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Chemistry: Atoms First 2e · Thermochemistry

Strengths of Ionic and Covalent Bonds

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Constants cross-checked against standard thermochemical references: NaCl formation −411.1 kJ/mol; Na sublimation 107.3, IE₁ 495.8; ½D(Cl–Cl) 121.3; EA(Cl) −348.6 kJ/mol; NaCl lattice energy ≈ −787 kJ/mol; bond energies C–H 413, O=O 498, C=O 799 (CO₂), O–H 463 kJ/mol; experimental ΔHcomb(CH4) ≈ −890 kJ/mol (2026-08).
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On this page 9 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Check yourself
  8. Study tools
  9. Sources & references

In 30 seconds

Bond strength is the energy cost of pulling a compound apart — and it explains why some substances melt at 30 °C while others melt near 2800 °C. For ionic compounds, the key quantity is : the energy released when one mole of solid forms from its separated gaseous ions. For covalent compounds, strength is the : the enthalpy change when one mole of a specific gas-phase bond is broken.

Three ideas follow: explains why lattice energies vary with ion charge and size; the — a Hess's-law loop of measurable steps — solves for lattice energy, which cannot be measured directly; and average bond energies from tables let you estimate reaction enthalpies without calorimetry.

Why this matters

Lattice energy predicts melting points and hardness: NaCl melts at 801 °C, while MgO — with doubly charged ions — melts near 2852 °C. Bond-energy estimates tell chemists whether a reaction will be exothermic or endothermic before running it — critical for fuel design and process safety, where an unexpectedly exothermic reaction is a hazard. Born–Haber cycles also explain why stable salts form at all: lattice assembly repays the energy invested in making ions.

The college version

Core Concepts

Coulomb's law sets the scale for ionic bonds

The energy of attraction between two ions follows Coulomb's law:

E = k q1 q2r

where k is Coulomb's constant, q1 and q2 are the ion charges, and r is the distance between ion centers. The negative sign means attraction (stabilization). Doubling both charges (Mg²⁺/O²⁻ versus Na⁺/Cl⁻) quadruples the attraction, since q1 q2 goes from 1 to 4; smaller ions attract more strongly because smaller r increases the magnitude of E.

Lattice energy

Lattice energy (U) is the energy released when gaseous ions combine to form one mole of ionic solid:

Na+(g) + Cl-(g) → NaCl(s)   ΔH = U ≈ -787 kJ/mol

It is exothermic (negative) for stable salts. Larger magnitude of U means tighter-held ions, higher melting point, and harder crystal.

The Born–Haber cycle: measuring what you cannot measure

Isolated gaseous ions can't be put in a calorimeter, so lattice energy is found indirectly. The Born–Haber cycle builds the formation reaction from elements as a loop of measurable steps — sublimation, ionization, bond breaking, electron attachment — with lattice energy as the only unknown. Because enthalpy is a state function, the loop's sum equals the measured formation enthalpy, and solving gives U.

Covalent bond strength: bond dissociation energy

Bond dissociation energy D is the enthalpy to break one mole of gas-phase bonds, e.g. D(H–H) = 436 kJ/mol. Breaking bonds is endothermic; forming them releases the same energy. Because a given bond type varies slightly between molecules, tables list average bond energies — good enough to estimate reaction enthalpies within roughly 5–10% of experiment.

Bond order, bond length, and bond strength

Adding shared electron pairs strengthens and shortens bonds: C–C (348 kJ/mol, 154 pm), C=C (614 kJ/mol, 134 pm), C≡C (839 kJ/mol, 120 pm). Triple bonds are strongest and shortest — a trend used constantly in organic and biochemistry.

How It Works / Step-by-Step Process

Born–Haber cycle for NaCl:

  1. Write the formation reaction: Na(s) + 12Cl2(g) → NaCl(s), ΔHf = -411.1 kJ/mol.
  2. List the measurable steps converting elements to gaseous ions (sublimation, ionization, bond breaking, electron attachment).
  3. Sum their enthalpies, set the total equal to ΔHf, and solve for U.
  4. Interpret: large negative U = tightly held lattice.

Estimating a reaction enthalpy from bond energies:

  1. Balance the reaction.
  2. Sum bond energies of bonds broken (reactants) — energy in.
  3. Sum bond energies of bonds formed (products) — energy out.
  4. Apply ΔHrxn = ∑Dbroken - ∑Dformed; negative = exothermic.

Common Confusions

Common ConfusionCorrect Understanding
Breaking bonds releases energy.Breaking bonds requires energy; energy is released when bonds form.
Ionic bonds are always stronger than covalent bonds.Ionic solids are strong materials, but lattice energy is a bulk property; a single ionic interaction vs. one covalent bond is a different comparison.
Lattice energy is the energy to melt the solid.It is the energy to separate gaseous ions; melting involves much smaller energies.
The Born–Haber cycle measures lattice energy directly.It solves for lattice energy from measurable steps via Hess's law.
A positive lattice energy means a strong bond.For stable salts the lattice step is exothermic (negative); large magnitude = strong.
Average bond energies give exact reaction enthalpies.They give estimates within ~5–10%; real bond energies vary by molecule.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Think of atoms as kids holding hands: a weak grip means they separate easily; a strong one takes real pulling. For salt, the pull is between plus and minus charges, and the Born–Haber cycle counts every relay step to find how strong the final grip is. Chemists have measured how hard each kind of hand-hold is to break, so they can predict whether a reaction gives off or needs energy.

