Covalent Bonding and Lewis Structures

The previous chapter developed the extreme, complete-transfer end of the electronegativity-difference spectrum: ionic bonding. This chapter develops the opposite end, where the electronegativity difference between two bonded atoms is small — most dramatically, zero, between two atoms of the same element. Here, neither atom can win the electrons outright, so instead they share one or more pairs of electrons, each pair simultaneously attracted to both nuclei. This is a covalent bond, and the systematic diagram used to represent it, the Lewis structure, is the main tool this chapter builds.

To follow the chapter you should have to hand the octet rule from the previous chapter, valence electron counts (equal to the group number for Groups 1–2, and to the group number minus $10$ for Groups 13–18), and electronegativity values. Nothing here yet addresses shape — molecular geometry is the subject of the VSEPR chapter two chapters ahead — nor expanded octets and resonance, which the next chapter treats as deliberate exceptions to the rules built here.

1. The Covalent Bond as Shared Electrons

A covalent bond forms when two atoms each contribute one electron to a shared pair, called a bonding pair, which is simultaneously attracted to both nuclei and occupies the region of space between them. This shared attraction is what holds the two atoms together — unlike an ionic bond, no electron is transferred away from either atom; both nuclei retain a claim on the shared pair.

The simplest example is the hydrogen molecule, $\text{H}_2$. Each isolated hydrogen atom has one electron; bringing two hydrogen atoms close enough lets their two electrons pair up and occupy the space between both nuclei simultaneously:

Each hydrogen atom, in the molecule, now effectively "sees" two electrons (the shared pair) around it, achieving the stable, filled $1s^2$ configuration of helium — the two-electron analogue of the octet rule for the first shell. This is why covalent bonding, exactly like ionic bonding, is still driven by the same underlying tendency towards a stable, noble-gas-like electron count; the two bonding types differ only in how that stability is reached — transfer versus sharing.

Key distinction. In an ionic bond, the bonding electron(s) belong, after transfer, to one atom; in a covalent bond, the bonding pair belongs to both atoms simultaneously, each atom counting it fully towards its own octet.

2. Counting Valence Electrons and the Steps for a Lewis Structure

A Lewis structure (or Lewis diagram) shows every atom of a molecule or polyatomic ion, every bonding pair as a shared line or pair of dots, and every lone pair (a pair of valence electrons belonging to just one atom, not involved in bonding). Constructing one correctly and systematically follows four steps:

1. Count the total valence electrons available, by summing the valence electrons of every atom in the formula (group number for Groups 1–2; group number minus $10$ for Groups 13–18, e.g. $4$ for carbon in Group 14). For a polyatomic ion, add one electron for each unit of negative charge, or subtract one for each unit of positive charge.
2. Identify the central atom. This is usually the atom written first in the formula (excluding hydrogen, which is never central, since it forms only one bond) or, when ambiguous, the least electronegative atom, since it can form the most bonds radiating outward.
3. Draw single bonds from the central atom to each surrounding (terminal) atom, using two electrons per bond, then distribute the remaining electrons as lone pairs on the terminal atoms first (to complete their octets), and finally on the central atom.
4. Check every atom for an octet (or a duplet, for hydrogen). If the central atom is short of an octet after step 3, convert one or more lone pairs on terminal atoms into additional shared (multiple) bonds with the central atom, as Section 3 develops.

Worked example. Construct the Lewis structure of methane, $\text{CH}_4$.

Step 1: Carbon (Group 14) contributes $4$ valence electrons; each of four hydrogen atoms (Group 1) contributes $1$, for a total of $4 + 4(1) = 8$ valence electrons.

Step 2: Carbon is the central atom (hydrogen can never be central).

Step 3: Four single C–H bonds use $4\times 2 = 8$ electrons — exactly the total available, leaving none for lone pairs.

Step 4: Each hydrogen now has $2$ electrons (a full duplet) via its single bond, and carbon has $4$ bonding pairs $=8$ electrons around it (a full octet). The structure is complete:

Worked example. Construct the Lewis structure of water, $\text{H}_2\text{O}$.

Step 1: Oxygen (Group 16) contributes $6$; two hydrogens contribute $1$ each, for a total of $6+2(1)=8$ valence electrons.

