Intramolecular Force and Potential Energy

Learning Objective 2.2.A Represent the relationship between potential energy and distance between atoms, based on factors that influence the interaction strength.

Quick Notes

Shorter bonds are generally stronger (higher bond energy).
Bond order controls length/strength: single < double < triple (length decreases, energy increases).
Potential energy vs. distance graph: the curve’s minimum gives the bond length; the depth from 0 gives the bond energy.
Coulomb’s law (ionic): F ∝ (q₁ × q₂) / r² → larger charges and/or smaller ion size (shorter r) give stronger attraction.

Full Notes

Covalent Bond Formation and Potential Energy

When two atoms form a covalent bond, there is electrostatic attraction between the positively charged nuclei and the shared electron pair. However, there is also repulsion between the nuclei themselves. The bond length is the internuclear distance that maximizes attraction while minimizing repulsion — the most stable arrangement.

This distance, along with the energy of the interaction, determines bond strength and bond length. These concepts are best visualized using a potential energy diagram.

Potential Energy and Bond Formation

A potential energy vs. internuclear distance graph illustrates how two atoms interact as they form a bond:

AP Chemistry potential energy versus internuclear distance curve showing approach of atoms and formation of a bond

As atoms move closer, attractive forces dominate, lowering potential energy.

At a certain distance, the energy reaches a minimum — this is the bond length.

AP Chemistry diagram highlighting bond length at the minimum of the potential energy curve

If atoms get too close, repulsive forces between nuclei cause the energy to rise steeply.

The bond energy is the energy required to separate the bonded atoms; it corresponds to the depth of the potential well from the zero‑energy line.

AP Chemistry diagram showing bond energy as the depth of the potential well from the zero-energy line

Key points from the graph:

Bond length = distance at minimum potential energy
Bond energy = energy needed to break the bond and fully separate the atoms

Bond Order, Bond Length, and Bond Strength

Bond order refers to the number of electron pairs shared between two atoms:

Single bond = 1 shared pair → bond order = 1
Double bond = 2 shared pairs → bond order = 2
Triple bond = 3 shared pairs → bond order = 3

As bond order increases:

Bond length decreases
Bond strength (bond energy) increases

Why?

More shared electrons lead to greater electrostatic attraction between the negatively charged electrons and both nuclei.

AP Chemistry comparison of single, double, and triple covalent bonds showing more shared electrons increase attraction and shorten the bond

This stronger attraction brings the nuclei closer together (shorter bond) and requires more energy to break (stronger bond)

Example:

C–C single bond: long and weak
C=C double bond: shorter and stronger
C≡C triple bond: shortest and strongest

AP Chemistry illustration of C–C, C=C, and C≡C showing single, double, and triple bonds

Factors Affecting Bond Length

Atomic size: Larger atoms form longer bonds because their outer electrons are farther from the nucleus.
Bond order: Higher bond order = more shared electrons = stronger attraction = shorter bond.

Coulomb’s Law and Ionic Bond Strength

For ionic compounds, the strength of the interaction between cations and anions can be explained by Coulomb’s law:

AP Chemistry Coulomb’s law panel showing F ∝ (q1 × q2) / r² with definitions of terms

F ∝ (q₁ × q₂) / r²

Where:

F = force of attraction
q₁ and q₂ = charges on the ions
r = distance between their nuclei

Implications:

Higher charges on ions → stronger attraction (e.g., Mg²⁺ and O²⁻ attract more strongly than Na⁺ and Cl⁻)
Smaller ions → stronger attraction due to shorter distance between nuclei (e.g., Li⁺ forms stronger interactions than K⁺)

This explains why lattice energy (see Lattice Energy) in ionic solids increases with higher charges and smaller ions.

Worked Example

Which bond is stronger and shorter: N≡N or N–N?

N≡N is a triple bond; N–N is a single bond.
Triple bonds have more shared electrons, increasing attraction between the nuclei and the shared electrons.
Answer: N≡N is both stronger and shorter than N–N.

Matt’s exam tip

Use Coulomb’s law when comparing ionic compounds, and use bond order and atomic size when comparing covalent bonds. If given an internuclear distance and energy graph, pay attention to the lowest point (bond length) and the depth (bond energy).

Summary

Bond strength and length are determined by a balance of attractive and repulsive forces between atoms.
On a potential energy diagram, bond length is the distance at minimum energy, and bond energy is the energy needed to break the bond.
Covalent: Higher bond order → shorter, stronger bonds.
Ionic: Coulomb’s law shows stronger attractions result from higher charges and smaller ionic radii.
Key points to remember:
- Bond energy = energy required to break a bond
- Bond length = distance at minimum potential energy
- Bond order ↑ → bond length ↓ and bond energy ↑
- Coulomb’s law: larger charges and smaller ions = stronger ionic bonds