Covalent bonding

A covalent bond is a shared pair of electrons between two non-metal atoms. Sharing lets each atom count the shared electrons towards a stable noble-gas configuration (the octet rule, or a duet for H).

Lewis formulas (electron-dot diagrams) show every valence electron:

• Each bonding pair is drawn as a line (or two dots) between the atoms.
• Each lone pair (non-bonding pair) is drawn as a pair of dots on one atom.
• Atoms may share one, two or three pairs, giving single, double or triple bonds.

To draw one:

1. Count the total valence electrons from all atoms.

2. Place the least electronegative atom in the centre (never H).

3. Add single bonds, then complete octets with lone pairs.

4. If an atom is short of an octet, form double or triple bonds.

For example, $\text{CO}_2$ has two $\text{C}{=}\text{O}$ double bonds and two lone pairs on each oxygen; $\text{N}_2$ has a triple bond and one lone pair on each nitrogen.

Covalent substances are usually molecular: discrete molecules held internally by strong covalent bonds but attracted to each other only by weaker intermolecular forces, so many are gases, liquids or low-melting solids.

Bond order is the number of shared pairs between two atoms: 1 (single), 2 (double) or 3 (triple).

As bond order increases:

• Bond length decreases - more shared electrons pull the nuclei closer.
• Bond strength (bond enthalpy) increases - more shared electron density means a stronger attraction to break.

So for carbon-carbon bonds:

$$\text{length: } \text{C–C} > \text{C=C} > \text{C}\equiv\text{C}$$

$$\text{strength: } \text{C–C} < \text{C=C} < \text{C}\equiv\text{C}$$

A shorter bond is (almost always) a stronger bond. Bond enthalpies are average values listed in the data booklet and are always positive because breaking bonds absorbs energy.

Bond length also depends on atomic radius: bonds between larger atoms are longer (e.g. $\text{H–I} > \text{H–Cl}$), and longer bonds are generally weaker. This trend explains why hydrogen halide bond strength falls down the group, which links to their thermal stability and acidity.

A coordination bond (also called a dative covalent bond) is a covalent bond in which both electrons of the shared pair come from the same atom - usually an atom with a lone pair.

It is often drawn with an arrow pointing from the donor atom to the acceptor atom, but once the bond has formed it is identical to any other covalent bond. There is no way to tell which electrons came from where.

Common examples:

• The ammonium ion $\text{NH}_4^{+}$: the lone pair on N in $\text{NH}_3$ forms a fourth N-H bond by donating to $\text{H}^{+}$. All four N-H bonds are then equivalent.
• The hydronium ion (oxonium) $\text{H}_3\text{O}^{+}$: a lone pair on O in water bonds to $\text{H}^{+}$.
• Many complex ions, where ligands such as $\text{H}_2\text{O}$ or $\text{NH}_3$ donate lone pairs to a central metal ion.

The key idea is the source of the electrons, not the final behaviour. To recognise dative bonding, look for a species formed by an atom with a lone pair joining to an electron-deficient atom or ion.

VSEPR (Valence Shell Electron Pair Repulsion) predicts molecular shape: electron domains around a central atom repel and arrange themselves as far apart as possible. A domain is a region of electron density - a single, double or triple bond each counts as one domain, and so does each lone pair.

By number of domains:

• 2 domains $\rightarrow$ linear, 180° (e.g. $\text{CO}_2$).
• 3 domains $\rightarrow$ trigonal planar, 120° (e.g. $\text{BF}_3$).
• 4 domains $\rightarrow$ tetrahedral, 109.5° (e.g. $\text{CH}_4$).

Lone pairs repel more strongly than bonding pairs, so they squeeze bond angles smaller than the ideal:

• $\text{NH}_3$: 4 domains, 1 lone pair $\rightarrow$ trigonal pyramidal, angle ~107°.
• $\text{H}_2\text{O}$: 4 domains, 2 lone pairs $\rightarrow$ bent (V-shaped), angle ~104.5°.

Method: count domains on the central atom, find the base geometry, then describe the shape of the atoms only (lone pairs are invisible in the named shape).

A polar bond forms when the two bonded atoms have different electronegativities. The more electronegative atom pulls the shared electrons closer, gaining a partial negative charge ($\delta^-$) while the other becomes $\delta^+$. This separation of charge is a bond dipole, shown with an arrow pointing towards $\delta^-$.

The larger the electronegativity difference, the more polar the bond. With a very large difference the bond becomes ionic; with zero difference (identical atoms, e.g. $\text{Cl}_2$) it is non-polar.

A molecule is polar overall only if the bond dipoles do not cancel - i.e. it has a net dipole moment. This depends on shape:

• $\text{H}_2\text{O}$ is polar: the two O-H dipoles do not cancel because the molecule is bent.
• $\text{CO}_2$ is non-polar: the two C=O dipoles are equal and opposite (linear), so they cancel.
• $\text{CCl}_4$ is non-polar: four symmetric C-Cl dipoles cancel in the tetrahedral shape.

So always check both the bond polarity and the symmetry of the molecule before deciding if it is polar.

