Topic 2.2 Notes – Intramolecular Force and Potential Energy

Intramolecular Forces and Potential Energy

Intramolecular forces are the forces within a compound that hold atoms together. In AP Chem, that means:

• Covalent bonds (shared electrons)
• Ionic attractions (electrostatic attraction between cations and anions)

Bonding makes sense when you think in terms of potential energy (PE).

• When atoms are far apart, PE is defined as ~0.
• When they bond, the system’s PE decreases.
• Lower PE = greater stability.

Bond formation releases energy because the system moves to a lower PE.
Bond breaking requires energy because you’re pulling atoms up out of that low-energy state.

Everything in this topic comes back to one idea:

Atoms arrange themselves at the distance where potential energy is minimized.

That distance shows up clearly on a graph.

Potential Energy vs. Internuclear Distance

This graph is one of the most testable visuals in Unit 2. Take a second to connect the shape of the curve to what we just discussed about stability and potential energy.

Potential energy curve for H₂

Three regions to understand

1. At large distances

• PE ≈ 0
• Atoms don’t interact
• No bond

2. As atoms move closer

• Electron-nucleus attractions increase
• PE decreases (more negative)
• System becomes more stable

3. Very short distances

• Nucleus-nucleus and electron-electron repulsion dominates
• PE increases sharply
• System becomes unstable

Equilibrium bond length

• The lowest point on the curve (labeled $r_e$ on the graph)
• Attractive and repulsive forces are balanced
• The actual bond length

Bond energy

• The energy required to separate atoms to infinite distance
• Shown as the vertical distance from the minimum up to PE = 0 (labeled $D_e$)
• Deeper well = stronger bond

A common MCQ move is showing two curves and asking which bond is stronger. The deeper curve always corresponds to higher bond energy.

Now let’s connect that to covalent bonding.

Covalent Bonds and Bond Length

Two big factors affect covalent bond strength and length:

Bond order

Bond order = number of shared electron pairs.

More shared electrons means:

• Greater electron density between nuclei
• Stronger attraction
• Shorter bond length
• Larger bond energy

On a PE graph, a triple bond would have a deeper minimum and slightly shorter equilibrium distance than a single bond.

Atomic size

Larger atoms have larger radii. That increases internuclear distance.

• Down a group → atoms get larger
• Bond length increases
• Bond energy decreases

On a PE curve:

• Larger atoms → minimum shifts right
• Weaker bond → well is shallower

If you compare $\ce{F-F}$ and $\ce{I-I}$, the iodine bond is longer and weaker. That’s periodic trends plus PE reasoning working together.

Ionic Bonds and Coulomb’s Law

Ionic bonding strength is explained by Coulomb’s law. Conceptually:

• Attraction increases with larger charges
• Attraction increases with smaller distance between ion centers

The relationship is:

$$F \propto \frac{q_{1} q_{2}}{r^{2}}$$

Where:

• $q_{1}, q_{2}$ = ionic charges
• $r$ = distance between nuclei

Effect of charge

Compare:

• $\ce{Na+}$ and $\ce{Cl-}$
• $\ce{Mg^{2+}}$ and $\ce{O^{2-}}$

The second pair has larger charges, so the electrostatic attraction is stronger. That leads to larger lattice energy and stronger ionic bonding.

Effect of size

Smaller ions bring charges closer together.

• Smaller $r$ → stronger attraction
• Larger $r$ → weaker attraction

So the strongest ionic interactions happen between:

• Highly charged ions
• Small ions

On FRQs, you’re often asked to justify which ionic compound has stronger attractions. The scoring almost always requires mentioning charge magnitude and distance between nuclei explicitly.