What a covalent bond is

A covalent bond is a chemical bond where a shared pair of electrons is attracted electrostatically to the positively charged nuclei of two bonded atoms. Don’t reduce it to “sharing electrons”. The bond comes from the attraction between the shared negative charge and both nuclei, and that attraction holds the atoms together.

Covalent bonding is most common between non-metal atoms, which usually have relatively high electronegativities without a large enough difference for full electron transfer. A covalent substance may be an element, such as Cl₂, or a compound, such as CH₃OH. Covalent bonding can therefore occur between atoms of the same element: if the atoms are identical, neither one has the stronger pull needed to take electrons from the other. Ionic bonding, by contrast, needs different elements with a substantial electronegativity difference, so electron transfer is a sensible model.

Octets and their limits

The octet rule is a guideline stating that many atoms tend to form arrangements with eight electrons in their valence shell. It fits many period 2 atoms such as C, N, O and F, since eight valence electrons gives the same outer-shell arrangement as a noble gas.

A valence electron is an electron in the outer occupied shell of an atom that can participate in bonding. Noble gases already have stable valence-shell arrangements, so they form covalent bonds less readily than most other elements. The phrase “less readily” matters here: the octet rule is a model, not a law of nature.

There are limits to the octet rule. Hydrogen is stable with two electrons. Some atoms, especially Be and B in compounds such as BeCl₂ and BF₃, can be stable with fewer than eight electrons around the central atom; these species are electron-deficient molecules, which are covalent species whose central atom has fewer than an octet. Some species have odd numbers of electrons, and larger atoms can have expanded octets, which you meet later in this topic.

Lewis formulas

A Lewis formula is a two-dimensional representation of a covalently bonded species that shows all valence electrons as bonding pairs and non-bonding pairs. You may see dots, crosses, dashes, or a mixture of them. Dots and crosses help when you want to show which atom supplied which electron; dashes are quicker once the bonding is understood.

A bonding pair is a pair of electrons shared between two atoms in a covalent bond. A lone pair is a pair of valence electrons localized on one atom and not shared in a bond. In Lewis formulas, draw bonding pairs between atoms and lone pairs on the atom that holds them.

A reliable drawing routine is:

1. Count total valence electrons. For an anion, add one electron for each negative charge; for a cation, subtract one electron for each positive charge.
2. Divide by two to find the number of electron pairs.
3. Arrange the atoms. The atom present in the smallest number is often central; hydrogen is never central.
4. Connect atoms with single bonds.
5. Complete octets on outer atoms, except hydrogen which needs only two electrons.
6. Put remaining electron pairs on the central atom.
7. If the central atom lacks an octet, convert a lone pair on an outer atom into a double or triple bond, unless the species is a valid electron-deficient exception.

For ions, put the whole Lewis formula in square brackets and write the charge outside the brackets. For example, NH₄⁺ has no lone pair on nitrogen after bonding, while NO₂⁻ needs resonance ideas later to describe its bonding fully. Organic examples such as CH₃Cl and HCN follow exactly the same electron-counting logic as inorganic examples such as OF₂ and NH₄⁺.

A single bond is a covalent bond with one shared pair of electrons. A double bond is a covalent bond with two shared pairs of electrons. A triple bond is a covalent bond with three shared pairs of electrons.

Bond order means the number of shared electron pairs between two bonded atoms. A single bond has bond order 1, a double bond has bond order 2, and a triple bond has bond order 3.

When bond order increases, the atoms are pulled closer together and the bond gets stronger. For the same two bonded elements, the usual pattern is:

A bond length is the average distance between the nuclei of two bonded atoms. A bond enthalpy is the enthalpy change required to break one mole of a particular covalent bond in gaseous species. A higher bond enthalpy shows a stronger bond.

Carbon–carbon examples show higher bond order gives shorter, stronger bonds.

Double and triple bonds affect reactivity too. They have electron density that suitable reagents can attack, and the extra bonding is not just “more of the same”. In organic chemistry, multiple bonds often act as sites for addition reactions. Still, a stronger multiple bond is not automatically less reactive: reactivity depends on both bond strength and the mechanism available to the molecule.

