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Intramolecular force and potential energy

Every bond is a truce between attraction pulling atoms together and repulsion pushing them apart. Draw that truce as a potential-energy curve and it tells you both how long the bond is and how strong it is.

§1

A bond is a balance of forces.

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As two atoms approach, their electrons and nuclei attract, lowering the system's potential energy. Come too close and the nuclei repel, and the energy shoots back up. The potential-energy curve plots energy against the distance between the nuclei.

The curve has a minimum. That lowest point is where attraction and repulsion balance, and its position along the distance axis is the bond length — the natural separation the atoms settle into.

The depth of the well, measured from the minimum up to the energy of the fully separated atoms, is the bond energy: the energy you must supply to pull the atoms completely apart. Deeper well, stronger bond.

UNIT 2 TOPIC 2.2 • INTRAMOLECULAR FORCE AND POTENTIAL ENERGY BOND WELL Potential energy vs. internuclear distance — the shape of a chemical bond. POTENTIAL-ENERGY CURVE 0 POTENTIAL ENERGY INTERNUCLEAR DISTANCE, r Dₑ bond energy bond length, rₑ REPULSION clouds overlap, nuclei push apart ATTRACTION nuclei pull the atoms together PE ≈ 0 TOO CLOSE r < rₑ Repulsion dominates — electron clouds overlap, nuclei push apart. High PE. AT MINIMUM r = rₑ Attraction and repulsion balance — most stable, lowest potential energy. FAR APART r → ∞ Weak attraction, almost no interaction between atoms. PE ≈ 0. BOND-ORDER TREND single < double < triple → bond length decreases → bond energy increases ION-PAIR STRENGTH Higher charges & smaller ions → stronger attraction. MgO > NaCl MOTION FROM MINIMUM far apart → closer → minimum → too close. Either way from rₑ raises PE. TAKEAWAY A stable bond sits at the PE minimum; its depth is the bond energy, and higher bond order → shorter, stronger bond. AP Chemistry · Unit 2 · Compound Structure & Properties
Fig. 2.2.1 The potential-energy curve of a bond. The minimum sits at the bond length (rₑ); the depth of the well from that minimum is the bond energy. Left of the minimum the curve rises steeply as the nuclei repel.
§2

Reading the curve.

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Two features carry the physics: where the minimum is, and how deep it is.

  1. Find the minimum. The lowest point of the curve is the equilibrium. Read its distance to get the bond length.
  2. Read the bond length off the horizontal axis. The distance coordinate of the minimum is the bond length, rₑ — not the value at zero energy.
  3. Measure the well depth. From the minimum up to the flat energy of the separated atoms is the bond energy: the energy to break the bond.
  4. Compare curves by shape. A deeper minimum means a stronger bond; a minimum at smaller distance means a shorter bond. Shorter bonds are usually stronger.
§3

The pieces you'll meet.

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Two numbers come off one curve; keep them straight.

rₑ
Bond length
The internuclear distance at the energy minimum, where forces balance.
Dₑ
Bond energy
The well depth: energy needed to pull the bonded atoms fully apart.
minimum
Energy minimum
The lowest point of the curve; the equilibrium position of the bond.
repulsion
Repulsion region
Left of the minimum, where nuclei crowd and energy rises steeply.
attraction
Attraction region
Right of the minimum, where pulling atoms apart raises energy toward zero.
depth
Well depth
How far the minimum lies below the separated-atom energy. Sets bond strength.
§4

Worked example: reading a bond's curve.

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Question. A potential-energy curve for a diatomic molecule has its minimum at 120 pm and 432 kJ/mol below the separated-atom energy. What are the bond length and bond energy?

Bond length. The horizontal position of the minimum is the bond length: 120 pm.

Bond energy. The depth of the well below the separated atoms is the bond energy: 432 kJ/mol, the energy required to break this bond.

Comparison. A different molecule whose curve dips only 240 kJ/mol has a weaker bond; one whose minimum sits at 90 pm has a shorter, and typically stronger, bond. Distance and depth are independent readings from the same curve.

§5

Mistakes that cost real points.

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Pitfall · 01

"The bond length is where the curve crosses zero energy."

The bond length is the distance at the energy minimum, not where the curve hits zero. Zero energy is the separated-atom reference far to the right; the atoms actually sit at the bottom of the well, closer in.

Fix. Read the bond length from the distance coordinate of the lowest point of the curve, the bottom of the well.

Pitfall · 02

"A deeper well means a longer bond."

Depth and position are separate. Depth measures strength (bond energy); horizontal position measures length. A deep well can sit at a short distance; in fact shorter bonds tend to be deeper (stronger), not longer.

Fix. Read length from the minimum's horizontal position and strength from its depth. Do not infer one from the other.

Pitfall · 03

"The energy released when the bond forms is unrelated to the energy needed to break it."

They are the same magnitude. Forming the bond releases the well depth of energy; breaking it requires supplying that same well depth back. The curve's depth is both the energy out on forming and the energy in on breaking.

Fix. Treat the well depth as the single bond energy: released on formation, required on breaking.

§6

Skill Check.

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