AP Chemistry Unit 2: Compound Structure & Properties

Quick-reference study sheet

Unit 1 explained how a single atom is built. Unit 2 explains what happens when atoms stick together. Every idea in this unit traces back to one rule: opposite charges attract, like charges repel, and atoms arrange themselves in whatever way lowers the potential energy the most. That single idea predicts bond type, bond strength, melting point, the shape of a molecule, and whether that molecule is polar.

1. Types of Chemical Bonds

Bonding is a spectrum, not three separate boxes. Classify a bond using the difference in electronegativity (ΔEN) between the two atoms, plus whether the atoms are metals or nonmetals.

Vocabulary you must be able to define

  • Electronegativity (EN): a measure of how strongly an atom pulls on the shared electrons in a bond. Higher EN means a stronger pull. It rises across a period (more protons, same shell) and falls down a group (the valence shell is farther from the nucleus and better shielded).
  • Polarity (of a bond): an uneven distribution of electron density in a bond, caused by a difference in electronegativity (ΔEN) between the two atoms. A bond with an uneven distribution is polar; one with an even distribution is nonpolar.
  • Partial charge (δ+ / δ−): the fraction of a charge that builds up on an atom in a polar bond. The more electronegative atom holds electron density longer, so it is δ−, and the atom it pulled away from is δ+. These are less than one full electron of charge, which is why they are called partial.
  • Net (full, formal) charge: what forms when an electron is transferred outright rather than shared. Na loses one electron entirely and becomes Na+; Cl gains it and becomes Cl-. Ions carry whole charges; atoms in covalent bonds carry partial ones.

How an atom ends up partially positive or fully charged

  1. ΔEN = 0 (or nearly 0): both nuclei pull equally, the cloud stays centered, and no atom gains a charge. Example: Cl–Cl, C–H (ΔEN = 0.35).
  2. ΔEN is moderate (~0.4–1.7): electrons are still shared, but shifted. The greedier atom sits at δ− and the other at δ+. Example: in H–O, ΔEN = 3.44 − 2.20 = 1.24, so O is δ− and H is δ+.
  3. ΔEN is large (> ~1.7): the pull is so lopsided that the electron is taken, not shared. Full ions form. Example: in NaCl, ΔEN = 3.16 − 0.93 = 2.23, giving Na+ and Cl-.

The bigger the ΔEN, the bigger the partial charges — it is one continuous scale from nonpolar covalent to ionic, not three separate categories.

Electronegativity values for the common elements

PeriodGp 1Gp 2Gp 13Gp 14Gp 15Gp 16Gp 17
1H 2.20
2Li 0.98Be 1.57B 2.04C 2.55N 3.04O 3.44F 3.98
3Na 0.93Mg 1.31Al 1.61Si 1.90P 2.19S 2.58Cl 3.16
4K 0.82Ca 1.00Ga 1.81Ge 2.01As 2.18Se 2.55Br 2.96
5Rb 0.82Sr 0.95In 1.78Sn 1.96Sb 2.05Te 2.10I 2.66

Pauling scale. Common metals for comparison: Zn 1.65, Fe 1.83, Pb 1.87, Cu 1.90, Ag 1.93. Electronegativity increases left to right across a period and decreases down a group, so F (3.98) is the highest of all and Cs/Fr the lowest. Noble gases are normally left unassigned.

Where Partial Charges Come From

Nonpolar covalent: Cl–ClClClΔEN = 0, so the shared cloud stayscentered: no partial chargesPolar covalent: H–ClHClδ+δ−the dipole arrow points toward themore electronegative atom

Chlorine (EN 3.16) pulls the shared pair harder than hydrogen (2.20), so the cloud shifts toward Cl. Cl becomes partially negative (δ−) and H is left partially positive (δ+). Neither atom carries a whole charge, and the molecule overall is still neutral.

