Covalent Bonding and Dative Covalent Bonding

A covalent bond is, at A-Level, defined as a shared pair of electrons attracted simultaneously to the nuclei of two atoms. This simple electrostatic picture — formalised by G. N. Lewis in 1916 — is the foundation of almost all molecular chemistry. In this lesson we go beyond the bare definition: we treat single, double and triple bonds; we introduce sigma (σ) and pi (π) character qualitatively to rationalise why C=C is not exactly twice C–C in enthalpy; we work through dot-cross diagrams for the canonical AQA examples (H₂, Cl₂, HCl, O₂, N₂, CO₂, CH₄, NH₃, H₂O); and we extend to dative (coordinate) covalent bonds where both electrons in the shared pair originate from the same atom — the key concept needed to handle NH₄⁺, H₃O⁺, the Al₂Cl₆ dimer and, looking ahead, transition-metal complexes. We close with bond-length and bond-enthalpy trends, and with the major exceptions to the octet rule (BF₃ as electron deficient; SF₆ via "expanded octet" — flagged here as a useful A-Level shorthand that undergraduate treatment refines).

Spec mapping (AQA 7405): This lesson anchors §3.1.3.2 (covalent and dative covalent bonding) within the broader §3.1.3 "Bonding" topic. It is the conceptual partner of §3.1.3.1 (ionic bonding — lesson 0 of this course) and feeds directly into §3.1.3.6 (shapes of molecules and ions — lesson 2), §3.1.3.5 (electronegativity and bond polarity — lesson 3), §3.1.3.7 (forces between molecules — lesson 4) and the whole of §3.3 (organic chemistry), which presupposes fluency with σ/π skeletons and electron-pair counting. Refer to the official AQA specification document for the exact wording of each section.

Assessment objectives: Definitions of covalent bond, dative covalent bond and lone pair are AO1 recall items, frequently asked as one- or two-mark openers. Drawing dot-cross diagrams for CO₂, NH₃, H₂O, NH₄⁺ and AlCl₃ dimers is AO2 — application of the electron-pair-counting procedure to specified molecules. Comparing bond enthalpies and bond lengths (e.g. C–C vs C=C vs C≡C, or rationalising why C=C is less than 2 × C–C) and explaining the dimerisation of AlCl₃ in the gas phase test AO3 — analysis and synthesis. Expect Paper 2 (Section A, inorganic and physical) to combine all three on a single multi-part question.

What Is a Covalent Bond?

Key Definition: A covalent bond is a shared pair of electrons between two atoms, where the bonding pair of electrons is attracted simultaneously to the nuclei of both atoms.

Covalent bonding typically occurs between non-metal atoms. Each atom contributes one electron to the shared pair (except in dative bonds — see below). The electrostatic attraction between the negatively charged shared pair and the two positively charged nuclei provides the bonding force; the inter-nuclear repulsion between the two nuclei is overcome at the equilibrium internuclear distance, where attractive and repulsive forces balance to give a potential-energy minimum. The depth of that minimum is the bond enthalpy; the position of the minimum on the internuclear-distance axis is the bond length. Both quantities are routinely tabulated for A-Level use.

Because the bonding electrons are localised between the two nuclei, simple covalent molecules tend to have low melting and boiling points (no extended electrostatic lattice — see lesson 0 for the contrast with ionic bonding), do not conduct electricity in any state (no free charge carriers), and dissolve preferentially in non-polar solvents. These macroscopic properties are downstream of the localised-pair model.

Single Covalent Bonds

A single bond involves one shared pair of electrons.

Hydrogen (H₂)

Each hydrogen atom has 1 electron. They share one pair to reach the helium duplet:

H • × H   →   H •× H   →   H—H

Chlorine (Cl₂)

Each Cl has 7 outer electrons; they share one pair to reach an octet:

    ××           ××           ××         ××
   ×Cl×   ×Cl×   →   ×Cl × ×Cl×   →   :Cl—Cl:
    ××           ××           ××         ××

Each Cl ends with 1 bonding pair and 3 lone pairs.

