Compound structure and properties · AP Chemistry

Chapter 2 · Compound structure and properties

bonds and the shapes they make

Atoms bond because electrons attracted to two nuclei at once have less energy than electrons held by one. How the electrons sit decides the rest: the kind of bond, the shape of the molecule, and how the substance behaves.

Electrons can be shared equally, shared unequally, handed from one atom to another, or pooled among a whole piece of metal. Those are covalent, polar covalent, ionic and metallic bonding.

In a molecule, the electron pairs around each atom push apart as far as they can. That sets the shape. The figure runs a central atom through 13 molecules: as bonds and lone pairs (red) are added or swapped, the shape changes.

This chapter covers the bond types, the energy curve that gives a bond its length, ionic and metallic solids, Lewis diagrams, resonance and formal charge, and the shapes, polarity and hybridization that follow from them.

2.1 · Types of chemical bonds

shared, pulled aside, handed over

A bond is two nuclei attracting the same electrons. What kind of bond forms depends on how hard each atom pulls on them.

Electronegativity is an atom’s pull on the electrons in a bond. It rises across a period and falls down a group; fluorine has the highest. Values on the Pauling scale:

H	C	N	O	F	Na	Cl
2.20	2.55	3.04	3.44	3.98	0.93	3.16

Two identical atoms share the pair equally: a nonpolar covalent bond. Between two different nonmetals the pair sits closer to the more electronegative atom, which carries a partial negative charge, δ−; the other is δ+. That is a polar covalent bond. Between a metal and a nonmetal the electron is in effect transferred, leaving a cation and an anion held by their attraction: an ionic bond.

bond	ΔEN	type
H–H	0.00	nonpolar covalent
H–C	0.35	nonpolar covalent (nearly)
H–Cl	0.96	polar covalent
H–O	1.24	polar covalent
H–F	1.78	polar covalent
Na–Cl	2.23	ionic

Bigger difference, more polar bond; there is no sharp line between polar covalent and ionic. As a working rule, metal with nonmetal is ionic and nonmetal with nonmetal is covalent, but the best evidence is the substance’s properties. Metal atoms bonded to each other share their valence electrons across the whole piece: metallic bonding (2.4).

2.2 · Intramolecular force and potential energy

why a bond has a length

As two hydrogen atoms approach, each electron is drawn to both nuclei, and the energy falls. Pushed closer still, the two nuclei repel, and it climbs steeply.

The graph plots potential energy against the distance r between the nuclei; zero is the two atoms far apart. The bottom of the well is where attraction and repulsion balance:

its distance is the bond length, 74 pm for H₂;
its depth is the bond energy, 436 kJ/mol: the energy needed to pull the atoms apart.

The red arrows on the atoms show the net force: inward beyond 74 pm, outward inside it.

Per bond. $\dfrac{436\,000\ \text{J/mol}}{6.022\times10^{23}\ \text{mol}^{-1}} = 7.24\times10^{-19}\ \text{J}$ for one H–H bond.

Cl₂ (blue) has larger atoms: its well is farther out, at 199 pm, and shallower, 242 kJ/mol. More shared pairs between the same two atoms make a shorter, stronger bond:

bond	order	length (pm)	energy (kJ/mol)
C–C	1	154	347
C=C	2	134	614
C≡C	3	120	839

Between ions the attraction follows Coulomb’s law, $F \propto \dfrac{q_1 q_2}{r^2}$ : larger charges and smaller ions attract more strongly.

2.3 · Structure of ionic solids

a lattice of alternating charges

An ionic solid has no molecules. Cations and anions stack in a repeating three-dimensional lattice, arranged so each ion is surrounded by ions of the opposite charge.

In sodium chloride each Na⁺ has six Cl⁻ neighbors and each Cl⁻ six Na⁺, 282 pm apart. The arrangement keeps attraction as high and repulsion as low as possible. Cl⁻ (181 pm) is much larger than Na⁺ (102 pm): adding an electron makes an anion larger than its atom, removing one makes a cation smaller.

The strength of the lattice follows Coulomb’s law in the ion charges and the distance between ion centers:

solid	charges	d (pm)	lattice energy (kJ/mol)
LiF	±1	209	1036
NaF	±1	235	923
NaCl	±1	283	786
KCl	±1	319	715
MgO	±2	212	3791

Example. MgO against NaF: the distances are close (212 and 235 pm), but the charges are doubled:

\frac{F_\text{MgO}}{F_\text{NaF}} = \frac{2\cdot2/212^2}{1\cdot1/235^2} = 4.9

So MgO melts far higher (2852 °C against NaF’s 993 °C). Charge matters more than size.

The same picture explains the properties. Ionic solids are hard, with high melting points. They are brittle: shift one layer by one ion and like charges sit on like, repel, and the crystal cleaves. They do not conduct as solids, since the ions are fixed; melted or dissolved, the ions move and carry current.

2.4 · Structure of metals and alloys

cations in a sea of electrons

In a metal the valence electrons leave their atoms and move through the whole solid. The metal is a lattice of cations held together by this sea of delocalized electrons.

That explains the properties of metals. They conduct electricity and heat, because the electrons are free to move. They are malleable and ductile: a layer of cations can slide past the next without breaking anything, since the electrons go with it and no like charges are ever brought face to face. Compare the ionic crystal in 2.3.

An alloy is a mixture of a metal with other elements, and it keeps metallic properties.

In a substitutional alloy the atoms are of similar size, and one replaces the other at lattice sites. Brass: zinc (134 pm) in copper (128 pm), radii 4.7% apart. Its density lies between those of the two metals.
In an interstitial alloy much smaller atoms fill the holes between the larger ones. Steel: carbon (77 pm) in iron (126 pm). The small atoms bond into the lattice and jam the layers, so steel is more rigid, and less malleable and ductile, than iron.

In the figure the top rows are pushed one atom sideways: copper and brass slide; steel sticks.

2.5 · Lewis diagrams

placing the valence electrons

A Lewis diagram shows every valence electron in a molecule or ion, as bonding pairs (lines) between atoms and lone pairs (dots) on one atom.

Drawing CO₂, step by step:

Count the valence electrons: $4 + 2\times6 = 16$ . Add one for each negative charge on an ion; take one away for each positive.
Connect the atoms with single bonds. The least electronegative atom goes in the middle; H is never central. 4 electrons used.
Fill the outer atoms to eight with lone pairs. All 16 are used, but carbon has only four.
If the central atom is short, move lone pairs from outer atoms into bonds. Two moves give O=C=O, and every atom has an octet.

An octet counts the bonding pairs as belonging to both atoms. Hydrogen holds two electrons, not eight.

Example. NH₃ has $5 + 3\times1 = 8$ valence electrons: three N–H bonds use six, and the last two are a lone pair on N.

Not every molecule obeys the octet rule. Boron in BF₃ has six electrons. NO has an odd number, 11, so one atom must be short. Atoms in period 3 and beyond can hold more than eight, as S does in SF₆ (twelve) and P in PCl₅ (ten).

2.6 · Resonance and formal charge

choosing and combining Lewis diagrams

Some molecules and ions have more than one valid Lewis diagram. Formal charge picks the best; resonance combines equivalent ones.

Formal charge is the charge an atom would carry if every bonding pair were shared exactly equally:

\text{FC} = V - L - \tfrac12 B

with V the atom’s valence electrons, L its lone-pair electrons, B its bonding electrons. The formal charges add up to the charge on the species. The best diagram has formal charges as close to zero as possible, and puts any negative formal charge on the more electronegative atom.

CO₂	O	C	O
O=C=O	0	0	0
O≡C–O	+1	0	−1

O=C=O wins: all zeros.

Resonance. Nitrate, NO₃⁻, has 24 valence electrons. Three diagrams fit, the same except for which O holds the double bond. In each, N has formal charge +1, the double-bonded O 0, the single-bonded O’s −1: total −1.

The ion is none of these. It is the resonance hybrid, the average: the π pair is delocalized over all three bonds. Each N–O bond has order (2 + 1 + 1)/3 = 4/3, all three are the same length, between a single and a double bond, and each O carries −⅔. The ion does not flip between the structures.

2.7 · VSEPR and molecular shape

electron domains spread out

The electron pairs around a central atom repel each other and spread as far apart as they can. That is valence shell electron pair repulsion, VSEPR.

Count electron domains on the central atom: each lone pair is one, and each bond is one, whether single, double or triple. The number of domains fixes their arrangement; the molecular shape is named from the atoms alone.

	domains	lone pairs	shape	angle
CO₂	2	0	linear	180°
BF₃	3	0	trigonal planar	120°
SO₂	3	1	bent	119°
CH₄	4	0	tetrahedral	109.5°
NH₃	4	1	trigonal pyramidal	107°
H₂O	4	2	bent	104.5°
PCl₅	5	0	trigonal bipyramidal	90°, 120°
SF₄	5	1	seesaw	< 90°, < 120°
ClF₃	5	2	T-shaped	< 90°
XeF₂	5	3	linear	180°
SF₆	6	0	octahedral	90°
BrF₅	6	1	square pyramidal	< 90°
XeF₄	6	2	square planar	90°

A lone pair is held by one nucleus only and spreads wider than a bonding pair, so it squeezes the bonds together: CH₄, NH₃ and H₂O all have four domains, but their angles fall from 109.5° to 107° to 104.5°.

With five domains, lone pairs take the equatorial positions, where they have the most room. With six, two lone pairs sit opposite each other.

2.7 · Molecular polarity

bond dipoles add up, or cancel

A molecule is polar if its charge is lopsided: one end δ+, the other δ−. That takes polar bonds and a shape in which they do not cancel.

Each polar bond has a bond dipole, drawn as an arrow toward the more electronegative atom. The molecule’s net dipole is their sum as vectors.

CO₂ is linear. Its two C=O dipoles are equal and opposite, so it is nonpolar, though both bonds are polar. BF₃ (trigonal planar) and CH₄ and CCl₄ (tetrahedral) cancel the same way.
H₂O is bent. Its two O–H dipoles point partly the same way and add to a net dipole toward O: it is polar. So is NH₃, a pyramid with its lone pair at the top.
Any atom swapped in a symmetric shape breaks the balance: CH₂Cl₂ is polar.

Between charged plates, a polar molecule feels a turning force. Water swings to point its O end at the positive plate and its H end at the negative one. CO₂ feels no net turning force and keeps tumbling freely.

A lone pair on the central atom usually means a polar molecule, unless the shape stays symmetric, as in XeF₂ (linear) and XeF₄ (square planar).

2.7 · Hybridization, σ and π bonds

what a double bond is made of

The first bond between two atoms is a σ (sigma) bond: orbitals overlap end to end, on the line between the nuclei. A second or third bond is a π (pi) bond: p orbitals overlap side by side, above and below that line.

	C–C	σ	π	each C	angle
C₂H₆	single	7	0	sp³	109.5°
C₂H₄	double	5	1	sp²	120°
C₂H₂	triple	3	2	sp	180°

A single bond is one σ; a double bond is one σ and one π; a triple bond is one σ and two π. Every C–H bond is σ.

A σ bond is symmetric around its axis, so ethane’s two ends turn freely. A π bond needs its two p orbitals parallel: twisting one end would break it, so ethene is held flat, the reason a C=C bond does not rotate.

Hybridization labels the central atom by its number of electron domains: two domains sp (linear, 180°), three sp² (trigonal planar, 120°), four sp³ (tetrahedral, 109.5°). In nitrate (2.6) the N has three domains: sp². The AP exam asks only for sp, sp² and sp³, not how hybrid orbitals are derived.