Bond TypeAtoms InvolvedΔEN GuidelineWhat the Electrons DoExamples
Nonpolar covalentNonmetal + nonmetal0 to ~0.4Shared about equallyH2, Cl2, CH4
Polar covalentNonmetal + nonmetal~0.4 to ~1.7Shared unequally; partial charges (δ+ and δ-) appearHCl, H2O, NH3
IonicMetal + nonmetalGreater than ~1.7Transferred; full + and - ions formNaCl, MgO, CaF2
MetallicMetal + metalBoth have low ENDelocalized over the whole solidCu, Fe, brass

What makes a bond stronger or weaker

“Strength” means the energy needed to break the bond (its bond energy, in kJ/mol), which is the depth of the potential energy well in Section 2. Four things control it:

FactorStronger bond when…Why (Coulomb’s law)Example
Bond orderMore shared pairsMore shared electron density between the nuclei, so a larger effective attractionN≡N (941) > N=N (418) > N–N (163 kJ/mol)
Atomic size / bond lengthSmaller atoms, shorter bondSmaller r means a larger attraction, since the pull goes as 1/r2H–F (565) > H–Cl (431) > H–Br (366) > H–I (299)
Ionic chargeLarger charges on the ionsq1q2 is bigger, so the lattice energy is biggerMgO (2+/2-) > NaF (1+/1-)
Bond polarity (ΔEN)Larger ΔEN, comparing similar-sized atomsThe δ+ and δ− ends attract each other on top of the normal shared-pair attractionH–F (ΔEN 1.78, 565) > H–I (ΔEN 0.46, 299)

How polarity changes bond strength

A polar bond has extra glue in it. Besides the two nuclei both attracting the shared pair, the δ+ end and the δ− end attract each other electrostatically. That added ionic character makes a polar bond stronger and shorter than a nonpolar bond between atoms of the same size would be.

  • Compare across a period: C–F (485 kJ/mol) is stronger than C–C (347) partly because ΔEN gives it partial charges that pull the atoms together.
  • Compare down a group: from H–F to H–I, ΔEN shrinks and the atoms get bigger, and both changes weaken the bond, which is why the trend is so steep.
  • Size can beat polarity, so check it first. A very long bond is weak no matter how polar it is: H–I is still polar but is the weakest hydrogen halide bond because I is huge. Rank by size/bond length first, then use ΔEN to break ties between atoms of similar size.

Properties that follow from bond type

Listed from the highest melting point down to the lowest, which is also the order from strongest to weakest forces holding the solid together.

SubstanceMelting PointWhat Must Be OvercomeConducts Electricity?Other Properties
1. Covalent networkVery high (diamond > 3500 °C, SiO2 ~1700 °C)Actual covalent bonds throughout the whole crystalNo (graphite is the exception)Very hard, rigid, insoluble
2. Ionic solidHigh (NaCl 801 °C, MgO 2852 °C)Coulombic attractions across the whole latticeOnly when molten or dissolvedHard but brittle; often water soluble
3. Metallic solidUsually high, but a wide range (W 3422 °C, Na 98 °C, Hg −39 °C)Attraction between cations and the delocalized electron seaYes, as a solid and as a liquidMalleable, ductile, lustrous
4. Molecular (covalent) solidLow (H2O 0 °C, CO2 sublimes at −78 °C)Only the weak forces between molecules, never the bonds inside themNoSoft, often a gas or liquid at room temperature

Metallic is placed third because it varies the most: transition metals with many delocalized electrons melt above most ionic solids, while alkali metals melt below room-temperature ionic compounds. When a question compares a specific metal, argue from the number of delocalized electrons and the cation size rather than from this ranking.

⚠ Watch out:The ΔEN cutoffs are guidelines, not laws. On the AP exam, justify the answer with reasoning (metal + nonmetal, large EN difference, electrons transferred) rather than quoting a number.

2. Intramolecular Force & Potential Energy

Coulomb’s law is the engine behind this entire unit. The force (and the potential energy) between two charged particles depends on how large the charges are and how far apart they sit.

Vocabulary you must be able to define

  • Internuclear separation: the distance between the nuclei (the centers) of two atoms. It is the r in Coulomb’s law and the x-axis of every potential energy curve. At the energy minimum, the internuclear separation is called the bond length.
  • Potential energy: stored energy that depends on position — here, on how far apart the charged particles are. Two particles infinitely far apart are defined as having zero potential energy. Attraction pulls the energy below zero (negative, more stable); repulsion pushes it above zero (positive, less stable).
  • Bond energy (bond enthalpy): the energy required to break one mole of a bond in the gas phase, in kJ/mol. It equals the depth of the well below zero. Breaking bonds always costs energy (endothermic, +); forming bonds always releases it (exothermic, −).
  • Lattice energy: the Coulombic version of bond energy for an ionic solid — the energy change when one mole of gaseous ions comes together into a crystal lattice (see Section 3).