In a covalent network (giant covalent) solid, atoms are joined by a continuous 3D lattice of strong covalent bonds. Breaking the solid means breaking covalent bonds, so these solids have very high melting points, are hard, and are usually insoluble.

Allotropes of carbon (same element, different bonding arrangements):

• Diamond: each C is bonded to 4 others, tetrahedrally, sp3-like. Extremely hard, very high melting point, does not conduct electricity (no free electrons).
• Graphite: each C is bonded to 3 others in flat hexagonal layers; the fourth electron is delocalized within each layer. Conducts electricity, and the layers slide easily so it is a good lubricant and is soft.
• Graphene: a single layer of graphite - one atom thick, very strong, an excellent electrical conductor.
• Fullerenes (e.g. $\text{C}_{60}$, buckminsterfullerene): closed cages of carbon; these are molecular, not network, so they have lower melting points and can dissolve in some solvents.

Silicon dioxide ($\text{SiO}_2$, quartz) is another network solid, with each Si bonded to 4 O and each O to 2 Si.

Intermolecular forces act between molecules and are much weaker than the covalent bonds within them. When a molecular substance melts or boils, only these intermolecular forces are overcome - the molecules stay intact.

There are three types:

1. London (dispersion) forces: present between all molecules. They arise from instantaneous, temporary dipoles caused by moving electrons. They get stronger with more electrons (larger molar mass / larger surface area), which is why boiling point rises down a group and along a homologous series.

2. Permanent dipole-dipole forces: between polar molecules, where $\delta^+$ of one is attracted to $\delta^-$ of another. These add to the dispersion forces.

3. Hydrogen bonding: the strongest for molecules of comparable size. It occurs when H is bonded to N, O or F and is attracted to a lone pair on N, O or F of a neighbour. It explains the unusually high boiling points of $\text{H}_2\text{O}$, $\text{NH}_3$ and $\text{HF}$, and why ice is less dense than water.

For molecules of similar size the strength generally increases London < dipole-dipole < hydrogen bonding. But this ordering is a per-comparison generalisation, not an absolute law: dispersion forces in a large, highly polarizable molecule (such as a big halogen or a long hydrocarbon) can outweigh the dipole-dipole or hydrogen bonding in a small molecule, because the total dispersion contribution grows with the number of electrons.

Stronger intermolecular forces $\rightarrow$ higher boiling point and lower volatility. Like dissolves like: polar solvents dissolve polar/ionic solutes; non-polar solvents dissolve non-polar solutes.

Chromatography separates a mixture based on how strongly each component is attracted to a stationary phase versus a moving mobile phase (solvent).

• Components that stick to the stationary phase move slowly.
• Components that prefer the mobile phase move far.

In paper or thin-layer chromatography (TLC), the sample is spotted on a baseline, the solvent rises and carries components different distances, and each forms a separate spot.

The retention factor is

$$R_f = \frac{\text{distance travelled by component}}{\text{distance travelled by solvent front}}$$

• Always measure both distances from the baseline (original spot).
• $R_f$ has no units and lies between 0 and 1.
• A given substance has a characteristic $R_f$ in a fixed solvent and stationary phase, so it can be used to identify components by comparison with known standards.

This formula is not given in the data booklet, so learn it. A higher $R_f$ means the component is more attracted to the mobile phase (more soluble / less polar interaction with the paper).

Resonance occurs when more than one valid Lewis structure can be drawn for a species, differing only in the positions of electrons (not atoms). The real molecule is none of these alone - it is a single resonance hybrid, a blend of all the contributors.

The extra electrons are delocalized - spread over several atoms rather than fixed in one bond. Consequences:

• Equal, intermediate bond lengths. In the carbonate ion $\text{CO}_3^{2-}$, three structures each show one $\text{C=O}$ and two $\text{C-O}$, but the real ion has three identical C-O bonds, intermediate between single and double.
• Extra stability. Delocalization lowers the energy, so resonance-stabilized species are more stable than any single structure suggests.

Other examples include the nitrate ion $\text{NO}_3^{-}$, the ozone molecule $\text{O}_3$, and the carboxylate ion $\text{RCOO}^{-}$ (which is why carboxylic acids are acidic - the conjugate base is delocalized and stabilized).

Draw resonance structures connected by a double-headed arrow ($\leftrightarrow$); this is not an equilibrium and must not use $\rightleftharpoons$.

Benzene, $\text{C}_6\text{H}_6$, is the classic example of delocalization. The molecule is a flat, regular hexagon of six carbons, each bonded to one hydrogen.

• Each carbon forms three sigma bonds (to two C and one H) and is sp2 hybridized, giving bond angles of 120°.
• Each carbon has one electron in a p orbital perpendicular to the ring. These six p orbitals overlap sideways all the way around, forming a continuous delocalized pi system above and below the ring plane.

Evidence for delocalization:

• All six C-C bonds are equal in length, intermediate between a single (0.154 nm) and a double bond (0.134 nm) at about 0.140 nm. There are no alternating single/double bonds.
• Benzene is more stable than the hypothetical 'cyclohexa-1,3,5-triene': its enthalpy of hydrogenation is less exothermic than three times that of an isolated $\text{C=C}$, and the difference is the resonance/delocalization (stabilization) energy.
• Benzene undergoes substitution, not addition, because addition would destroy the stable delocalized ring.