A coordination bond is a covalent bond where the same atom donates both electrons in the shared pair. You may also see it called a “dative covalent bond”; it means the same thing.

A Lewis base donates an electron pair to form a bond. A Lewis acid accepts an electron pair to form a bond. In Lewis acid-base reactions, coordination bonds form naturally: the base provides both electrons, while the acid provides an empty orbital or an electron-deficient site.

For example, NH₃ can use the lone pair on its nitrogen atom to bond to H⁺, forming NH₄⁺. In a Lewis formula, the new coordination bond may be drawn as an arrow from the donor atom to the acceptor atom. Once the bond has formed, though, it is not weaker or “half a bond”; the N–H bonds in NH₄⁺ are equivalent.

A ligand is an ion or molecule that donates a lone pair to a central metal ion to form a coordination bond. This type of bonding is common in transition element complexes. In [Co(NH₃)₆]³⁺, for instance, each ammonia molecule donates a lone pair from nitrogen to the cobalt ion. To spot coordination bonds, look for an electron-pair donor with a lone pair bonded to an electron-pair acceptor, commonly H⁺, BF₃, AlCl₃, or a transition metal ion.

The VSEPR idea

The VSEPR model predicts the shape of a molecule from the repulsions between electron domains around a central atom. Lewis formulas are flat; real molecules are three-dimensional, so VSEPR gives a way to move from the drawing to the shape.

An electron domain is a region of high electron density around an atom, and these regions repel one another. A single bond, a double bond, a triple bond and a lone pair each count as one electron domain. For geometry, a multiple bond still counts as one domain, even though it contains more than one electron pair.

The method is simple:

1. Draw or imagine the Lewis formula.
2. Count electron domains around the central atom.
3. Name the electron domain geometry.
4. Count how many domains are bonding domains and how many are non-bonding domains.
5. Name the molecular geometry, which describes the positions of atoms, not lone pairs.

Two, three and four domains

A bond angle is the angle between two bonds that meet at the same atom. Lone pairs repel more strongly than bonding pairs, since a lone pair is held by only one nucleus and takes up more space. That’s why NH₃ has a smaller H–N–H angle than CH₄, and H₂O has a smaller H–O–H angle than NH₃.

Multiple bonds repel more strongly than single bonds as well. In H₂CO, for example, the C=O domain pushes the C–H domains slightly closer together, so the angles are not exactly the ideal trigonal planar value.

VSEPR is very useful for quick predictions, especially with small main-group molecules and ions. It does have limits. It mainly predicts shape; it does not calculate exact bond angles from first principles, and it does not by itself explain electron energies, magnetism or the full bonding in delocalized systems. In class, I would call it a very good map, not the territory itself.

Digital molecular models help a lot here. Rotate the models, record electron domain geometry, molecular geometry and bond angles where available, then compare species with and without lone pairs or multiple bonds. You can then see why a flat Lewis formula is only the starting point.

Electronegativity is a dimensionless measure of how strongly an atom in a bond attracts the shared electron pair towards itself. Data booklet values let you compare atoms directly.

A polar covalent bond is a covalent bond where one bonded atom attracts the shared electron pair more strongly, so partial charges form. The more electronegative atom is δ−, while the less electronegative atom is δ+.

A non-polar covalent bond is a covalent bond where electron density is distributed symmetrically enough that no bond dipole forms. Bonds between identical atoms, such as Br–Br, are non-polar because the electronegativity difference is zero.

A bond dipole is the separation of partial positive and partial negative charge across a covalent bond. You can show it with partial charges, δ+ and δ−, or with a vector arrow pointing towards the more electronegative atom, with a small cross or plus sign at the positive end.

To work out bond polarity, compare electronegativity values. The larger the difference, the more polar the bond. If the difference is very large, the ionic model becomes more useful; if it is small, the covalent model usually fits better. There isn’t a magical cliff edge. Bonding lies on a continuum.