Coulombic Force

F = kq1q2r2

Coulombic Potential Energy

E ∝q1q2r

Where:

  • q1, q2 = the two charges (for an ionic compound, the ionic charges)
  • r = distance between the centers of the two particles
  • k = Coulomb constant

Larger charges or a smaller distance means a stronger attraction, a deeper energy well, and a higher melting point.

Coulombic force vs. Coulombic potential energy

They come from the same physics and differ by one power of r, but they answer different questions. Force asks which way and how hard are the particles being pushed right now; potential energy asks how much energy is stored in this arrangement, and how much would it take to pull them apart.

Coulombic ForceCoulombic Potential Energy
EquationF = kq1q2/r2E ∝ q1q2/r
What it isA push or a pull, a vector with a direction, in newtonsStored energy of the arrangement, a scalar, in joules or kJ/mol
Distance dependence1/r2, so it dies off quickly1/r, so it reaches farther
Sign conventionNegative = attraction pulling them together; positive = repulsion pushing apartNegative = more stable than separated atoms; positive = less stable
At the bond lengthNet force is zero: attraction and repulsion exactly balanceEnergy is at its minimum (most negative)
Why it mattersExplains why atoms move toward each other and why they stop: it sets where the bond length isGives the number you can measure and compare: bond energy, lattice energy, melting point, stability

The link between them: force is the slope of the potential energy curve. Where the curve slopes down to the right, the net force pulls the atoms together; where it slopes up steeply at short distance, the net force pushes them apart; at the bottom of the well the slope is flat, so the net force is zero — and that is exactly why the atoms settle there.

On the exam: use force language when you are explaining motion or why a lattice resists being deformed; use potential energy language when you are ranking bond strengths, lattice energies, or melting points. Both are justified with the same two variables: charge and distance.

Potential Energy vs. Internuclear Distance

E = 0 (atoms far apart)bond lengthbond energy(depth of the well)repulsiondominatesattractiondominatesPotential energyInternuclear distance

The minimum is the most stable arrangement: the distance there is the bond length, and the depth below zero is the bond energy. Stronger bonds are deeper (more energy needed to break them) and shorter.

How to read a potential energy vs. internuclear separation graph

  1. Start at the far right. The atoms are separated and not interacting, so the curve flattens out at E = 0. Every real curve must approach zero from below.
  2. Move left. Attraction between the nucleus of one atom and the electrons of the other takes over, so the energy drops below zero. Falling energy means a more stable arrangement.
  3. Find the minimum. This is the bond. Its x-value is the bond length and its depth below zero is the bond energy. The net force here is zero.
  4. Keep going left. The two nuclei (both positive) and the two electron clouds start repelling each other, which the 1/r2 term makes blow up fast, so the curve shoots steeply upward past zero. This is why atoms cannot simply be squeezed together.

Which sketch is actually a bond?

Repulsion only

0

No bond

Energy is positive everywhere and only falls toward zero. The atoms are most stable apart.

Attraction only

0

No bond

Energy keeps dropping with no minimum, so nothing stops the nuclei from collapsing together.

Attraction + repulsion

0

Real bond

Steep positive wall at short r, a minimum (the bond), and a flattening approach to zero at large r.

Comparing Three Diatomic Molecules on One Graph

0CBAPotential energyInternuclear separation (r)all curves approach 0 as r → ∞

Read left to right: the horizontal position of each minimum is that molecule’s bond length. Curve C bottoms out farthest left, so C has the shortest bond.

Read top to bottom: the depth of each minimum below zero is that molecule’s bond energy. Curve A is deepest, so A has the strongest bond.

The two usually track together. For the same pair of atoms, a higher bond order means a shorter and stronger bond: N≡N (941 kJ/mol) sits deeper and farther left than O=O (498) which sits deeper and farther left than F–F (159). Watch for a graph that breaks the pattern, since the depth (strength) is what the question is usually testing.