It is best represented as a hexagon with an inner circle showing the delocalized electrons.

Some central atoms can hold more than eight electrons in their valence shell - an expanded octet. This is only observed for atoms in Period 3 and below, which are larger and lie beyond Period 2, so they can accommodate extra electron pairs around the central atom. Period 2 atoms (C, N, O, F) cannot expand their octet.

(Older textbooks attribute this to 'empty d orbitals', but modern bonding theory finds that d-orbital involvement in main-group species such as $\text{SF}_6$ and $\text{PF}_5$ is negligible; for IB purposes treat the expanded octet as an empirical fact about Period 3+ atoms rather than something caused by d orbitals.)

These atoms can therefore have 5 or 6 electron domains, giving new geometries:

• 5 domains $\rightarrow$ trigonal bipyramidal, with angles of 90° and 120° (e.g. $\text{PF}_5$, phosphorus has 10 electrons).
• 6 domains $\rightarrow$ octahedral, with 90° angles (e.g. $\text{SF}_6$, sulfur has 12 electrons).

Lone pairs change the named shape just as in simpler VSEPR:

• $\text{XeF}_4$ (6 domains, 2 lone pairs) is square planar.
• $\text{ClF}_3$ (5 domains, 2 lone pairs) is T-shaped.

To work these out: count the total electron domains (bonds + lone pairs) on the central atom, choose the base 5- or 6-domain geometry, then place lone pairs in the positions that minimise repulsion and describe the shape of the atoms only.

Formal charge helps you choose the most likely Lewis structure when several can be drawn. It is the charge an atom *would* have if all bonding electrons were shared equally.

The formula (constructed, not in the data booklet) is:

$$\text{FC} = (\text{valence electrons}) - (\text{non-bonding electrons}) - \tfrac{1}{2}(\text{bonding electrons})$$

or equivalently $\text{FC} = V - L - \tfrac{1}{2}B$, where $L$ is lone-pair electrons and $B$ is the number of electrons in bonds.

Rules for using it:

• The sum of all formal charges must equal the overall charge of the species.
• The best (most stable) Lewis structure has formal charges closest to zero.
• Where formal charges are unavoidable, the negative formal charge should sit on the most electronegative atom.

For example, in $\text{CO}_2$ with two double bonds, C has $\text{FC} = 4 - 0 - 4 = 0$ and each O has $\text{FC} = 6 - 4 - 2 = 0$ - all zero, confirming this is the preferred structure over alternatives with single and triple bonds.

Covalent bonds form by orbital overlap, and there are two types:

• Sigma ($\sigma$) bond: formed by end-on (head-on) overlap of orbitals along the axis joining the two nuclei. Electron density lies directly between the nuclei. Every single bond is a sigma bond. Rotation is possible about a sigma bond when it is a lone single bond (as in the C-C bond of an alkane), but is prevented when a pi bond is also present (as in a double or triple bond).
• Pi ($\pi$) bond: formed by sideways overlap of parallel p orbitals, putting electron density above and below the bond axis. A pi bond locks rotation, which is why double bonds give rise to cis-trans (E/Z) isomerism.

Counting bonds:

• Single bond = 1 $\sigma$.
• Double bond = 1 $\sigma$ + 1 $\pi$.
• Triple bond = 1 $\sigma$ + 2 $\pi$.

So in ethyne $\text{HC}\equiv\text{CH}$ there are 3 sigma bonds (two C-H and one C-C) and 2 pi bonds. A pi bond is generally weaker than a sigma bond because sideways overlap is less effective, which is why the first bond of a double bond (the sigma) is harder to break than the second (the pi) - and why C=C undergoes addition reactions at the pi bond.

Hybridization is the mixing of an atom's atomic orbitals to form an equal number of equivalent hybrid orbitals that point towards the bonded atoms. It explains how a central atom's geometry arises and is read directly from the number of electron domains:

• 2 domains $\rightarrow$ sp (one s + one p) $\rightarrow$ linear, 180° (e.g. the carbons in $\text{HC}\equiv\text{CH}$, $\text{CO}_2$).
• 3 domains $\rightarrow$ sp2 (one s + two p) $\rightarrow$ trigonal planar, 120° (e.g. the carbons in ethene and benzene).
• 4 domains $\rightarrow$ sp3 (one s + three p) $\rightarrow$ tetrahedral, 109.5° (e.g. carbon in $\text{CH}_4$, the O in water).

Key link to bonding:

• The hybrid orbitals form sigma bonds and hold any lone pairs.
• Unhybridized p orbitals form pi bonds. An sp2 carbon keeps one p orbital for one pi bond (a double bond); an sp carbon keeps two p orbitals for two pi bonds (a triple bond or two perpendicular double bonds).

Quick method: count the electron domains on the atom, then assign sp / sp2 / sp3 for 2 / 3 / 4 domains. Lone pairs count as domains, so the O in water and the N in ammonia are both sp3.