Hydrogen Chloride (HCl)

        ××
H• ×  ×Cl×   →   H—Cl (with 3 lone pairs on Cl)
        ××

Water (H₂O)

Oxygen has 6 outer electrons and needs 2 more. It shares one pair with each of two hydrogen atoms:

         ••
    H—O—H
         ••

Oxygen has 2 bonding pairs and 2 lone pairs (4 electron pairs total).

Ammonia (NH₃)

Nitrogen has 5 outer electrons and shares one pair with each of three hydrogen atoms:

         ••
    H—N—H
       |
       H

Nitrogen has 3 bonding pairs and 1 lone pair.

Methane (CH₄)

Carbon has 4 outer electrons; each H provides 1. Four shared pairs give carbon a full octet:

Carbon has 4 bonding pairs and 0 lone pairs → tetrahedral, all H–C–H angles 109.5°.

Multiple Bonds

Double Bonds (Two Shared Pairs)

Oxygen (O₂): Each oxygen needs 2 more electrons. They share two pairs:

    ••       ••
    :O ═══ O:
    ••       ••

Each oxygen has 2 bonding pairs (in one double bond) and 2 lone pairs. (At A-Level we treat O₂ as having a double bond; the experimentally observed paramagnetism of O₂ — which the simple Lewis picture cannot explain — is taken up in the Going Further section.)

Carbon dioxide (CO₂): Carbon shares two pairs with each oxygen:

    ••           ••
    :O ═══ C ═══ O:
    ••           ••

Carbon has 4 bonding pairs (in two double bonds) and no lone pairs.

Ethene (C₂H₄):

The C═C double bond consists of one sigma (σ) bond and one pi (π) bond.

Triple Bonds (Three Shared Pairs)

Nitrogen (N₂): Each nitrogen needs 3 more electrons. They share three pairs:

    :N ≡≡≡ N:

Each nitrogen has 3 bonding pairs (in one triple bond) and 1 lone pair. The N≡N triple bond is very strong (mean bond enthalpy = 944 kJ mol⁻¹), which is why N₂ is so kinetically inert and why fixing atmospheric nitrogen industrially (Haber process) requires aggressive conditions.

Hydrogen cyanide (HCN):

    H—C ≡≡≡ N:

Carbon forms a single bond with hydrogen and a triple bond with nitrogen.

Sigma (σ) and Pi (π) — Qualitative

A σ bond is formed by head-on overlap of orbitals along the internuclear axis (s–s, s–p or p–p). Electron density is concentrated along the bond axis. Every single bond is one σ bond.
A π bond is formed by sideways overlap of parallel p-orbitals above and below the internuclear axis. Electron density is concentrated off-axis. π overlap is geometrically less efficient than σ overlap, so a π bond is weaker than the corresponding σ bond.

Counting up:

single bond = 1 σ
double bond = 1 σ + 1 π
triple bond = 1 σ + 2 π

This bookkeeping immediately rationalises a key A-Level observation: the enthalpy of a C=C bond (612 kJ mol⁻¹) is less than 2 × the enthalpy of a C–C bond (2 × 347 = 694 kJ mol⁻¹). The σ component is roughly the same in both, but the additional π in C=C is intrinsically weaker than the σ, so the doubling falls short. The same logic explains why C≡C (839) is well below 3 × C–C (1041).

Dative Covalent (Coordinate) Bonds

Key Definition: A dative covalent bond (also called a coordinate bond) is a covalent bond in which both electrons in the shared pair come from the same atom — the donor. The other atom — the acceptor — must have a vacant orbital able to receive the pair.

The atom that donates both electrons must possess a lone pair. Once formed, a dative bond is identical in length, strength and properties to an ordinary covalent bond — the historical distinction lives only in the bookkeeping of where the electrons originated.