Example: three curves are labeled X2, Y2, and Z2. Which is H2, N2, and O2?

  1. Rank the known bond energies: N≡N 941 > O=O 498 > H–H 436 kJ/mol, so N2 owns the deepest well.
  2. Rank the known bond lengths: H–H 74 pm < N≡N 110 pm < O=O 121 pm, so H2 owns the leftmost minimum.
  3. Match both facts at once: the leftmost but only moderately deep curve is H2; the deepest curve is N2; the remaining shallower, rightmost curve is O2.
  4. Depth answers “which bond is strongest,” horizontal position answers “which bond is shortest.” Read them separately, since H2 is the classic trap: a very short bond that is not the strongest.

Bond order, bond length, and bond energy

BondBond OrderLengthEnergy (strength)Example
Single1LongestWeakestC–C (~347 kJ/mol)
Double2ShorterStrongerC=C (~614 kJ/mol)
Triple3ShortestStrongestC≡C (~839 kJ/mol)

Bond length also grows as the bonded atoms get bigger: H–F < H–Cl < H–Br < H–I in length, and the bond energy falls in that same order.

⚠ Watch out:Do not confuse intramolecular forces (the bonds inside a molecule, this unit) with intermolecular forces (the attractions between molecules, Unit 3). Boiling water breaks intermolecular forces, not O–H bonds.

3. Structure of Ionic Solids

Ionic compounds are not made of molecules. They form a repeating three-dimensional crystal lattice in which every cation is surrounded by anions and every anion is surrounded by cations, which maximizes attraction and minimizes repulsion. A formula such as NaCl gives the smallest whole-number ratio of ions, called a formula unit.

Lattice Energy

lattice energy ∝q1q2r

the energy released when gaseous ions come together to form one mole of an ionic solid

Lattice Energy Diagram for NaCl

EnergyNa⁺(g) + Cl⁻(g)separated gaseous ions (higher energy)+NaCl(s)ionic lattice (lower energy, more stable)++++++lattice energy releasedΔH = −787 kJ/mol(exothermic: ions attract and fall to lower energy)+787 tobreak apart

Read the drop downward: free ions in the gas phase are high in energy, and letting them snap into the lattice releases energy, so lattice energy is negative (exothermic) when written as a formation. Read the dashed arrow upward and it is the energy you must put in to pull one mole of solid apart into gaseous ions. Some textbooks report lattice energy as that positive number instead, so always state which direction you mean.

How to read the diagram, and why it matters

  • The axis is energy, not time. Higher on the page means higher potential energy and less stability. The two horizontal lines are the two states being compared: loose gaseous ions on top, the assembled crystal on the bottom.
  • The drop is the lattice energy. Na+(g) + Cl-(g) → NaCl(s) releases 787 kJ/mol, so ΔH = −787 kJ/mol. The ions attract, fall to lower energy, and the surroundings warm up. This is just the deep well of a potential energy curve redrawn as levels.
  • The dashed arrow up is the same number reversed. To rip the solid apart into free gaseous ions you must supply +787 kJ/mol. That is why the size of the drop is the strength of the ionic bonding.
  • Why it is important: a bigger drop predicts a higher melting point, a harder and less soluble solid, and a smaller heat of solution. Every “rank these by melting point” ionic question is really asking you to rank the depth of this drop, and Coulomb’s law tells you the depth from charge and radius alone.
  • Sign warning: some sources define lattice energy as the positive energy needed to break the solid apart. Both describe the same 787 kJ/mol. State the process you mean (“energy released when the lattice forms”) and your sign can never be marked wrong.

Larger charge → stronger lattice

MgO (2+ with 2-) melts near 2850 °C, while NaCl (1+ with 1-) melts near 800 °C. Charge outweighs size.

Smaller ions → stronger lattice

For equal charges, ions closer together attract more strongly: LiF > NaCl > KBr > CsI in lattice energy.

Properties explained by the lattice

  • High melting and boiling points: many strong Coulombic attractions must be overcome at once.
  • Hard but brittle: striking a crystal shifts one layer, lining up like charges, and the repulsion splits the crystal.
  • Conductivity: the solid does not conduct because ions are locked in place; molten (l) and aqueous (aq) forms conduct because the ions can move.
  • Often water soluble: polar water molecules pull ions out of the lattice.

