Intramolecular Force and Potential Energy
Read the bond-energy minimum: separate equilibrium distance, dissociation energy and interaction force.
AP Chemistry Topic 2.2 · CED printed p. 46 / PDF p. 53. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Coulomb’s law
- Charge magnitude
A bond is a potential-energy minimum
Bring two distant atoms closer. Nuclear–electron attractions initially lower the total potential energy. Bring them too close and electron–electron and nucleus–nucleus repulsions rise sharply. The balance creates an energy minimum at the equilibrium internuclear distance. “Equilibrium” does not mean no forces exist; net force is zero at the minimum, and real bonded atoms vibrate around it.
Take separated atoms as the zero-energy reference. A stable bond lies below that reference. The vertical rise from the minimum to zero is the energy needed to dissociate the bond: breaking a bond requires energy. Bond formation releases energy for the reverse path. Minimum position and well depth encode different properties, so a deep well need not be the leftmost curve. This graph is potential energy versus separation, not energy versus time.
Compare the right factors
For the same bonded elements, greater bond order generally makes a shorter, stronger bond: C≡C is shorter and requires more dissociation energy than C=C, which is shorter and stronger than C–C. When comparing different elements, larger atomic cores generally allow a longer bond. Bond order gives a particularly clean comparison when the atom pair is held constant; do not claim every triple bond is stronger than every single bond between arbitrary different atoms.
For ionic pairs, larger charge products and smaller center-to-center distances mean stronger Coulombic interactions. The force magnitude depends on |q1q2|/r². The electrostatic pair potential energy has a 1/r dependence, so force and energy cannot be interchanged. In real crystals many neighbors contribute; this pair model predicts useful qualitative lattice trends without requiring specific crystal structures.
Let's work through it
Work it through
Curve A has a minimum at 150 pm and −300 kJ mol−1; curve B at 120 pm and −500 kJ mol−1, relative to separated atoms. Compare bond lengths and dissociation energies, then predict whether MgO or NaCl should have stronger ionic interactions.
- Read the x coordinates of the minima: B is shorter, 120 pm versus 150 pm.
- Read the rise to zero: A needs +300 kJ mol−1; B needs +500 kJ mol−1. B is stronger in this specified comparison.
- Mg2+/O2− has charge-product magnitude 4e², versus e² for Na+/Cl−. The MgO ions also generally have smaller center separation. Both factors support stronger ionic interactions in MgO.
- State the model: this is a qualitative comparison, not a complete numerical lattice-energy calculation from one ion pair.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
What physical quantities come from a potential curve’s minimum location and its depth?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
What physical quantities come from a potential curve’s minimum location and its depth?
Worked answer and reason
The location gives equilibrium bond length; depth below the separated-atom reference gives dissociation energy.
Horizontal distance and vertical energy are different axes.
Retrieval 2
Does bond breaking release energy?
Worked answer and reason
No. Raising a bonded pair out of its energy minimum requires energy; formation along the reverse path releases it.
The graph measures the energy difference between bonded and separated states.
Catch the tempting mistake
- Shorter always means stronger for any atom pair.
- It is most reliable for comparisons of bond order within the same atom pair; other chemistry also matters.
- A negative well minimum means a negative energy is required to break the bond.
- Dissociation moves upward from negative energy to zero, so its energy change is positive.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 2 problem 3 · ap application · data
- Unit 2 problem 4 · ap synthesis · symbolic
Scientific calculator workspace
Use this workspace for arithmetic, logarithms and elementary functions. Keep intermediate precision and report final values with appropriate units and significant figures. Graphing and general equation solving need a suitable approved tool.
Scientific calculator
This calculator requires JavaScript. Use the physics formula sheets and show your working manually.
+ − * / ^ ! · pi · e · sqrt · sin, cos, tan · asin, acos, atan · atan2(y,x) · ln, log · abs · exp · hypot(x,y). Use * between factors. Keep units in your written working.
For the teacher
- Require a vertical dissociation arrow and an x-axis bond-length mark.
- Distinguish charge product from charge sum in ionic comparisons.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 2.2.A
- Represent the relationship between potential energy and distance between atoms, based on factors that influence the interaction strength.
- 2.2.A.1
- A graph of potential energy versus the distance between atoms (internuclear distance) is a useful representation for describing the interactions between atoms. Such graphs illustrate both the equilibrium bond length (the separation between atoms at which the potential energy is lowest) and the bond energy (the energy required to separate the atoms).
- 2.2.A.2
- In a covalent bond, the bond length is influenced by both the size of the atom’s core and the bond order (i.e., single, double, triple). Bonds with a higher order are shorter and have larger bond energies.
- 2.2.A.3
- Coulomb’s law can be used to understand the strength of interactions between cations and anions. i. Because the interaction strength is proportional to the charge on each ion, larger charges lead to stronger interactions. ii. Because the interaction strength increases as the distance between the centers of the ions (nuclei) decreases, smaller ions lead to stronger interactions.
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 (supplied source) — Exact topic-numbered learning objectives, essential knowledge, science practices and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
Glossary and deeper reading · 3 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
-
Chemical equilibrium
Chemical equilibrium is a dynamic state in which forward and reverse reaction rates are equal. Macroscopic composition remains constant in a closed system under fixed conditions, but reactant and product concentrations need not be equal. For example, a reversible reaction can reach equilibrium with much more reactant than product.
-
Bond order
Bond order describes the degree of bonding between two atoms in a specified bonding model. Localized single, double, and triple bonds have orders one, two, and three, while delocalized models can give fractional values. For example, equivalent bonds in a resonance description can have bonding intermediate between a single and double bond.
-
Crystal lattice
A crystal lattice describes the repeating arrangement of structural sites in a crystalline solid. The occupants can be ions, atoms, or molecules depending on the material. For example, an ionic lattice places opposite charges near one another throughout a sodium chloride crystal.