Why is there a preferred distance between bonded atoms?
You will be able to: Read equilibrium separation and dissociation energy from a potential-energy graph.
Why is there a preferred distance between bonded atoms?
Imagine moving two atoms slowly toward one another. Very far apart they barely interact. At a suitable separation their combined energy is lower; forcing them too close makes the energy rise sharply.
A useful starting point: Which end of a bond attracts electrons more strongly? →
Words and symbols before equations
- Internuclear distance r
- Distance between nuclei, here in picometers (pm).
- Potential energy U
- Energy associated with configuration, here kJ per mole of identical pairs.
- Equilibrium separation rₑ
- Position of the potential-energy minimum.
- Dissociation energy D
- Energy to take a pair from the minimum to the chosen separated-atom reference.
What this picture assumes
Schematic Morse potential: D = 200 kJ/mol, rₑ = 120 pm, a = 0.025 per pm. Separated atoms set U = 0. This is a teaching curve, not fitted data or a model of quantum vibration.
Read the picture in three steps
- Read the species and labels first. A Lewis line represents two electrons; a spatial stick indicates connectivity. Use the stated quantities and units for numerical comparisons.
- r = 120 pm; U = -200 kJ/mol. Net force zero at the minimum. Well depth is 200 kJ/mol.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
Our graph sets U = 0 for atoms infinitely far apart. A negative U means the bonded configuration lies below that reference; it does not mean energy has disappeared.
At rₑ the attractive and repulsive effects balance, so the net force is zero. To the left, the strong short-range repulsion favors increasing separation. To the right, attraction favors decreasing separation.
The depth from the minimum up to zero is the energy required to separate the atoms in this ideal model. Actual bonds vibrate; the curve is not a literal track and this schematic model omits quantum vibrational energy.
A worked example, step by step
A schematic curve reaches −200 kJ/mol at 120 pm and approaches zero at large separation. Interpret it.
- Read the horizontal coordinate of the lowest point: rₑ = 120 pm.
- Read the minimum energy: −200 kJ/mol relative to separated atoms.
- Compute separation energy: 0 − (−200) = +200 kJ/mol.
- Separation requires energy; forming the same ideal bonds from separated atoms releases that energy to the surroundings.
Breaking a bond requires energy. A reaction can still release energy if forming its new bonds releases more.
At the energy minimum, have all electric interactions vanished?
Compare with an explanation
No. Their effects balance; the net force is zero.
Predict. Change one thing. Explain.
Keep the well depth and equilibrium distance fixed. Move separation from below the minimum through it and outward. Predict the force direction before reading the feedback.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
r = 120 pm; U = -200 kJ/mol. Net force zero at the minimum. Well depth is 200 kJ/mol.
Schematic Morse potential: D = 200 kJ/mol, rₑ = 120 pm, a = 0.025 per pm. Separated atoms set U = 0. This is a teaching curve, not fitted data or a model of quantum vibration.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using electron accounting, electrostatic interactions or spatial geometry. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionCurve A has its minimum at 100 pm, −400 kJ/mol. Curve B has its minimum at 140 pm, −250 kJ/mol. Compare equilibrium distances and energies; predict the force direction just to the right of A’s minimum.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: A has the shorter equilibrium distance: 100 versus 140 pm.
- 1 point: A requires more energy to dissociate: 400 versus 250 kJ/mol.
- 1 point: Both dissociation energies are positive relative to separated atoms at zero.
- 1 point: Just to the right of A’s minimum, attraction favors smaller separation.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Where is equilibrium on U versus r?
At the energy minimum.
RECALL 2What does well depth represent?
Energy required for separation from the model minimum.
RECALL 3Does bond formation absorb or release energy?
Formation from separated atoms lowers energy and releases energy elsewhere.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Why is there a preferred distance between bonded atoms?
- D = U(separated) − U(minimum).
- At the minimum, net force is zero; individual interactions remain.
Remember: Breaking a bond requires energy. A reaction can still release energy if forming its new bonds releases more.
Conditions: Schematic Morse potential: D = 200 kJ/mol, rₑ = 120 pm, a = 0.025 per pm. Separated atoms set U = 0. This is a teaching curve, not fitted data or a model of quantum vibration.
Refresh Kid · AP Chemistry Unit 2 · Objectives 2.2.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.2, objectives 2.2.A. CED effective Fall 2024, current official file checked September 16, 2026, together with the published clarifications. This is Unit 2: Compound Structure and Properties, Topics 2.1–2.7. The focused lesson breakdown is Refresh Kid’s editorial sequence. Models and original practice are teaching materials, not official AP questions. Numerical potential curves, ion comparisons and orbital-alignment indices state their approximations. Five- and six-domain shapes are included; d-orbital hybridization and molecular-orbital diagrams are not required here. GitHub’s 3D website examples, including the Three.js Mars camera-control example, informed the use of rotatable scenes. Our scientific geometry and viewer code are original; no repository artwork or tutorial code was copied. The self-hosted Three.js library retains its MIT license. Camera rotation does not alter chemistry. See also the official clarifications.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
Want to work through this with a tutor?
Bring your question about Why is there a preferred distance between bonded atoms? Your explanation and answers remain free to access.