Unit 2 · Topic 2.2 Beta

Intramolecular Force and Potential Energy

As two atoms approach, attraction lowers their potential energy until repulsion between the nuclei makes it rise again.

Practice 3: Representing Data and PhenomenaPractice 4: Model AnalysisPractice 6: Argumentation

Question set for this topic

Part 1 · Hook

Why this matters

Two magnets snap together and stop when they touch; you need a tug to pull them apart. Two atoms behave the same way. They pull toward each other, stop at a set distance, and it costs a set amount of energy to separate them. One graph shows both numbers.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. By Coulomb's law, how does the attraction between two opposite charges change if the distance between them is halved?

  1. It becomes four times stronger
  2. It becomes twice as strong
  3. It becomes half as strong
  4. It does not change
Show the answer

The force is proportional to 1/r²; halving r multiplies 1/r² by 2² = 4.

  • Correct: It becomes four times stronger:
  • It becomes twice as strong:
  • It becomes half as strong:
  • It does not change:

2. In a covalent bond, what holds the two atoms together?

  1. Both nuclei attract the shared pair of electrons between them
  2. The two nuclei attract each other
  3. The electrons of one atom repel the other atom
  4. A transferred electron makes the atoms neutral
Show the answer

The shared electrons sit between the nuclei, and both nuclei attract them.

  • Correct: Both nuclei attract the shared pair of electrons between them:
  • The two nuclei attract each other:
  • The electrons of one atom repel the other atom:
  • A transferred electron makes the atoms neutral:

Part 4 · See it

See it first

Graph of potential energy in kilojoules per mole against distance between two hydrogen nuclei in picometers. Far apart the energy is near zero; as the atoms approach it falls to a minimum of minus 436 kilojoules per mole at 74 picometers, marked as the bond length and bond energy; closer than that it rises steeply because the nuclei repel.
The potential energy of two hydrogen atoms falls as they attract, reaches a minimum at the bond length (74 pm), and rises steeply when the nuclei are pushed too close. The depth of the minimum, 436 kJ/mol, is the bond energy. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Two atoms far apart do not interacttheir potential energy is taken as zero
  2. As they approach, each nucleus attracts the other atom's electronsthe potential energy falls below zero
  3. Closer still, the nuclei and the electron clouds repel, and repulsion grows fasterthe potential energy rises steeply
  4. Attraction and repulsion balance at one distancethe curve has a minimum: its distance is the bond length, its depth the bond energy
  5. More shared pairs between the same two atoms attract both nuclei more stronglydouble and triple bonds are shorter and stronger than single bonds

Part 6 · Key ideas

Key ideas

  • An intramolecular force acts within a particle: covalent, ionic or metallic bonding.
  • The minimum of the potential energy curve sits at the bond length; its depth below zero is the bond energy.
  • Breaking a bond requires energy; forming one releases energy.
  • Between the same two atoms, a triple bond is shorter and stronger than a double bond, which is shorter and stronger than a single bond.
  • For ions, Coulomb's law (F ∝ q₁q₂/r²): larger charges and a shorter distance give a stronger attraction.

Part 7 · Misconception

A common mistake

The wrong idea: Breaking a chemical bond releases energy.

What actually happens: Bonded atoms sit at the bottom of an energy well. Pulling them apart means climbing out of it, which requires energy. Energy is released when bonds form.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Graph

Potential energy curves for three molecules

The graph shows how the potential energy of a pair of atoms changes with the distance between their nuclei, for three molecules: H₂, Cl₂ and HCl. The dot on each curve marks its minimum.

−500−400−300−200−1000100200300050100150200250300350400Distance between the nuclei (pm)Potential energy (kJ/mol)Curve 1Curve 2Curve 3

1. What is the bond length of the molecule shown by Curve 2?

  1. About 436 pm
  2. About 74 pm
  3. About 30 pm
  4. About 400 pm
Show the answer

The bond length is the distance at the curve's minimum, where the potential energy is lowest. Curve 2's minimum is at about 74 pm.

  • About 436 pm: 436 is the depth of the minimum in kJ/mol, an energy, not a distance.
  • Correct: About 74 pm: Right: the x-coordinate of the minimum.
  • About 30 pm: At 30 pm the nuclei would be pushed together so hard that the energy is far above zero; that is not where the atoms settle.
  • About 400 pm: At 400 pm the curve is nearly flat at zero: the atoms are hardly interacting, so this is not a bond length.

2. About how much energy is needed to separate one mole of the Curve 1 molecules into free atoms?

  1. About 0 kJ
  2. About 200 kJ
  3. About 480 kJ
  4. About 240 kJ
Show the answer

Separating the atoms means climbing from the minimum (about −240 kJ/mol) to zero, where the atoms no longer interact. That takes about 240 kJ per mole: the bond energy.

  • About 0 kJ: Zero would mean the atoms are already free. Energy is released when a bond forms; breaking it is the reverse, so about 240 kJ must be added.
  • About 200 kJ: About 199 is the distance in pm at the minimum, read from the wrong axis.
  • About 480 kJ: The climb is from about −240 to 0, which is 240 kJ, not twice that.
  • Correct: About 240 kJ: Right: the depth of the well.

3. On Curve 2, why does the potential energy rise steeply at distances shorter than 74 pm?

  1. The nuclei, and the electron clouds, repel more strongly as they are pushed together
  2. The bond breaks at short distances, so the atoms fly apart and the energy goes up
  3. The attraction between each nucleus and the shared electrons grows weaker as they approach
  4. The atoms lose their valence electrons when they get too close to each other
Show the answer

Closer than the bond length, the repulsion between the positive nuclei (and between the electron clouds) grows faster than the attraction, so the energy climbs.