Step 2: Oxygen is the central atom.

Step 3: Two single O–H bonds use $2\times2=4$ electrons, leaving $8-4=4$ electrons, placed as two lone pairs on oxygen (hydrogen can take no further electrons once its duplet is complete).

Step 4: Each hydrogen has a full duplet; oxygen has $2$ bonding pairs $+\,2$ lone pairs $=8$ electrons, a complete octet. The structure — two bonds and two lone pairs on oxygen — is exactly the starting point the VSEPR chapter uses to predict water's bent shape.

3. Multiple Covalent Bonds

When step 3 leaves the central atom short of a full octet even after all available electrons are distributed as lone pairs, one or more terminal lone pairs are converted into an additional shared pair with the central atom, forming a double bond (two shared pairs, four electrons) or a triple bond (three shared pairs, six electrons).

Worked example. Construct the Lewis structure of carbon dioxide, $\text{CO}_2$.

Step 1: Carbon contributes $4$; two oxygens contribute $6$ each, for a total of $4+2(6)=16$ valence electrons.

Step 2: Carbon is the central atom.

Step 3: Two single C–O bonds use $4$ electrons, leaving $16-4=12$, placed as three lone pairs on each oxygen ($6$ electrons each).

Step 4: Checking octets: each oxygen now has $1$ bonding pair $+\,3$ lone pairs $=8$ electrons (complete), but carbon has only $2$ bonding pairs $=4$ electrons — four short of an octet. One lone pair from each oxygen is converted into a second bonding pair with carbon, forming two C=O double bonds:

Re-checking: carbon now has $2$ double bonds $=8$ electrons (complete octet), and each oxygen has $1$ double bond ($4$ electrons) $+\,2$ remaining lone pairs ($4$ electrons) $=8$ electrons (complete octet). All $16$ electrons are accounted for, and every atom satisfies the octet rule.

The same reasoning gives nitrogen gas, $\text{N}_2$, a triple bond: each nitrogen (Group 15, $5$ valence electrons, $10$ total) needs three shared pairs between the two atoms to reach an octet, with one lone pair remaining on each nitrogen, $:\text{N}\!\equiv\!\text{N}\!:$.

Warning. A double or triple bond is still counted as one connection between two atoms for the purposes of molecular shape (Section 4 of the VSEPR chapter) — it occupies one region of electron density, not two or three separate ones, even though it involves two or three shared pairs.

4. Bond Order, Bond Length and Bond Strength

The bond order is the number of shared electron pairs between two bonded atoms: $1$ for a single bond, $2$ for a double bond, $3$ for a triple bond. Increasing bond order has two consistent, related consequences:

• Bond length decreases as bond order increases: more shared pairs pull the two nuclei closer together, since each additional pair adds further electrostatic attraction between the nuclei and the shared electron density.
• Bond strength (bond enthalpy) increases as bond order increases: more shared pairs require more energy to separate, since every pair contributes to holding the atoms together.

For carbon-carbon bonds specifically, this gives the ordering $l(\text{C}\!-\!\text{C}) > l(\text{C}\!=\!\text{C}) > l(\text{C}\!\equiv\!\text{C})$ for bond length, and the reverse ordering for bond enthalpy — a relationship returned to quantitatively in the bond enthalpy chapter later in this block.

5. Coordinate (Dative) Covalent Bonds

An ordinary covalent bond forms from one electron contributed by each atom. A coordinate bond (also called a dative bond) is a covalent bond in which both electrons of the shared pair are donated by a single atom — the donor, which must have a lone pair available — while the other atom, the acceptor, contributes none but has an empty orbital able to accept the pair.

Worked example. Construct the Lewis structure of the ammonium ion, $\text{NH}_4^{+}$, formed when ammonia, $\text{NH}_3$, reacts with $\text{H}^+$.

Neutral ammonia already has three N–H covalent bonds and one lone pair on nitrogen ($5 + 3(1) = 8$ valence electrons, satisfying nitrogen's octet). The incoming $\text{H}^{+}$ ion has no electrons of its own (it is a bare proton), so the new N–H bond can only form if nitrogen's existing lone pair becomes the shared pair — nitrogen donates both electrons, hydrogen accepts:

Once formed, a coordinate bond is indistinguishable from an ordinary covalent bond: all four N–H bonds in $\text{NH}_4^{+}$ have identical length and strength, since all four shared pairs are equally attracted to both the nitrogen and the relevant hydrogen nucleus. The "coordinate" label only describes the bond's origin (both electrons from one atom), not any lasting difference in the finished bond.