Example: rank NaF, MgO, and KBr by melting point

  1. Find the charges: NaF is 1+/1-, MgO is 2+/2-, KBr is 1+/1-.
  2. MgO has the largest charge product (2 × 2 = 4), so it wins outright.
  3. NaF and KBr both have a product of 1, so compare size: Na+ and F- are smaller than K+ and Br-, so r is smaller for NaF.
  4. Answer: MgO > NaF > KBr
⚠ Watch out:Never write “an NaCl molecule.” Say formula unit or refer to the lattice. Also compare charge first and radius second, since charge almost always dominates.

4. Structure of Metals & Alloys

Metals have low ionization energies, so their valence electrons are not held by any one atom. The “sea of electrons” model treats a metal as a lattice of cations sitting in a pool of delocalized valence electrons.

Metallic Bonding: the “Sea of Electrons” Model

+++++++++++++++

Fixed cations sit in a lattice while the valence electrons (small teal dots) are delocalized over the whole solid. Mobile electrons explain conductivity and luster; nondirectional bonding explains malleability.

Vocabulary you must be able to define

  • Malleable: able to be hammered, pressed, or rolled into thin sheets without shattering (gold leaf, aluminum foil). The cations can slide to new positions because the electron sea is nondirectional and simply flows with them.
  • Ductile: able to be drawn out into a wire. Same cause as malleability, just pulled in one direction instead of flattened (copper wiring).
  • Conductivity: the ability to let electric charge or heat flow through a material. Metals conduct because the delocalized valence electrons are free to move through the entire solid, carrying charge and transferring kinetic energy.
  • Luster: the shiny, reflective appearance of a metal surface. The mobile electrons absorb and immediately re-emit visible light of all wavelengths instead of letting it pass through.

Contrast with an ionic solid, which is brittle: shifting a layer lines up like charges, and the repulsion cracks the crystal. Metals are malleable for exactly the reason ionic solids are not.

Why metals behave the way they do

  • Conductivity: delocalized electrons carry charge and heat through the solid.
  • Malleable and ductile: the bonding is nondirectional, so layers of cations slide past each other and the electron sea simply follows.
  • Luster: mobile electrons absorb and re-emit visible light.
  • Strength: increases with more delocalized electrons per atom and smaller cations, so transition metals are generally stronger than alkali metals.

Alloys: two kinds

Interstitial Alloy

Much smaller atoms fill the holes between host atoms. Harder, stronger, less malleable. Example: steel (Fe + C).

Substitutional Alloy

Atoms of similar radius swap into lattice sites. Keeps metallic character. Examples: brass (Cu + Zn), bronze (Cu + Sn).

Alloy TypeAtomic RadiiArrangementEffectExamples
InterstitialVery different; the added atom is much smallerSmall atoms fill holes between host atomsBlocks layers from sliding: harder, stronger, less malleableSteel (Fe + C)
SubstitutionalSimilar, within roughly 15%Added atoms replace host atoms at lattice sitesKeeps malleability; tunes strength, color, corrosion resistanceBrass (Cu + Zn), bronze (Cu + Sn), sterling silver (Ag + Cu)

Both types are still metals: they conduct electricity and keep the sea of delocalized electrons. Alloys usually melt over a range of temperatures instead of at one sharp point.

5. Lewis Diagrams

A Lewis diagram shows every valence electron in a molecule or polyatomic ion as either a bonding pair (a line) or a lone pair (two dots). Most atoms end up with an octet of 8 valence electrons; hydrogen takes a duet of 2.

Six steps that always work

  1. Count total valence electrons. Add one per negative charge and subtract one per positive charge.
  2. Pick the central atom: the least electronegative atom that is not hydrogen (carbon is central whenever it is present).
  3. Connect every outer atom to the center with a single bond.
  4. Complete the octets of the outer atoms with lone pairs, giving hydrogen nothing extra.
  5. Place any electrons still left over on the central atom.
  6. If the central atom is short of an octet, pull a lone pair from an outer atom in to make a double or triple bond.

