AP Chemistry · Unit 2 · Topic 2.2
Intramolecular Force and Potential Energy
Imagine bringing two atoms together from a very large separation. Their energy does not fall forever as the distance decreases. A stable bond occurs where attractive and repulsive effects balance, producing a minimum in the potential-energy curve.
Read both axes and the reference
The horizontal axis is internuclear distance, often in picometers. The vertical axis is potential energy, commonly per mole of atom pairs. A convenient zero represents separated atoms. Negative values therefore mean the pair is lower in energy than that reference, not that energy has stopped existing. The depth of the well is measured from its minimum up to the separated-atom level.
Why there is a minimum
At moderately large separations, electron–nucleus attractions can lower the energy as orbitals overlap. At very short distances, repulsive contributions become dominant and the energy rises sharply. At the minimum, the net force is zero; the individual attractions and repulsions have not vanished. A vibrating molecule spends time on both sides of its equilibrium distance rather than remaining perfectly motionless there.
Compare two original model curves
| Model bond | Minimum distance / pm | Minimum energy / kJ mol⁻¹ | Interpretation |
|---|---|---|---|
| A–B | 150 | −280 | Longer and easier to dissociate |
| C–D | 110 | −420 | Shorter and harder to dissociate |
These invented values summarize hypothetical curves. They support a comparison of the two particular bonds; they are not a rule that every short bond across all chemical species must be stronger than every long one.
Worked example: separating a sample of bonds
In the model, completely separating one mole of C–D pairs from their minimum-energy state requires 420 kJ. For 0.0250 mol of those pairs:
The process absorbs energy. Forming the same amount of bonds from the same separated atoms releases that amount in the idealized reverse process. A real sample's thermal and phase contributions must be handled separately.
The slope tells you the force direction
To the right of the minimum, a pair typically experiences a net attraction that pulls the atoms closer. To the left, the net repulsion pushes them apart. Thus a shallow slope means a small net force, while the well depth measures an energy difference. Confusing steepness with total dissociation energy can lead to the wrong comparison between curves.
Evidence from stretching vibrations
Bond stretching produces characteristic vibrational frequencies. A stiffer potential near the minimum generally corresponds to a higher stretching frequency when the reduced mass is comparable. Isotopic substitution can shift that frequency without substantially changing the electronic bond potential, because the moving nuclei have different masses. Frequency is therefore not controlled by bond strength alone.
Do not describe breaking as releasing stored energy
Breaking a bond in isolation requires an input. A reaction may release energy overall because formation of product bonds releases more energy than reactant-bond breaking consumes. The net result depends on both steps. This distinction prevents a common error when discussing fuels, batteries, or energy-carrying biological molecules.
Practice, then check your reasoning
Which model bond in the table requires more energy per mole to break?
Answer and reasoning: C–D, because its energy well is deeper by 140 kJ mol−1.
At a distance shorter than the equilibrium separation, which way does the net force act?
Answer and reasoning: It pushes the nuclei farther apart, back toward the energy minimum.
Scientific references: OpenStax: bond formation and energy curves; OpenStax: bond energies. OpenStax Chemistry 2e authors: Paul Flowers, Klaus Theopold, Richard Langley, and William R. Robinson. Consult source pages for their license terms. Accessed September 13, 2026. Explanations, comparison tables, and practice tasks were independently written for this site; numerical teaching datasets are illustrative unless explicitly identified otherwise.
Official curriculum reference: College Board AP Chemistry course page. The explanation and worked example are independently written for this study site.