2.2 Potential Energy

Bond Potential Energy

Push two atoms together and read the equilibrium bond length and bond energy off the curve. Isolate core size from bond order, then switch to cations and anions and rank them by Coulombic force.

Bond LengthBond EnergyBond OrderCoulomb's Law
Topic 2.2

Intramolecular Force and Potential Energy

Represent the relationship between potential energy and distance between atoms, based on factors that influence the interaction strength.

A graph of potential energy versus internuclear distance is the CED's preferred model for a chemical bond. Read two quantities off it:

  • Equilibrium bond length (re) — the separation at the minimum of the curve. Atoms vibrate around it, but this is where the system is most stable.
  • Bond energy — the depth of the well, i.e. the energy required to pull the atoms completely apart.

The shape has a physical story. At very large r there is essentially no interaction and PE is flat at zero. As the atoms approach, attraction between each nucleus and the other's electrons lowers the energy. Push them too close and nucleus–nucleus (and core electron) repulsion sends PE steeply upward. The minimum is the balance point.

Two factors control where that minimum sits and how deep it is:

  • Size of the atomic core. Bigger atoms cannot get their nuclei as close, so bonds are longer and weaker. H–F < H–Cl < H–Br < H–I in bond strength.
  • Bond order. Higher bond order (single → double → triple) means more shared electron density holding the nuclei together: shorter bond, larger bond energy. C–C 348 kJ/mol, C=C 614, C≡C 839.

For ionic interactions, EK 2.2.A.3 says to reason with Coulomb's law directly:

  • Interaction strength is proportional to the charge on each ion, so larger charges → stronger attraction. MgO (2+/2−) has a far higher lattice energy and melting point than NaCl (1+/1−).
  • Interaction strength increases as the distance between ion centers decreases, so smaller ions → stronger attraction. LiF melts higher than KI.

Key points

  • Minimum of the curve → bond length. Depth of the well → bond energy.
  • Higher bond order = shorter and stronger. Larger atoms = longer and weaker.
  • For ionic strength, charge magnitude usually dominates size: a 2+/2− pair beats a 1+/1− pair.
  • Energy is always required to break a bond; energy is always released when a bond forms.

Equations

  • on the exam sheetApplied here to cation–anion attraction. Larger |q|, smaller r → stronger interaction.
    • ionic charges
    • distance between ion centers

Common mistakes

  • The well minimum is negative, not zero. Zero PE is the separated-atoms reference at r → ∞.
  • Do not confuse bond length with atomic radius. Bond length is measured between nuclei of bonded atoms.
  • Compare charges before sizes when ranking ionic strength; the q₁q₂ factor usually wins over the 1/r² factor for the ion pairs the AP Exam uses.
  • A deeper well means a stronger bond, not a longer one. Depth and position are independent readings.

Worked example

Rank NaF, MgO, and KBr by expected melting point, highest first. Justify with Coulomb’s law.

MgO > NaF > KBr

MgO has Mg²⁺ and O²⁻. The product of the charges is (2)(2) = 4, four times larger than for any 1+/1− pair, so the Coulombic attraction is far stronger and much more energy is needed to separate the ions.

NaF vs KBr — both are 1+/1−, so charge cannot distinguish them. Na⁺ is smaller than K⁺ and F⁻ is smaller than Br⁻, so the internuclear distance r in NaF is smaller. Since force is proportional to 1/r², NaF has the stronger attraction and the higher melting point.

Full notes for topic 2.2 →