Worked Lewis Diagrams

H2O (8 e⁻)

OHH

2 bonding pairs + 2 lone pairs on O

NH3 (8 e⁻)

NHHH

3 bonding pairs + 1 lone pair on N

CH4 (8 e⁻)

CHHHH

4 bonding pairs, no lone pairs: a perfect octet

CO2 (16 e⁻)

OCO

two double bonds; 2 lone pairs left on each O (8 bonding + 8 lone = 16 e⁻)

N2 (10 e⁻)

NN

triple bond plus 1 lone pair on each N

HCN (10 e⁻)

HCN

H gets a duet; C≡N triple bond; 1 lone pair on N

Every line is one shared pair (2 electrons) and every pair of dots is one lone pair. Count the electrons in your finished drawing and it must match the valence-electron total you started with.

Example: draw CO2

  1. Valence electrons: 4 (C) + 2 × 6 (O) = 16
  2. Carbon is central because it has the lower electronegativity: O–C–O
  3. Two single bonds use 4 electrons; the remaining 12 fill both oxygens with 3 lone pairs each
  4. Carbon now has only 4 electrons, so move one lone pair from each oxygen into the bond
  5. Answer: O=C=O, with 2 lone pairs left on each oxygen and an octet on every atom

Octet rule exceptions

ExceptionDescriptionExamples
DuetHydrogen is stable with 2 electronsH2, H2O
Electron deficientBe is stable with 4 electrons; B and Al with 6BeCl2, BF3, AlCl3
Expanded octetPeriod 3 and below can hold 10 or 12 because empty d orbitals are availablePCl5, SF6, XeF4
Odd electron (radical)An odd electron total leaves one unpaired electronNO, NO2

Vocabulary: isomer and isomeric

  • Isomer: one of two or more compounds that have the same molecular formula but a different arrangement of atoms. Same atoms, same count, different connectivity or different geometry — and therefore different properties.
  • Isomeric: the adjective. Two substances are “isomeric” (or are “isomers of each other”) when they stand in that relationship, as in “ethanol and dimethyl ether are isomeric C2H6O compounds.”
  • Structural (constitutional) isomers: the atoms are connected in a different order, as in ethanol (C–C–O–H) versus dimethyl ether (C–O–C).
  • Geometric (cis/trans) isomers: the connectivity is the same but the groups are locked on the same side (cis) or opposite sides (trans) of a double bond, which cannot rotate. Cis-1,2-dichloroethene is polar; the trans form is nonpolar.

Do not confuse isomers with resonance structures (Section 6). Isomers are genuinely different substances you could bottle separately, because the atoms moved. Resonance structures are two drawings of one substance, because only the electrons moved.

Isomers: Same Formula (C2H6O), Different Structure

Ethanol

CCOHHHHHH

O–H group; polar, hydrogen bonds. Boils at 78 °C, liquid at room temperature.

Dimethyl ether

COCHHHHHH

No O–H; cannot hydrogen bond. Boils at −24 °C, a gas at room temperature.

Both are C2H6O with 20 valence electrons, yet a 100 °C difference in boiling point comes purely from where the atoms are connected. Lone pairs on oxygen are omitted for clarity.

⚠ Watch out:Elements in periods 1 and 2 (C, N, O, F) can never exceed an octet. Put brackets and the charge around a polyatomic ion, and never place hydrogen in the center.

6. Resonance & Formal Charge

Resonance occurs when more than one valid Lewis structure can be drawn by moving only electrons, not atoms. The real molecule is not flipping between them; it is a single resonance hybrid with the electrons delocalized, so all of the equivalent bonds have the same length and strength.

Resonance Structures and the Hybrid

Ozone, O3 — two equivalent structures

OOO+
OOO+

Only the electrons move; the three oxygen atoms never change position. Neither drawing is the real molecule. Experiments show both O–O bonds are identical, at 128 pm, between a single bond (148 pm) and a double bond (121 pm).

The resonance hybrid — what the molecule really is

OOO+½−½−

Dashed half-bonds show the delocalized pair spread over both positions. Bond order = 3 bonds ÷ 2 positions = 1.5, and the −1 charge is smeared as ½− on each outer oxygen. Delocalizing electrons over more atoms lowers the energy, which is why resonance-stabilized species such as benzene are unusually stable.

