IMAT Chemistry · Chemical Bonding

Covalent Bonds, Lewis Structures and the Octet Rule

A covalent bond is a shared pair of electrons; a Lewis structure shows every shared pair and lone pair, and most atoms end with eight electrons around them.

All Chemical Bonding notes

Why this matters

The papers ask how many electrons an atom uses in bonding (2011, 2022), how single, double and triple carbon bonds compare in length and strength (2013), and which central atoms break the octet rule. Expect a "which statements are correct" format.

Concept 1 of 4: Single, double and triple covalent bonds

Two non-metal atoms both want more electrons, so neither can take them from the other. Instead each puts electrons into a shared pair that both nuclei attract. Sharing two or three pairs pulls the atoms closer together and holds them more tightly.

Definition

A covalent bond is a pair of electrons shared between two atoms, usually one electron from each.

Single bond: one shared pair (2 electrons). Double: two pairs (4). Triple: three pairs (6).
The first bond between two atoms is a σ (sigma) bond; the second and third are π (pi) bonds. How carbon's orbitals make them (hybridisation) is taught in Organic Chemistry.
More shared pairs: shorter and stronger bond.
For carbon, a double bond is less than twice as strong as a single bond, because a π bond is weaker than a σ bond. Do not assume this for every element.
Breaking any bond takes in energy (endothermic); forming one gives energy out.

Carbon to carbon bond	Shared electrons	Made of	Length (pm)	Bond energy (kJ/mol)
Single, as in ethane	2	1 σ	154	about 348
Double, as in ethene	4	1 σ + 1 π	134	about 614
Triple, as in ethyne	6	1 σ + 2 π	120	about 839

Twice the single bond would be 696 kJ/mol, so the double bond (614) is less than twice as strong.

Practice this conceptself-check · 3 quick reps

A triple bond shares six electrons, not three

Each bond is a pair. A double bond shares four electrons and a triple bond six. Options that count the bond lines (2 or 3) as the number of electrons are wrong.

A C=C bond is not twice as strong as a C-C bond

The π bond is weaker than the σ bond, so the carbon double bond (about 614 kJ/mol) is less than double the single bond (about 348 kJ/mol). It is still stronger and shorter than the single bond.

Concept 2 of 4: Drawing a Lewis structure by counting electrons

Only outer (valence) electrons take part in bonding, and for main group elements their number is the group number. Count them all, connect the atoms with single bonds, then hand out the rest so each atom gets eight. If you run out, turn lone pairs into extra bonds.

Definition

A Lewis structure shows every valence electron: shared pairs as lines and lone pairs (non-bonding pairs) as dots.

Valence electrons: Group 1 has 1, Group 2 has 2, Groups 13 to 17 have 3 to 7. Hydrogen has 1.
For an ion, add one electron per negative charge and remove one per positive charge.
The octet rule: most atoms end with eight electrons around them (shared pairs count for both atoms). Hydrogen ends with two.
Steps: put the least electronegative atom (never H) in the centre; join each outer atom with a single bond; complete the outer atoms' octets; put any electrons left on the central atom; if the central atom is short of eight, move a lone pair from an outer atom into a double bond.
An atom with no lone pairs has used all its valence electrons in bonds, as carbon does in $\mathrm{CH_4}$ .

Electrons to place in a Lewis structure

N_e = \sum V - q

$V$ valence electrons of each atom (its group number for groups 13 to 17)
$q$ charge of the ion, with its sign (0 for a neutral molecule)
$N_e$ total electrons to place; $N_e/2$ pairs

Worked example

Draw the Lewis structure of hydrogen cyanide, HCN, and count its bonding pairs and lone pairs.

Practice this conceptself-check · 4 quick reps

Count the charge of an ion

A negative ion has extra electrons and a positive ion has fewer. Leaving the charge out gives the wrong number of lone pairs, and IMAT offers that wrong count among the options.

Concept 3 of 4: Dative (coordinate) covalent bonds

Usually each atom gives one electron to a shared pair. But an atom with a lone pair can share the whole pair with an atom or ion that has an empty space. Once formed, the bond is just a shared pair like any other: you cannot tell it apart.

Definition

A dative (coordinate) covalent bond is a shared pair in which both electrons come from the same atom.