  • Correct: The nuclei, and the electron clouds, repel more strongly as they are pushed together: Right: repulsion wins at short distance.
  • The bond breaks at short distances, so the atoms fly apart and the energy goes up: Nothing breaks: the atoms are pushed too close together. Breaking a bond means moving to the right, toward large distances.
  • The attraction between each nucleus and the shared electrons grows weaker as they approach: Coulomb's law says attraction gets stronger, not weaker, as the distance shrinks. It is the repulsion that grows even faster.
  • The atoms lose their valence electrons when they get too close to each other: The valence electrons stay; the rise comes from charges of the same sign being forced close together.

4. Curve 1 is Cl₂ and Curve 2 is H₂. Which explanation for the longer bond in Cl₂ is best?

  1. Cl₂ has a greater mass, and a heavier molecule has a longer bond
  2. Cl atoms have more protons, so their two nuclei attract each other and pull the bonded atoms apart
  3. Cl's valence electrons are in the third shell, far from the nucleus, so the nuclei settle farther apart
  4. The bond in Cl₂ is weaker, and a weaker bond has to be a longer bond
Show the answer

The shared electrons of Cl₂ are in n = 3, much farther from each nucleus than H's 1s electrons, and Cl's core electrons repel at short range. The minimum energy is reached at a larger separation: 199 pm against 74 pm.

  • Cl₂ has a greater mass, and a heavier molecule has a longer bond: Mass alone does not set bond length; the number of occupied shells (distance from the nucleus) does.
  • Cl atoms have more protons, so their two nuclei attract each other and pull the bonded atoms apart: Two nuclei repel each other; they do not attract. More protons do not pull atoms apart.
  • Correct: Cl's valence electrons are in the third shell, far from the nucleus, so the nuclei settle farther apart: Right: atom size, set by the occupied shells, sets the bond length.
  • The bond in Cl₂ is weaker, and a weaker bond has to be a longer bond: Weaker and longer often go together, but one does not cause the other here; both follow from Cl's larger size.

5. Two hydrogen atoms far apart move toward each other and form H₂. Which statement about energy is correct?

  1. Energy is absorbed, because forming a bond takes energy
  2. Energy is released, because the bonded atoms have lower potential energy
  3. No energy changes, because the same atoms are present before and after
  4. Energy is released, because the bond breaks as the atoms get close
Show the answer

Separate atoms are at zero potential energy; at the bond length H₂ is at −436 kJ/mol. Moving to lower potential energy releases the difference, for example as heat. Bond formation releases energy; bond breaking requires it.

  • Energy is absorbed, because forming a bond takes energy: This is the most common sign mistake: it is breaking a bond that takes energy. Forming one releases energy.
  • Correct: Energy is released, because the bonded atoms have lower potential energy: Right: forming a bond lowers the potential energy.
  • No energy changes, because the same atoms are present before and after: The atoms are the same, but their arrangement and attractions change, and so does the potential energy.
  • Energy is released, because the bond breaks as the atoms get close: As the atoms approach, a bond forms; nothing breaks.

6. Ion pairs are compared at their usual center-to-center distances: Na⁺ and F⁻ (231 pm), and Mg²⁺ and O²⁻ (210 pm). Which pair attracts more strongly, and why?

  1. The attractions are equal, because each pair has one cation and one anion
  2. Na⁺ and F⁻: F is the most electronegative element, so F⁻ attracts most strongly
  3. Mg²⁺ and O²⁻: the ions are heavier, so they attract each other more
  4. Mg²⁺ and O²⁻: both charges are larger and the ions are closer together
Show the answer

Coulomb's law: the force is proportional to q₁q₂/r². The product of the charges is 2 × 2 = 4 for Mg²⁺ and O²⁻ against 1 × 1 = 1 for Na⁺ and F⁻, and r is smaller (210 against 231 pm). Both factors make the Mg²⁺–O²⁻ attraction stronger.

  • The attractions are equal, because each pair has one cation and one anion: The charges are different (1+ and 1− against 2+ and 2−), so the attractions differ.
  • Na⁺ and F⁻: F is the most electronegative element, so F⁻ attracts most strongly: Electronegativity is about attracting shared electrons in a bond, not about the attraction between two ions. Use the charges and the distance.
  • Mg²⁺ and O²⁻: the ions are heavier, so they attract each other more: Mass does not appear in Coulomb's law; charge and distance do.
  • Correct: Mg²⁺ and O²⁻: both charges are larger and the ions are closer together: Right: the answer compares both charge and distance for both pairs.

7. Which is an intramolecular force?

  1. An attraction between one water molecule and a different water molecule
  2. The covalent bond holding O and H together inside one water molecule
  3. The pull of Earth's gravity on a sample of water in a glass
  4. The push that a liquid exerts on the walls of its container
Show the answer

"Intra" means within. An intramolecular force acts between the atoms inside one particle, such as a covalent, ionic or metallic bond.

  • An attraction between one water molecule and a different water molecule: That attraction acts between separate molecules, not within one. Unit 3 covers those forces.
  • Correct: The covalent bond holding O and H together inside one water molecule: Right: a bond inside one molecule.
  • The pull of Earth's gravity on a sample of water in a glass: Gravity on a whole sample is not a force between atoms within a particle.
  • The push that a liquid exerts on the walls of its container: A push on container walls comes from particles hitting them, not from bonding within a particle.

Part 9 · Summary

Summary

As two atoms approach, attraction lowers their potential energy until repulsion between the nuclei makes it rise again. The minimum of the potential energy curve gives the bond length (its distance) and the bond energy (its depth): the energy needed to break the bond. Larger atoms form longer bonds, and more shared pairs between the same atoms make shorter, stronger bonds. For ions, Coulomb's law shows that larger charges and smaller distances give stronger attractions.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections