2.1 Ionic and Covalent Bonding

Types of Chemical Bonds

Ionic and Covalent Bonding Fundamentals

Chemical bonds fall on a spectrum. At one end, you have ionic bonds with full electron transfer. At the other, nonpolar covalent bonds with perfectly equal sharing. Most real bonds land somewhere in between.

Ionic bonds form between metals and nonmetals through electron transfer. One atom gives up one or more electrons entirely, and another atom accepts them. This creates oppositely charged ions (cations and anions) held together by electrostatic attraction. Sodium chloride ($\text{NaCl}$) is the classic example: sodium loses one electron to become $\text{Na}^+$, and chlorine gains it to become $\text{Cl}^-$. The result isn't a discrete molecule but an extended crystal lattice of alternating ions.

Covalent bonds form between nonmetals through electron sharing. Instead of transferring electrons, atoms share one or more pairs to fill their valence shells. This produces discrete molecules (like $\text{CH}_4$) or extended network structures (like diamond). The shared electrons are attracted to both nuclei simultaneously, which is what holds the atoms together.

Within covalent bonds, there's an important distinction:

• Polar covalent bonds involve unequal sharing. The more electronegative atom pulls electron density toward itself, creating partial charges: $\delta^+$ on the less electronegative atom and $\delta^-$ on the more electronegative one. Water ($\text{H}_2\text{O}$) is a prime example, with oxygen pulling electron density away from hydrogen.
• Nonpolar covalent bonds involve equal (or nearly equal) sharing. Electron density is distributed symmetrically. This happens in homonuclear diatomics like $\text{O}_2$ or $\text{N}_2$, where both atoms have identical electronegativities.

Bond Polarity and Partial Charges

Bond polarity is determined by the electronegativity difference ($\Delta \chi$) between the two bonded atoms. As a rough guide:

• $\Delta \chi < 0.4$: nonpolar covalent
• $0.4 < \Delta \chi < 1.7$: polar covalent
• $\Delta \chi > 1.7$: ionic

These cutoffs aren't rigid boundaries. Bonding is a continuum, and context matters (for instance, $\text{HF}$ with $\Delta \chi = 1.78$ is still considered a covalent molecule).

Partial charges ($\delta^+$ and $\delta^-$) in polar bonds have real consequences. They drive intermolecular forces like hydrogen bonding and dipole-dipole interactions, which in turn affect boiling points, solubility, and other physical properties.

Dipole moments quantify the overall polarity of a molecule. A dipole moment is the vector sum of all individual bond dipoles, measured in Debye (D). This means molecular geometry matters: $\text{CO}_2$ has two polar $\text{C}=\text{O}$ bonds, but because they point in opposite directions (linear geometry), the bond dipoles cancel and the molecule has zero net dipole moment. Compare that to $\text{H}_2\text{O}$, where the bent shape means the bond dipoles don't cancel, giving water a dipole moment of 1.85 D.

Factors Influencing Bond Formation

Atomic Properties and Bonding Tendencies

Three periodic trends largely determine how atoms bond:

• Electronegativity measures an atom's ability to attract shared electrons in a bond. It increases left to right across a period (greater nuclear charge) and decreases top to bottom within a group (greater atomic radius and shielding). Fluorine has the highest electronegativity at 3.98 on the Pauling scale. Electronegativity differences between atoms tell you what type of bond will form.
• Electron affinity is the energy change when a gaseous atom gains an electron. A large negative electron affinity means the atom strongly "wants" that extra electron. Halogens have the most negative electron affinities among the main group elements, which is why they readily form anions ($\text{F}^-$, $\text{Cl}^-$, etc.).
• Ionization energy is the energy required to remove an electron from a gaseous atom. It increases across a period and decreases down a group. Alkali metals have low first ionization energies, making them prone to forming cations. Keep in mind that successive ionization energies increase dramatically, especially when you break into a filled shell. That's why sodium forms $\text{Na}^+$ but not $\text{Na}^{2+}$ under normal conditions.

Energetics of Ionic Compound Formation

Ionic compounds are thermodynamically stable because of lattice energy, the energy released when separated gaseous ions come together to form a crystalline solid. Lattice energy depends on two factors:

• Ionic charge: Higher charges mean stronger electrostatic attraction. $\text{MgO}$ (with $\text{Mg}^{2+}$ and $\text{O}^{2-}$) has a much larger lattice energy than $\text{NaCl}$ (with $\text{Na}^+$ and $\text{Cl}^-$).
• Ionic radius: Smaller ions pack more closely, increasing attraction. $\text{LiF}$ has a larger lattice energy than $\text{CsI}$.

This relationship is captured quantitatively by the Born-Landé equation, but the qualitative trend (higher charge and smaller size = larger lattice energy) is what you need to internalize.

The octet rule provides a useful guideline: main group atoms tend to gain, lose, or share electrons to achieve a noble gas configuration of 8 valence electrons (2 for hydrogen). This explains common ion charges like $\text{Na}^+$, $\text{Ca}^{2+}$, and $\text{Cl}^-$. But don't treat it as absolute. Elements in the third period and below can form expanded octets (like $\text{PCl}_5$ with 10 electrons around P), and some stable molecules have incomplete octets (like $\text{BF}_3$ with only 6 electrons around B).

The Born-Haber cycle is a thermodynamic tool that breaks the formation of an ionic compound from its elements into individual steps, each with a known energy:

1. Sublimation of the metal (solid → gas)
2. Dissociation of the nonmetal (e.g., $\frac{1}{2}\text{Cl}_2 \rightarrow \text{Cl}$)
3. Ionization of the metal atom (removing electrons)
4. Electron affinity of the nonmetal atom (gaining electrons)
5. Formation of the crystal lattice (gaseous ions → solid)

By Hess's law, the sum of all these steps equals the enthalpy of formation ($\Delta H_f$). You can use this cycle to calculate any one unknown step if you know the others. In practice, it's most often used to determine lattice energies, since those can't be measured directly.

Molecular Structure and Geometry

Lewis Structures and Electron Arrangement

Lewis structures are the starting point for understanding molecular bonding and shape. They map out how valence electrons are distributed as bonding pairs and lone pairs.

Steps to draw a Lewis structure:

1. Count total valence electrons. Sum the valence electrons of all atoms. For polyatomic ions, add electrons for negative charges and subtract for positive charges.
2. Identify the central atom. This is usually the least electronegative atom (hydrogen and fluorine are always terminal).
3. Connect atoms with single bonds. Each single bond uses 2 electrons. Subtract these from your total.
4. Distribute remaining electrons as lone pairs. Start with the terminal atoms, giving each an octet. Then place leftover electrons on the central atom.
5. Check octets. If the central atom lacks an octet, convert lone pairs on adjacent atoms into double or triple bonds.

Formal charge helps you evaluate competing Lewis structures. Calculate it as:

$\text{Formal charge} = \text{valence electrons} - \text{lone pair electrons} - \frac{1}{2}(\text{bonding electrons})$

The best Lewis structure minimizes formal charges across all atoms, and any negative formal charges should sit on the more electronegative atoms.

Resonance structures arise when more than one valid Lewis structure can be drawn for the same molecule. The nitrate ion ($\text{NO}_3^-$) is a classic case: you can place the double bond on any of the three oxygen atoms, giving three equivalent resonance structures. The real electron distribution is a weighted average (the resonance hybrid), with each $\text{N-O}$ bond having a bond order of $\frac{4}{3}$. Resonance structures are connected by a double-headed arrow ($\leftrightarrow$), not an equilibrium arrow.

Predicting Molecular Shapes

VSEPR theory (Valence Shell Electron Pair Repulsion) predicts molecular geometry based on a simple idea: electron domains around a central atom repel each other and arrange themselves to maximize the distance between them.

An electron domain is any region of electron density around the central atom: a single bond, a double bond, a triple bond, or a lone pair each count as one domain. The number of electron domains determines the electron-domain geometry:

The molecular geometry describes only the positions of atoms, ignoring lone pairs. This is where things get interesting: lone pairs occupy space but are invisible to molecular geometry. For example, water has 4 electron domains (tetrahedral electron-domain geometry), but 2 of those are lone pairs, so the molecular geometry is bent with a bond angle of about 104.5°.

Lone pairs compress bond angles because they exert stronger repulsion than bonding pairs (lone pair electron density is held closer to the nucleus and spreads over a larger angular range). The repulsion hierarchy is:

Common molecular geometries that result from lone pair effects:

• 3 electron domains, 1 lone pair → bent (e.g., $\text{SO}_2$)
• 4 electron domains, 1 lone pair → trigonal pyramidal (e.g., $\text{NH}_3$, bond angle ~107°)
• 4 electron domains, 2 lone pairs → bent (e.g., $\text{H}_2\text{O}$, bond angle ~104.5°)
• 5 electron domains, 1 lone pair → seesaw (e.g., $\text{SF}_4$)
• 5 electron domains, 2 lone pairs → T-shaped (e.g., $\text{ClF}_3$)
• 5 electron domains, 3 lone pairs → linear (e.g., $\text{XeF}_2$)
• 6 electron domains, 1 lone pair → square pyramidal (e.g., $\text{BrF}_5$)
• 6 electron domains, 2 lone pairs → square planar (e.g., $\text{XeF}_4$)

In trigonal bipyramidal geometries, lone pairs preferentially occupy equatorial positions because these have only two 90° interactions (vs. three for axial positions), minimizing repulsion.