Ammonium Ion (NH₄⁺)

Ammonia has a lone pair on nitrogen. When it reacts with H⁺ (which has an empty 1s orbital), nitrogen donates its lone pair:

         H
         |
    H—N: + H⁺  →  H—N→H    (overall charge +1)
         |              |
         H              H

The arrow → represents the dative bond pointing from donor (N) to acceptor (H⁺). In the finished NH₄⁺ ion, all four N–H bonds are crystallographically and spectroscopically identical — you cannot pick out the dative one. The shape is tetrahedral, H–N–H = 109.5°.

Oxonium Ion (H₃O⁺)

Water has two lone pairs on oxygen. One of them is donated to H⁺:

              H
              |
    H—O: + H⁺  →  H—O→H    (overall charge +1)
              |          |
              H          H

All three O–H bonds in H₃O⁺ are identical; the shape is pyramidal with bond angle ≈ 107° (three bonding pairs, one lone pair on O).

Carbon Monoxide (CO)

Carbon has 4 outer electrons, oxygen has 6. A naive double bond gives C only 6 electrons. To attain an octet on both atoms, the picture is: two shared pairs (one σ, one π) drawn from one electron each, plus a third dative pair donated from oxygen to carbon:

    :C ←══ O:    or equivalently    :C≡O:

Each atom ends with three bonding pairs (in a triple bond) and one lone pair. CO is isoelectronic with N₂ and — like N₂ — has a very high bond enthalpy (~1077 kJ mol⁻¹).

Aluminium Chloride Dimer (Al₂Cl₆)

In the gas phase, monomeric AlCl₃ is electron deficient — Al has only 6 electrons in its valence shell after sharing one pair with each of three chlorines. Two AlCl₃ units therefore dimerise: a chlorine on one monomer donates a lone pair to the empty orbital on the aluminium of the other, and vice versa, generating two bridging dative bonds:

        Cl       Cl
          \     /
           Al        Al
          / | \    / | \
        Cl  |  Cl    |  Cl
            |   |    |
            +---+----+
            (two bridging Cl with dative bonds)

Each Al now has four bonding pairs (octet); each bridging Cl uses one ordinary covalent bond and one dative bond. Al₂Cl₆ is the molecular form observed in the gas phase up to several hundred kelvin.

Transition-Metal Complexes (Forward Link)

The bonding in transition-metal complexes — e.g. [Cu(H₂O)₆]²⁺, [Fe(CN)₆]³⁻ — is the same dative-bond pattern at scale: lone pairs on a ligand (donor) point into vacant d-orbitals on the metal (acceptor). The ligand is then a Lewis base, the metal a Lewis acid. This Lewis acid–base extension of dative bonding is developed in detail in the A2 inorganic chemistry course (§3.2.5 transition metals); flag it now and revisit later.

Exam Tip: In dot-cross diagrams, dative bonds are conventionally shown with an arrow from donor to acceptor during their formation. In the final structure, the bond is drawn as a normal line — it behaves identically to any other covalent bond.

Exceptions to the Octet Rule

The octet rule (8 electrons in the valence shell) is the dominant pattern for second-period atoms (C, N, O, F), but several A-Level exceptions must be mastered:

Electron-deficient molecules (fewer than 8)

BF₃ — boron has only 6 electrons in its valence shell after forming three B–F bonds. This is why BF₃ is a Lewis acid: it readily accepts a lone pair to complete an octet (e.g. BF₃ + NH₃ → F₃B←NH₃).
AlCl₃ monomer — Al has 6 electrons; the dimer (above) resolves the deficiency.
BeCl₂ — Be has only 4 valence electrons; the gas-phase monomer has two bonding pairs only.