Carbonate, CO32− — three equivalent structures

COOO
COOO
COOO

The double bond can sit on any of the three oxygens, so all three C–O bonds are the same in the real ion. Bond order = 4 bonds ÷ 3 positions = 1.33, each oxygen carries an average of ⅔−, and the ion is flat (trigonal planar).

How to spot resonance: you have a double (or triple) bond that could just as legitimately have been drawn in another position among equivalent atoms. Same skeleton, different electron placement.

Note: lone pairs are left off every sketch above so the bonds and formal charges stay readable. On the AP exam you must draw them — O3 has 18 valence electrons and CO32− has 24, and a structure is only complete when every one of them is on the page.

Formal Charge

FC = V − (L + B)

V = valence electrons on the free atom, L = lone-pair electrons, B = number of bonds (shared pairs)

Average Bond Order

total bonds between the two atomsnumber of bonding positions

Choosing the best (dominant) structure

  • Formal charges should be as close to zero as possible.
  • Any negative formal charge belongs on the more electronegative atom.
  • Avoid like charges on adjacent atoms.
  • Formal charges must sum to the overall charge of the species, which is zero for a neutral molecule.

Example: formal charge on carbon in CO2 (O=C=O)

  1. V = 4 valence electrons for carbon
  2. L = 0 lone-pair electrons on carbon
  3. B = 4 bonds, since there are two double bonds
  4. FC = 4 − (0 + 4) = 0, exactly what a good structure should give

Example: bond order in the carbonate ion, CO32-

  1. Each resonance structure has one C=O and two C–O bonds, so 4 bonds total
  2. There are 3 carbon-to-oxygen bonding positions
  3. Bond order = 43 = 1.33
  4. All three C–O bonds are identical, with a length between a single and a double bond

Other classic resonance species: O3 and SO2 (bond order 1.5), NO3- (1.33), and benzene C6H6 (1.5).

⚠ Watch out:Formal charge is a bookkeeping tool, not a real charge. Resonance structures are joined by a double-headed arrow, not an equilibrium arrow, because the molecule never actually exists as any one of them.

7. VSEPR & Molecular Geometry

VSEPR (Valence Shell Electron Pair Repulsion) theory says electron domains around a central atom spread as far from each other as they can. An electron domain is any lone pair or any bond, and a double or triple bond still counts as one domain.

Two different names to keep straight:

  • Electron-domain geometry counts every domain, lone pairs included.
  • Molecular geometry is the shape traced by the atoms alone: lone pairs are invisible but still push.

Repulsion strength runs lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair, which is why each lone pair squeezes the bond angles below the ideal value.

DomainsBonds / LPElectron GeometryMolecular GeometryShapeBond AngleHybrid.Example
22 / 0LinearLinear180°spCO2, BeCl2
33 / 0Trigonal planarTrigonal planar120°sp2BF3, SO3
32 / 1Trigonal planarBent< 120°sp2SO2, O3
44 / 0TetrahedralTetrahedral109.5°sp3CH4, CCl4
43 / 1TetrahedralTrigonal pyramidal~107°sp3NH3, PCl3
42 / 2TetrahedralBent~104.5°sp3H2O, SCl2
55 / 0Trigonal bipyramidalTrigonal bipyramidal90° and 120°PCl5
54 / 1Trigonal bipyramidalSeesaw< 90°, < 120°SF4
53 / 2Trigonal bipyramidalT-shaped~90°ClF3
52 / 3Trigonal bipyramidalLinear180°XeF2, I3-
66 / 0OctahedralOctahedral90°SF6
65 / 1OctahedralSquare pyramidal< 90°BrF5
64 / 2OctahedralSquare planar90°XeF4

In the shape column, blue circles are bonded atoms and gray dot pairs are lone pairs on the central atom. The AP course assesses hybridization only for sp, sp2, and sp3, so the 5- and 6-domain rows are marked —.

Hybridization and sigma / pi bonds

Count domains, then name the hybrid

  • 2 domains → sp (180°)
  • 3 domains → sp2 (120°)
  • 4 domains → sp3 (109.5°)

The number of hybrid orbitals equals the number of atomic orbitals mixed, which equals the number of electron domains.