Compounds with strongly polar covalent bonding can show some properties that resemble ionic compounds, such as relatively high boiling points compared with similar non-polar molecules, or greater solubility in polar solvents. Unless mobile ions are present, though, they will not conduct electricity in the same way as molten or aqueous ionic compounds.

Molecular polarity means electron density is unevenly spread across a whole molecule or ion, giving a net dipole. Two things have to be considered together: bond polarity and the geometry of the species.

A dipole moment is a vector quantity that shows the size and direction of charge separation in a bond or molecule. The symbol μ is the dipole moment, where μ represents charge separation (commonly reported in debye, D, rather than an SI unit in this course). If μ = 0, the molecule is non-polar overall; if μ is greater than 0, it is polar overall.

A safe routine is:

1. Decide which bonds are polar using electronegativity.
2. Draw or deduce the molecular geometry.
3. Add the bond dipoles as vectors.
4. Decide whether they cancel.

CO₂ has polar C=O bonds, but its linear shape makes the two equal bond dipoles cancel. BF₃ has polar B–F bonds, but the trigonal planar arrangement cancels the dipoles. H₂O has polar O–H bonds and a bent shape, so the dipoles do not cancel. CHCl₃ is polar because the tetrahedral bonds are not all the same, so the vector sum is not zero.

Hydrocarbons are usually treated as non-polar: C–C bonds are non-polar, and C–H bonds are only weakly polar. Larger molecules may contain both a polar region and a non-polar region. Surfactants show this well, with a polar or ionic head and a long non-polar hydrocarbon tail.

A molecule is infrared active when a vibration changes its dipole moment. This is why molecular polarity and bond polarity matter later in IR spectroscopy: the key test is not simply “has polar bonds”, but whether the vibration gives a changing dipole.

A covalent network structure is a giant structure where atoms are joined by covalent bonds in a continuous lattice. These substances are not made from separate small molecules, so their properties come from the covalent lattice rather than from intermolecular forces.

An allotrope is a different structural form of the same element in the same physical state. Allotropes contain the same element, but their bonding patterns and structures differ, so their properties can be very different.

Carbon allotropes

In diamond, each carbon atom forms four covalent bonds in a tetrahedral arrangement, producing a rigid three-dimensional covalent network. Diamond is extremely hard and has a very high melting point because many strong C–C bonds must be broken to disrupt the lattice. It does not conduct electricity because its valence electrons are localized in covalent bonds.

Graphite has a layered covalent network. Each carbon atom bonds to three others in a trigonal planar hexagonal sheet, leaving one electron per carbon delocalized across the layer. Because these electrons are mobile, graphite conducts electricity along the layers. The layers can slide over each other because only weak London dispersion forces act between them, which explains its use as a lubricant and in pencil “lead”.

Graphene is one layer of graphite. It is one atom thick, strong, flexible and electrically conducting because the same delocalized electron system extends across the sheet.

Fullerenes are carbon allotropes made from closed cages or tubes containing rings of carbon atoms. Buckminsterfullerene, C₆₀, is molecular rather than giant covalent: individual C₆₀ molecules are held together by intermolecular forces. Carbon nanotubes have strong covalent bonding within the tube and can conduct because they contain delocalized electrons.

Silicon and silicon dioxide

Silicon forms a covalent network broadly similar to diamond: each silicon atom bonds tetrahedrally to four other silicon atoms. Silicon has a high melting point, but Si–Si bonds are generally weaker than C–C bonds because silicon atoms are larger, so orbital overlap is less effective and the bond is longer.

In silicon dioxide, SiO₂, each silicon atom is bonded to four oxygen atoms, and each oxygen atom bridges two silicon atoms in a covalent network. Quartz, sand and many glasses are based on this Si–O network. Silicon dioxide is hard, has a high melting point, is insoluble in water and is a poor electrical conductor because there are no mobile charged particles.

An intermolecular force is an electrostatic attraction between separate molecules. An intramolecular bond is a chemical bond within a molecule. Keep the two separate: when iodine sublimes or water boils, the intermolecular forces are overcome, while the covalent bonds inside the molecules stay intact.