"Expanded octet" — period 3 and below

For elements from period 3 onwards (P, S, Cl, etc.) A-Level treatment allows expanded valence shells using "available d-orbitals":

PCl₅ — 10 electrons around P (5 bonding pairs).
SF₆ — 12 electrons around S (6 bonding pairs).
SO₄²⁻ — sulfur drawn with two S=O double bonds and two S–O single bonds, giving 12 electrons.

A-Level shorthand alert: the "expanded octet via d-orbital participation" picture is the AQA-required A-Level explanation, and it scores marks. Modern computational chemistry shows that 3d orbitals contribute very little to the bonding; the better picture is 3-centre 4-electron bonding (hypervalence) — which we revisit in Going Further. For the exam, "expanded octet using d-orbitals" is the answer; for undergraduate study, expect this to be re-told.

Bond Length and Bond Energy

Bond Length

Bond length is the equilibrium internuclear distance — where the potential-energy curve reaches its minimum. It is measured in picometres (pm).

Bond	Bond Length (pm)	Bond Order
C—C	154	Single
C═C	134	Double
C≡C	120	Triple
C—O	143	Single
C═O	122	Double
C—N	147	Single
C═N	129	Double
C≡N	116	Triple
N—N	145	Single
N═N	125	Double
N≡N	110	Triple

Trend: As bond order increases, bond length decreases. More shared pairs draw the nuclei closer together against the screened internuclear repulsion.

Bond Enthalpy

The mean bond enthalpy is the energy required to break one mole of that bond in the gas phase, averaged over a range of typical chemical environments. Values are positive (bond breaking is endothermic).

Bond	Mean Bond Enthalpy (kJ mol⁻¹)
C—C	347
C═C	612
C≡C	839
C—H	413
C—O	358
C═O	805
O—H	464
N—H	391
N≡N	944
H—H	436
F—F	158
Cl—Cl	242

Trend: As bond order increases, bond enthalpy increases. The π component, while individually weaker than σ, still adds significant binding energy.

Comparison with ionic and metallic. The strongest single covalent bonds (e.g. C–F, ~485 kJ mol⁻¹) are comparable to the lattice enthalpy per ion pair of a typical ionic solid (NaCl ≈ 786 kJ mol⁻¹ per mole of formula units, but distributed over six nearest neighbours so ~130 kJ per pairwise interaction). The strongest covalent multiple bonds (C≡C, N≡N, C≡O) easily exceed any single ionic pairwise interaction. Metallic bonding strengths (judged by atomisation enthalpies) range from ~80 kJ mol⁻¹ (group 1) to ~850 kJ mol⁻¹ (W, transition metals).

Key Relationship: Bond length and bond enthalpy are inversely related across the series single → double → triple: shorter bonds are stronger bonds (for a given pair of elements).

Worked Example: Comparing Bond Strength

Question: Explain why the C≡C bond in ethyne is shorter and stronger than the C═C bond in ethene.

Answer: The triple bond has three shared pairs between the carbon nuclei, the double bond only two. The greater electron density between the nuclei in C≡C increases the attraction pulling the nuclei together (shorter: 120 pm vs 134 pm) and requires more energy to break (839 vs 612 kJ mol⁻¹). However, the increase is non-linear: C≡C (839) is markedly less than 3 × C–C (1041), because the additional π bonds are intrinsically weaker than the σ.

Worked Example: Drawing Dot-Cross Diagrams

Question: Draw a dot-cross diagram for phosphorus trichloride (PCl₃).

Procedure:

Count outer electrons. P has 5; each Cl has 7.
Each Cl needs 1 more electron; P needs 3 more.
P shares one pair with each Cl: 3 bonding pairs, 1 lone pair on P; each Cl has 1 bonding pair and 3 lone pairs.

            ××
       ×Cl× — •P• — ×Cl×
            ××   |   ××
                 |
            ××
           ×Cl×
            ××

3 bonding pairs + 1 lone pair on P → pyramidal, H–P–H ≈ 107° (lesson 2 will use this VSEPR logic systematically).

Covalent Bonding and Dative Covalent Bonds