Covalent Bonding

Core Concepts

Sharing electron pairs

Two nonmetal atoms each contribute one valence electron to a shared pair, and the pair counts toward both atoms' octets. Hydrogen is the exception: it needs only two electrons (a duet), matching helium. A few molecules violate the octet rule: boron compounds like BF₃ have incomplete octets, elements of period 3 and beyond (P, S, Cl) can expand their octets (PCl₅, SF₆), and odd-electron species like NO exist with an unpaired electron.

Single, double, and triple bonds

The number of shared pairs is the bond order: one pair = single bond, two = double, three = triple. More shared pairs pull the nuclei closer and hold them more firmly:

So a triple bond is shorter and stronger than a double bond, which is shorter and stronger than a single bond — the same pattern holds for O–O, N–N, and most element pairs.

Electronegativity and bond polarity

Electronegativity (Pauling scale) measures how strongly an atom attracts bonding electrons. Values for common elements: F 3.98, O 3.44, Cl 3.16, N 3.04, C 2.55, H 2.20, Na 0.93. For a bond between atoms A and B:

ΔEN = |EN_A - EN_B|

Rules of thumb: ΔEN < 0.4 → nonpolar covalent (electrons shared evenly, e.g., H–H, C–H); 0.4 ≤ ΔEN ≤ 2.0 → polar covalent (electrons pulled toward the more electronegative atom, creating partial charges δ+ and δ−, e.g., H–Cl); ΔEN > 2.0 → ionic (transfer dominates, e.g., Na–Cl). These cutoffs are conventions, not sharp walls — bonding is a continuum.

Bond energy and reaction enthalpy

Bond dissociation energy is the energy needed to break one mole of a given bond in the gas phase. Breaking bonds costs energy; forming bonds releases it, so reaction enthalpy can be estimated from tabulated average bond energies:

ΔH ≈ ∑BE(bonds broken) - ∑BE(bonds formed)

The "approximately" matters: tabulated bond energies are averages over many compounds, so the estimate suits predictions, not exact calorimetry.

Worked Example: Classifying Bonds by Electronegativity

Problem. Classify the bonds in H–H, H–Cl, and Na–Cl as nonpolar covalent, polar covalent, or ionic.

Solution. Compute the electronegativity difference for each pair:

ΔEN = |EN_A - EN_B|

H–H: ΔEN = |2.20 - 2.20| = 0 → nonpolar covalent (identical atoms share evenly). H–Cl: ΔEN = |2.20 - 3.16| = 0.96 → polar covalent (0.4–2.0 range); chlorine pulls the shared pair, giving δ+ on H and δ- on Cl. Na–Cl: ΔEN = |0.93 - 3.16| = 2.23 → ionic (> 2.0); the electron spends almost all its time on chlorine.

This one calculation explains why hydrogen gas is a simple molecule, hydrogen chloride is a polar gas that dissolves to form an acid, and table salt is an ionic crystal.

Worked Example: Estimating Reaction Enthalpy from Bond Energies

Problem. Estimate ΔH for the reaction H₂(g) + Cl₂(g) → 2HCl(g) using average bond energies: H–H = 436 kJ/mol, Cl–Cl = 243 kJ/mol, H–Cl = 432 kJ/mol.

Solution. Write the bond-energy formula first:

ΔH ≈ ∑BE(bonds broken) - ∑BE(bonds formed)

Reactants have one H–H and one Cl–Cl (broken); products have two H–Cl (formed). Substitute:

ΔH ≈ (436 + 243) - 2(432) = 679 - 864 = -185 kJ

The negative sign means the reaction is exothermic — about 185 kJ released per mole of reaction, matching the measured −184.6 kJ closely. All terms are kJ/mol, so units check out.

Worked Example: Bond Order vs. Bond Strength

Problem. Rank C–C, C=C, and C≡C by bond length and by bond energy.

Solution. Bond order rises from 1 to 3 across the series. From the table: lengths 154 > 134 > 120 pm and energies 347 < 611 < 837 kJ/mol, so the triple bond is shortest and strongest. More shared pairs hold nuclei closer and harder to separate — why acetylene (triple bond) reacts far more readily than ethane (single bonds).

Common Confusions