Sigma (σ) vs. pi (π) bonds

  • Single bond = 1 σ
  • Double bond = 1 σ + 1 π
  • Triple bond = 1 σ + 2 π

Sigma bonds form by head-on overlap and allow free rotation; pi bonds form by side-on overlap of unhybridized p orbitals and lock the molecule rigid.

⚠ Watch out:Count domains, not bonds. CO2 has 4 bonds but only 2 domains, so it is linear and sp hybridized. When a question asks for a shape, give the molecular geometry unless it specifically says electron-domain geometry.

8. Molecular Polarity

A molecule is polar only if it has both polar bonds and a shape in which those bond dipoles fail to cancel. Bond dipoles are vectors: they point toward the more electronegative atom and add like arrows.

Vocabulary you must be able to define

  • Dipole: a separation of positive and negative charge across a bond or a molecule, with a δ+ end and a δ− end.
  • Dipole moment (μ): the size of that separation, measured as μ = q × d — the amount of separated charge times the distance between the centers of charge. It is a vector, drawn as an arrow pointing toward the δ− end with a plus sign on the tail, and is reported in debyes (D). A larger ΔEN or a longer bond gives a larger dipole moment. Bond dipole moments add as vectors, so a molecule’s net (molecular) dipole moment is zero when the shape makes them cancel: μ = 0 for CO2, 1.85 D for H2O.
  • Enthalpy (H): the heat content of a system at constant pressure. Only the change, ΔH, is measurable. ΔH < 0 is exothermic (heat released, products more stable); ΔH > 0 is endothermic (heat absorbed).
  • Bond enthalpy (bond dissociation energy): the enthalpy change to break one mole of a specific bond in the gas phase, always positive because breaking bonds costs energy. Forming the same bond releases the same magnitude. This is the number tabulated as “bond energy” and it is the well depth from Section 2.
  • Estimating a reaction enthalpy from bond enthalpies: ΔHrxn ≈ Σ(bonds broken) − Σ(bonds formed). If the bonds in the products are stronger, the reaction is exothermic.

polar bonds + asymmetric shape = polar molecule

a symmetric shape with identical outer atoms is nonpolar, even when the individual bonds are very polar

Symmetric shapes (dipoles cancel)

Linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral, and square planar, as long as all outer atoms are the same.

Nonpolar: CO2, BF3, CH4, CCl4, SF6, XeF4

Asymmetric shapes (dipoles add up)

Bent, trigonal pyramidal, seesaw, T-shaped, and square pyramidal, plus any shape with different outer atoms.

Polar: H2O, NH3, SO2, CHCl3, CH3Cl

Example: why is CO2 nonpolar but H2O polar?

  1. Both contain very polar bonds, since oxygen is far more electronegative than carbon or hydrogen
  2. CO2 has 2 domains on carbon, so it is linear and the two C=O dipoles point in exactly opposite directions
  3. Those dipoles cancel, so CO2 is nonpolar
  4. H2O has 4 domains on oxygen (2 bonds and 2 lone pairs), so it is bent at about 104.5°
  5. The bent shape lets the two O–H dipoles add to a net dipole, so water is polar
⚠ Watch out:A polar bond does not guarantee a polar molecule, and swapping a single outer atom breaks the symmetry: CCl4 is nonpolar but CHCl3 is polar.

9. Unit 2 Problem-Solving Checklist

Almost every Unit 2 free-response question follows the same chain. Run it in order and the answer falls out.

  1. Classify the bonding: metal + nonmetal, nonmetal + nonmetal, or metal + metal
  2. For an ionic question, go straight to Coulomb’s law: compare charges first, then radii
  3. Count total valence electrons and draw the Lewis diagram
  4. Check for resonance; if it exists, calculate formal charges and bond order
  5. Count electron domains on the central atom, remembering that multiple bonds count once
  6. Name the electron geometry, then subtract lone pairs to get the molecular geometry and bond angle
  7. Assign hybridization from the domain count: sp, sp2, or sp3
  8. Judge polarity from bond polarity plus the symmetry of the shape
⚠ Scoring tip:AP graders want a claim plus a reason at the particle level. Do not just say “MgO has a higher melting point.” Say that MgO has 2+ and 2- ions rather than 1+ and 1-, so the Coulombic attraction and lattice energy are greater and more energy is required to separate the ions.