Worked example

Example 1: Lattice energy of NaCl from the Born–Haber cycle

Given (kJ/mol): ΔHf(NaCl, s) = -411.1; sublimation of Na = +107.3; ionization of Na = +495.8; 12D(Cl–Cl) = +121.3; electron affinity of Cl = −348.6.

Set the cycle equal to the formation enthalpy:

ΔHf = ΔHsub + IE1 + 12D(Cl–Cl) + EA(Cl) + U

Substitute:

-411.1 = 107.3 + 495.8 + 121.3 + (-348.6) + U

-411.1 = 375.8 + U   ⇒  U = -787 kJ/mol

This matches the accepted Born–Haber lattice energy for NaCl. The huge exothermic lattice step is what pays for sodium's expensive ionization — the reason NaCl exists at all.

Example 2: Heat of combustion of methane from average bond energies

Average bond energies (kJ/mol): C–H 413, O=O 498, C=O 799 (in CO₂), O–H 463.

Balanced reaction: CH4(g) + 2O2(g) → CO2(g) + 2H2O(g).

Bonds broken (reactants): 4 C–H + 2 O=O

∑Dbroken = 4(413) + 2(498) = 1652 + 996 = 2648 kJ/mol

Bonds formed (products): 2 C=O + 4 O–H

∑Dformed = 2(799) + 4(463) = 1598 + 1852 = 3450 kJ/mol

Apply the formula:

ΔHrxn = 2648 - 3450 = -802 kJ/mol

The estimate is exothermic, matching reality, though it differs from the experimental value (about −890 kJ/mol) because average bond energies approximate real bonds that vary with molecular environment.

Key takeaways

  • Lattice energy = energy released when gaseous ions form one mole of ionic solid; always exothermic for stable salts.
  • Coulomb's law: attraction scales with charge product q1 q2, inversely with distance r.
  • Doubly charged ions give roughly 4× the lattice energy of singly charged — hence much higher melting points.
  • Born–Haber: formation enthalpy = sublimation + ionization + ½(bond dissociation) + electron affinity + lattice energy; lattice energy is the solved unknown.
  • Bond breaking is endothermic; bond forming is exothermic.
  • Reaction estimate: ΔHrxn ≈ ∑Dbroken - ∑Dformed.
  • Higher bond order → shorter, stronger bond (C–C < C=C < C≡C).
  • Average bond energies give estimates within ~5–10% — good for prediction, not precision.

Check yourself

5 review questions from the chapter. Try each one, then open the answer.

  1. What is lattice energy, and is it exothermic or endothermic for a stable ionic solid?

    Show answer

    Lattice energy is the energy released when one mole of ionic solid forms from gaseous ions; for stable salts it is exothermic (negative), typically −600 to −4000 kJ/mol.

  2. Using Coulomb's law, explain why MgO has a much larger lattice energy than NaCl.

    Show answer

    The charge product q1q2 is 4× larger for Mg²⁺/O²⁻ than Na⁺/Cl⁻, and Mg²⁺ is smaller, so E = kq1q2/r is far larger — MgO's lattice energy is about −3795 kJ/mol vs. −787 kJ/mol for NaCl.

  3. List the five Born–Haber steps for NaCl and state which is the unknown.

    Show answer

    Sublimation of Na, ionization of Na, half the Cl–Cl dissociation, electron attachment to Cl, and lattice formation (the unknown U).

  4. Is bond breaking endothermic or exothermic? What about bond forming?

    Show answer

    Bond breaking is endothermic; bond forming is exothermic.

  5. Estimate the sign of ΔHrxn for methane combustion from bond energies, and explain why the estimate differs from the experimental value.

    Show answer

    Negative (exothermic): bonds formed (3450 kJ/mol) exceed bonds broken (2648 kJ/mol). The estimate (−802 vs. −890 kJ/mol) differs because average bond energies approximate real bonds.

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

lattice energy
Energy released when one mole of ionic solid forms from gaseous ions
Born–Haber cycle
Hess's-law loop of measurable steps that solves for lattice energy
bond dissociation energy
Enthalpy to break one mole of a specific gas-phase bond
average bond energy
Table value averaged over many molecules for a bond type
Coulomb's law
Attraction between charges: E = kq1q2/r
bond order
Number of shared electron pairs between two atoms
electron affinity
Energy change when a gaseous atom gains an electron

Sources & references

  1. openstax.org — Chemistry Atoms First 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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