Ionic and Covalent Bonding, Lewis Structures and Octet Rule

Atoms bond to achieve a stable, completely filled outer shell — a duplet of 2 for H and Li, an octet of 8 for most others (the octet rule). The three bond types:

• Ionic (electrovalent) bond — a metal transfers electrons to a non-metal, forming oppositely-charged ions held by electrostatic attraction. Example: $\text{Na}^{+}\text{Cl}^{-}$, MgO.
• Covalent bond — two non-metals share one or more pairs, one electron of each shared pair coming from each atom. Example: $\text{H}_2\text{O}$, $\text{SCl}_2$.
• Coordinate (dative) bond — a covalent bond in which both shared electrons come from the same atom. Example: the fourth N–H bond in $\text{NH}_4^{+}$, or $\text{H}_3\text{O}^{+}$.

Electrovalency = number of electrons lost or gained; covalency = number of shared pairs an atom forms.

Fajans' rules — covalent character (and lattice strength) rise when the cation polarises the anion more strongly:

• Smaller cation → higher polarising power → more covalent. Among group-1 halides $\text{Li}^{+}$ (smallest) gives the most covalent bond.
• Larger anion → more polarisable → more covalent. For a fixed metal, covalent character rises $\text{MF} < \text{MCl} < \text{MBr} < \text{MI}$; so ionic character falls in the same order (MI is least ionic).
• Higher cation charge → more polarising → more covalent. $\text{SnCl}_4$ ($\text{Sn}^{4+}$) is more covalent than $\text{SnCl}_2$ ($\text{Sn}^{2+}$).
• Lattice enthalpy follows charge density: small, highly-charged ions ($\text{Be}^{2+}$, $\text{F}^{-}$) give the highest lattice enthalpy, e.g. $\text{BeF}_2$.

Three families break the octet rule:

• Incomplete octet — the central atom has fewer than 8 electrons. Examples: $\text{BF}_3$, $\text{BeCl}_2$, and $\text{LiCl}$ ($\text{Li}^{+}$ has only a 2-electron duplet).
• Expanded octet — a period-3 (or lower) central atom holds more than 8 electrons using its d-orbitals. Examples: $\text{PCl}_5$ (10), $\text{SF}_6$ (12), $\text{H}_2\text{SO}_4$ (12 around S).
• Odd-electron molecules — an odd total number of valence electrons leaves one unpaired, so the octet cannot be completed. Examples: NO (11 valence electrons), $\text{NO}_2$.

A molecule like $\text{SCl}_2$ (2 bond pairs + 2 lone pairs on S) obeys the octet.

Working with Lewis structures:

• Each single bond = 1 shared pair = 2 electrons; count them together with the atom's lone pairs to total the electrons around it.
• Resonance structures are the several valid Lewis structures that differ only in where the double bond sits. The **nitrite ion $\text{NO}_2^{-}$ has 2** resonance structures (the N=O double bond can be on either oxygen).
• **Electrons around S in $\text{H}_2\text{SO}_4$** = 2 single (S–O–H) + 2 double (S=O) bonds = 4 bonds $\times$ 2 = 12 electrons (an expanded octet).
• A Lewis acid is an electron-pair acceptor; a Lewis base is an electron-pair donor. This is broader than the H⁺ (Brønsted) definition — it needs no proton at all.

The formal charge of an atom in a Lewis structure:

• Take the atom's valence electrons, subtract its lone-pair (non-bonding) electrons, and subtract half its bonding electrons.
• The best Lewis structure is the one with formal charges closest to zero.
• Example — carbon in $\text{CO}_2$ (O=C=O): valence $= 4$, lone electrons $= 0$, bonding electrons $= 8$ (two double bonds), so FC $= 4 - 0 - \tfrac{8}{2} = 0$.