Key distinction. A coordinate bond is still a true covalent bond — equal sharing of the pair once formed — not a weaker or different type of interaction. It is classified separately only to track where the bonding electrons originated, which matters for electron-counting during Lewis-structure construction.

6. Polar and Non-Polar Covalent Bonds

Not every covalent bond shares its pair perfectly equally. When the two bonded atoms have different electronegativities, the shared pair is pulled closer to the more electronegative atom, which develops a partial negative charge, $\delta^-$, while the other atom develops a partial positive charge, $\delta^+$. This is a polar covalent bond — intermediate on the electronegativity-difference spectrum between a non-polar covalent bond (zero or negligible difference) and a fully ionic bond (very large difference).

A non-polar covalent bond forms either between two atoms of the same element (zero electronegativity difference, as in $\text{H}_2$ or $\text{Cl}_2$) or between two different elements whose electronegativities happen to be very close. The magnitude of the bond's dipole moment — a vector pointing from the partial-positive to the partial-negative end — increases with increasing electronegativity difference, which is the direct bridge from the bonding classification of this chapter to the molecular-polarity chapter two ahead, where whole-molecule polarity is built from individual bond dipoles and molecular shape together.

Warning. A polar bond does not automatically mean a polar molecule. Individual bond dipoles can cancel by symmetry (e.g. in $\text{CO}_2$, whose two polar C=O bonds point in exactly opposite directions), leaving the whole molecule non-polar overall — the precise subject of the molecular polarity chapter, which requires shape as well as bond polarity.

7. Common Exam Pitfalls

• Miscounting valence electrons for an ion. Forgetting to add an electron per unit of negative charge, or subtract one per unit of positive charge, before distributing electrons throws off the entire structure.
• Placing hydrogen as a central atom. Hydrogen can form only one bond (its duplet is complete with just one shared pair), so it is always terminal, never central.
• Stopping after single bonds without checking every atom's octet. A structure with every available electron used as single bonds and lone pairs can still leave the central atom short of an octet — multiple bonds must be formed to fix this, as in $\text{CO}_2$.
• Treating a coordinate bond as weaker or different once formed. All four N–H bonds in $\text{NH}_4^{+}$ are identical; the "coordinate" label describes only the electron's origin, not a lasting property of the finished bond.
• Assuming a polar bond always gives a polar molecule. Symmetric arrangements of polar bonds (e.g. $\text{CO}_2$, $\text{CCl}_4$) can cancel to zero net dipole; shape must always be considered alongside bond polarity, which is why this topic is picked up again once VSEPR shapes are available.
• Confusing bond order with the number of connected atoms. A triple bond is one connection between two atoms using three shared pairs — it is not three separate bonds to three different atoms.

Summary

• A covalent bond forms when two atoms share a pair of electrons, each contributing one (or, for a coordinate/dative bond, both electrons coming from a single donor atom), so that both atoms count the shared pair towards their own octet (or duplet, for hydrogen).
• A Lewis structure is built in four steps: count total valence electrons (adjusting for ionic charge), identify the central atom, draw single bonds and distribute remaining electrons as lone pairs (terminal atoms first), then check and fix every atom's octet.
• When single bonds and lone pairs cannot complete the central atom's octet, a terminal lone pair is converted into an additional shared pair, forming a double bond (bond order $2$) or triple bond (bond order $3$).
• Increasing bond order decreases bond length and increases bond strength (bond enthalpy), since more shared pairs draw the bonded nuclei more strongly together.
• A coordinate (dative) bond, once formed, is identical in every physical respect to an ordinary covalent bond — only its electron origin differs.
• Bonds are classified along the electronegativity-difference spectrum as non-polar covalent (zero/negligible difference), polar covalent ($\delta^+ / \delta^-$ charge separation, intermediate difference), or ionic (very large difference, previous chapter); a polar bond does not guarantee a polar molecule, since bond dipoles can cancel by symmetry.