The donor has a lone pair (N in $\mathrm{NH_3}$ , O in $\mathrm{H_2O}$ , Cl in a chloride).
The acceptor has an empty orbital ( $\mathrm{H^+}$ , B in $\mathrm{BF_3}$ , Al in $\mathrm{AlCl_3}$ ).
It is drawn as an arrow from donor to acceptor, but after it forms it is identical to the other bonds: the four N to H bonds in $\mathrm{NH_4^+}$ are all the same.
Common examples: $\mathrm{NH_4^+}$ , $\mathrm{H_3O^+}$ , carbon monoxide (one of its three bonds), $\mathrm{Al_2Cl_6}$ , and the bonds between metal ions and ligands in complexes such as haemoglobin's iron.

Worked example

Ammonia,

\mathrm{NH_3}

, reacts with boron trifluoride,

\mathrm{BF_3}

, to form

\mathrm{H_3N{\rightarrow}BF_3}

. Explain the bond formed and the electrons around boron before and after.

Practice this conceptself-check · 3 quick reps

A dative bond is not weaker or different once formed

The arrow only records where the electrons came from. In

\mathrm{NH_4^+}

all four N to H bonds have the same length and strength, and the ion is a regular tetrahedron.

Concept 4 of 4: Exceptions to the octet rule

The octet rule is a strong habit, not a law. Atoms with very few valence electrons cannot reach eight by sharing alone. Atoms from period 3 onwards are larger and can fit more than four pairs around them. And a molecule with an odd number of electrons cannot pair them all.

Definition

Three kinds of exception:

Incomplete octet: Be and B (and Al in its chloride) form compounds with fewer than 8 electrons on the central atom. These are electron-pair acceptors.
Expanded octet: elements of period 3 and below (P, S, Cl, Xe) can hold 10 or 12 electrons. Period 2 elements (C, N, O, F) never can: $\mathrm{PCl_5}$ exists but $\mathrm{NCl_5}$ does not.
Odd-electron molecules (radicals): NO and $\mathrm{NO_2}$ have an odd total, so one atom has an unpaired electron.
Hydrogen is complete with 2 electrons (a duet).

Molecule	Kind of exception	Electrons around central atom	Note
$\mathrm{BeCl_2}$ (gas)	Incomplete octet	4	Two bonding pairs, linear
$\mathrm{BF_3}$	Incomplete octet	6	Accepts a lone pair to reach 8
$\mathrm{AlCl_3}$	Incomplete octet	6	Pairs up as $\mathrm{Al_2Cl_6}$ , where each Al has 8
$\mathrm{PCl_5}$	Expanded octet	10	Five bonding pairs
$\mathrm{SF_6}$	Expanded octet	12	Six bonding pairs
NO	Odd electron	11 valence electrons in total	One unpaired electron

Practice this conceptself-check · 3 quick reps

Only period 3 and lower can expand the octet

Phosphorus and sulfur can hold 10 or 12 electrons; nitrogen and oxygen, just above them in the same groups, cannot. An option giving nitrogen five bonds or oxygen four bonds in a neutral molecule is wrong.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Drawing a Lewis structure by counting electrons
Electrons to place in a Lewis structure
$N_e = \sum V - q$

Reference tables (2)

Single, double and triple covalent bonds3 rows

Carbon to carbon bond	Shared electrons	Made of	Length (pm)	Bond energy (kJ/mol)
Single, as in ethane	2	1 σ	154	about 348
Double, as in ethene	4	1 σ + 1 π	134	about 614
Triple, as in ethyne	6	1 σ + 2 π	120	about 839

Twice the single bond would be 696 kJ/mol, so the double bond (614) is less than twice as strong.

Exceptions to the octet rule6 rows

Molecule	Kind of exception	Electrons around central atom	Note
$\mathrm{BeCl_2}$ (gas)	Incomplete octet	4	Two bonding pairs, linear
$\mathrm{BF_3}$	Incomplete octet	6	Accepts a lone pair to reach 8
$\mathrm{AlCl_3}$	Incomplete octet	6	Pairs up as $\mathrm{Al_2Cl_6}$ , where each Al has 8
$\mathrm{PCl_5}$	Expanded octet	10	Five bonding pairs
$\mathrm{SF_6}$	Expanded octet	12	Six bonding pairs
NO	Odd electron	11 valence electrons in total	One unpaired electron

Watch out for (5)

A triple bond shares six electrons, not three
→ Single, double and triple covalent bonds
A C=C bond is not twice as strong as a C-C bond
→ Single, double and triple covalent bonds
Count the charge of an ion
→ Drawing a Lewis structure by counting electrons
A dative bond is not weaker or different once formed
→ Dative (coordinate) covalent bonds
Only period 3 and lower can expand the octet
→ Exceptions to the octet rule

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