Chemists usually use “bond” for strong attractions that define particles such as molecules, lattices or metallic structures. “Force” is broader; it includes attractions between particles. Hydrogen bonding is still historically called a “bond”, but in this topic it counts as an intermolecular force.

A van der Waals force is any of the intermolecular attractions that include London dispersion forces, dipole-induced dipole forces and dipole-dipole forces. Hydrogen bonding is dealt with separately because it needs a more specific structure and is usually stronger.

London dispersion forces

A London dispersion force is an intermolecular attraction caused by temporary instantaneous dipoles inducing dipoles in neighbouring particles. Since all molecules have electrons, all molecules experience London dispersion forces.

London dispersion forces get stronger as polarizability increases. Polarizability is the ease with which an electron cloud can be distorted to form an induced dipole. Larger molecules with more electrons are usually more polarizable. Shape plays a part too: long, straight molecules have more surface contact than compact branched molecules, so they usually have stronger dispersion forces.

Dipole-induced dipole and dipole-dipole forces

A dipole-induced dipole force is an intermolecular attraction in which a polar molecule induces a temporary dipole in a neighbouring non-polar molecule. For example, small amounts of non-polar gases can dissolve in polar water because this interaction exists, though it is weak.

A dipole-dipole force is an intermolecular attraction between permanent dipoles in polar molecules. Polar molecules still have London dispersion forces as well; do not replace LDFs with dipole-dipole forces. Add them.

Hydrogen bonding

A hydrogen bond is an attractive interaction in which a hydrogen atom covalently bonded to a highly electronegative atom is attracted to an electronegative atom in a neighbouring molecule or another part of the same molecule. At school level, look especially for H bonded directly to N, O or F, interacting with a lone pair on N, O or F.

Hydrogen bonding accounts for several unusual properties of water, including its high boiling point for such a small molecule, high surface tension and the lower density of ice compared with liquid water. In ice, hydrogen bonding forms an open network. In liquid water, the arrangement is more disordered and the molecules pack closer together.

Real gases deviate from ideal behaviour partly because real molecules attract each other. At low temperature, intermolecular attractions matter more because particles have less kinetic energy to overcome them. Scientific definitions can shift over time as well: improved experimental and theoretical tools have led organizations such as IUPAC to refine the definition of hydrogen bonding beyond a simple classroom rule.

For molecules with similar molar masses, the usual strength order is:

London dispersion forces < dipole-dipole forces < hydrogen bonding.

Don’t apply this order mechanically when molar masses are very different. A large non-polar molecule can have stronger London dispersion forces than a much smaller polar molecule.

Volatility

Volatility is the tendency of a substance to vaporize. Molecular covalent substances are often volatile because boiling or evaporation only requires intermolecular forces to be overcome. Stronger intermolecular forces give lower volatility and a higher boiling point.

Covalent network substances are non-volatile and have very high melting and boiling points, since melting or vaporizing them disrupts strong covalent bonds throughout the lattice.

Comparison of typical properties of molecular covalent and covalent network substances.

Electrical conductivity

Electrical conductivity is the ability of a material to carry charge through mobile charged particles. Most molecular covalent substances don’t conduct electricity, as they have no mobile ions or delocalized electrons. Most covalent networks also fail to conduct for the same reason.

Graphite and graphene are important exceptions. They contain delocalized electrons that can move through the carbon layers. Silicon is a semiconductor, so its conductivity lies between that of a conductor and an insulator.

Solubility

Solubility is the extent to which a solute dissolves in a solvent to form a solution. A solute is the substance being dissolved, while a solvent is the substance that does the dissolving.

A useful rule is “like dissolves like”: polar solutes tend to dissolve in polar solvents, and non-polar solutes tend to dissolve in non-polar solvents. New solute-solvent attractions must compensate for the attractions broken between solute particles and between solvent particles.

