Topic 2.2 Intramolecular Force and Potential Energy: interpret a potential-energy versus internuclear-distance curve to define bond length and bond energy, and explain how bond order, atomic size and charge affect bond strength.

What this topic is asking

The College Board (Topic 2.2) wants you to read a potential-energy versus internuclear-distance curve for a bond, to define bond length and bond energy from it, and to explain how three factors, bond order, atomic size and ionic charge, control how strong a bond is. The unifying tool is Coulomb's law.

The potential-energy curve

The shape encodes a balance of two Coulombic effects. As atoms approach, the attraction between each nucleus and the other atom's electrons lowers the energy. But if they get too close, the like-charged nuclei (and inner electrons) repel strongly, raising the energy sharply. The minimum is the distance where these balance, the most stable arrangement, and that is where the bond sits.

Bond length and bond energy

Bond length is the equilibrium internuclear distance, and bond energy is the energy needed to break one mole of those bonds. The two are linked: a stronger bond is generally a shorter bond, because a deeper potential well pulls the nuclei closer. So if you know one quantity's trend you can usually predict the other.

What controls bond strength

Three factors recur:

• Bond order (covalent): triple > double > single in strength, and triple < double < single in length. More shared pairs means more electron density between the nuclei and a stronger attraction.
• Atomic size: smaller atoms bond at shorter distances, so their nuclei attract the shared electrons more strongly (a shorter bond is generally stronger).
• Ionic charge and size (ionic): by Coulomb's law, $F \propto \dfrac{q_1 q_2}{r^2}$, larger ionic charges and smaller ions (shorter $r$) give a stronger attraction and a higher lattice energy.

The thread through all three is Coulomb's law: bond strength grows with the magnitude of the interacting charges and shrinks with distance. This is why $\text{N}\equiv\text{N}$ (bond order 3) is one of the strongest bonds known, why $\text{MgO}$ ($2+$ and $2-$ ions) has a far higher lattice energy than $\text{NaCl}$ ($1+$ and $1-$), and why bond and lattice energies underpin the energetics you meet later in thermochemistry. Reading the potential-energy curve is the qualitative version of this same idea, and the College Board often pairs a curve with a "compare and explain" prompt.

Try this

Q1. State what the depth of the minimum on a potential-energy curve represents. [1 point]

• Cue. The bond energy (the energy required to break the bond).

Q2. Predict which has the stronger interaction, $\text{NaF}$ or $\text{MgO}$, and justify with Coulomb's law. [2 points]

• Cue. $\text{MgO}$; its ions carry charges of $2+$ and $2-$ versus $1+$ and $1-$ for $\text{NaF}$, and the larger charges give a stronger Coulombic attraction.