eight Valence Electrons

   Certain stable covalent compounds contain a central atom surrounded by fewer than eight valence electrons. These are referred to as electron-deficient molecules.

   Key Examples: Beryllium and Boron

   • Beryllium ($\text{Be}$): Beryllium has two valence electrons. In gaseous beryllium chloride ($\text{BeCl}_2$), the central $\text{Be}$ atom forms two single covalent bonds with chlorine atoms, possessing only 4 valence electrons in its outer shell.
   • Boron ($\text{B}$): Boron possesses three valence electrons. In boron trifluoride ($\text{BF}_3$) and boron trichloride ($\text{BCl}_3$), the boron atom forms three single bonds, resulting in a stable configuration of only 6 valence electrons.

   Chemical Reactivity of Electron-Deficient Species

   Because their octets remain incomplete, molecules such as $\text{BF}_3$ readily act as Lewis acids (electron-pair acceptors), reacting with Lewis bases like ammonia ($\text{NH}_3$) to form coordinate covalent adducts in which the boron octet becomes fully satisfied.

   Free Radicals and Odd Valence Electron Counts

   A second major exception to the octet rule occurs in molecules that have an odd total number of valence electrons. In such species, it is mathematically impossible for every atom to pair all of its electrons or achieve an octet.

   Prominent Examples

   • Nitrogen Monoxide ($\text{NO}$): Nitrogen contributes 5 valence electrons and oxygen contributes 6, giving a total of 11 valence electrons. The Lewis structure places an unpaired electron on the nitrogen atom, leaving it with 7 valence electrons rather than 8.
   • Nitrogen Dioxide ($\text{NO}_2$): With 5 electrons from nitrogen and 12 from two oxygens, $\text{NO}_2$ has 17 valence electrons. The unpaired electron resides primarily on the central nitrogen atom, which again has only 7 valence electrons.

   Molecules containing an unpaired electron are classified as free radicals. They are typically paramagnetic and exhibit high chemical reactivity, often undergoing dimerization (such as $2\,\text{NO}_2 ightleftharpoons \text{N}_2\text{O}_4$) to pair their lone odd electrons and satisfy the octet rule.

   Exceeding the Octet: Hypervalency

   Elements residing in Period 3 and beyond of the periodic table have energetically accessible $d$ subshells in their valence shell. Consequently, their central atoms can accommodate more than eight valence electrons, forming an expanded octet.

   Conditions for Expansion

   • Principal Quantum Number: Central atoms must belong to Period 3, 4, 5, or below (e.g., $\text{P}$, $\text{S}$, $\text{Cl}$, $\text{Xe}$). Second-period elements ($\text{C}$, $\text{N}$, $\text{O}$, $\text{F}$) have only $2s$ and $2p$ valence orbitals and can never expand their octet.
   • Ligand Electronegativity: Expansion is particularly favored when central atoms are bonded to small, highly electronegative atoms such as fluorine, chlorine, or oxygen.

   Common Hypervalent Examples

   • Phosphorus Pentachloride ($\text{PCl}_5$): The central phosphorus atom forms five covalent bonds, accommodating 10 valence electrons.
   • Sulfur Hexafluoride ($\text{SF}_6$): The central sulfur atom forms six single bonds to fluorine atoms, holding 12 valence electrons.
   • Sulfur Trioxide ($\text{SO}_3$) and Sulfate Ion ($\text{SO}_4^{2-}$): Lewis structures drawn to minimize formal charges place 12 valence electrons around sulfur via multiple bonds.

   Summary of Octet Rule Exceptions

   When analyzing a molecular formula or Lewis structure, classify the octet behavior using this systematic checklist:

   • Rule-Adhering Molecules: Second-period nonmetals ($\text{C}$, $\text{N}$, $\text{O}$, $\text{F}$) in standard molecules such as $\text{CH}_4$, $\text{NH}_3$, and $\text{CO}_2$ strictly follow the octet rule (and $\text{H}$ follows the duet rule).
   • Incomplete Octet: Common for $\text{Be}$ (4 electrons) and $\text{B}$ or $\text{Al}$ (6 electrons) in monomeric covalent halides and hydrides.
   • Odd-Electron Species: Identified whenever the sum of valence electrons is an odd number (e.g., $\text{NO}$, $\text{NO}_2$, $\text{ClO}_2$).
   • Expanded Octet: Central atom is in Period 3 or higher and bonded to 5 or more atoms, or uses expanded structures to minimize formal charge (e.g., $\text{SF}_4$, $\text{BrF}_5$, $\text{XeF}_4$).

   Recognizing the period and valence electron total of the central atom allows reliable prediction of whether a molecule obeys the octet rule or constitutes an exception.