A miscible liquid is a liquid that mixes with another liquid in all proportions. A hydrophobic group is a non-polar part of a molecule that interacts poorly with water. A hydrophilic group is a polar or ionic part of a molecule that interacts favourably with water. A surfactant is a molecule or ion with both hydrophilic and hydrophobic regions that can help disperse non-polar grease in water.

Functional groups often control intermolecular forces. An –OH group can allow hydrogen bonding; a C=O group gives a strong dipole but no hydrogen bonding between identical molecules unless H is bonded to N, O or F elsewhere; a long hydrocarbon chain increases London dispersion forces and decreases water solubility.

Experimental data can reveal the properties of covalent substances: melting point, boiling point or volatility observations, electrical conductivity of solid and liquid samples, and solubility tests in water and non-polar solvents. To distinguish sugar, sand and sodium chloride, for example, you would combine solubility, conductivity of aqueous solution, and heating behaviour, with appropriate safety controls.

Chromatography is a separation technique where the components of a mixture move at different rates because they’re attracted differently to a mobile phase and a stationary phase. Those attractions come from intermolecular forces.

The mobile phase moves through or over the stationary phase. The stationary phase stays fixed during the separation. If a component is more strongly attracted to the mobile phase, it travels further; if it is more strongly attracted to the stationary phase, it travels less far.

In paper chromatography, water held by cellulose fibres in the paper acts as the stationary phase, while the mobile phase is a solvent. In thin layer chromatography, the stationary phase is often polar silica or alumina on a plate, with a solvent as the mobile phase. When the solvent is non-polar and the stationary phase is polar, less polar components usually travel further than more polar components.

For a spot on a chromatogram:

RF = b / a, where RF is the retardation factor (dimensionless), b is the distance travelled by the centre of the spot from the baseline (m), and a is the distance travelled by the solvent front from the baseline (m).

If measured correctly, RF lies between 0 and 1. Use it for identification only under the same conditions: same stationary phase, solvent, temperature and method. In a real experiment, mark the baseline and solvent front in pencil, keep the sample spot above the solvent level, cover the chamber to reduce solvent evaporation, measure distances carefully and record uncertainties.

You don’t need the operational details of gas chromatography or high-performance liquid chromatography here, and you’re not required to know about locating agents. For this topic, focus on paper chromatography and TLC as practical methods, and on interpreting separation through intermolecular attractions.

A resonance structure is one of two or more valid Lewis formulas for the same arrangement of atoms; only the electron placement changes. You usually meet resonance when a double bond, or a lone-pair/π-electron arrangement, can be drawn in more than one position.

Delocalization means electrons spread over more than two atoms, rather than being held between just one pair of atoms. The actual species does not rapidly flip from one resonance structure to another. It is better represented as a resonance hybrid, with delocalized electron density.

Ozone, O₃, is the classic first example. You can draw two Lewis formulas, each with one O–O single bond and one O=O double bond. In experiments, though, the two O–O bonds are equal. Their bond order is 1.5: three bonding electron pairs are spread over two O–O bonding regions.

The same idea works for ions such as NO₂⁻ and CO₃²⁻. In carbonate, π bonding is delocalized over three C–O regions, so each C–O bond has bond order 1⅓. As a result, the C–O bonds are equal, with lengths and strengths between typical single and double C–O bonds.

Resonance also connects to ultraviolet absorption by oxygen allotropes. O₂ has an O=O bond with higher bond order than the O–O bonds in O₃, so it takes different photon energies, and therefore different wavelengths, to dissociate them. That is why oxygen and ozone absorb different parts of ultraviolet radiation in the atmosphere.

Benzene, C₆H₆, is a planar cyclic molecule made of six carbon atoms and six hydrogen atoms. Each carbon bonds to two neighbouring carbons and one hydrogen, so the geometry around each carbon is trigonal planar, with bond angles close to 120°.

A first Lewis formula for benzene uses alternating C–C single bonds and C=C double bonds in a six-membered ring. A second, equivalent resonance structure puts the double bonds in the alternate positions. The usual better model is a hexagon with a circle inside it, showing the delocalized π electrons spread around the ring.

Physical evidence supports this delocalized structure. X-ray diffraction shows a regular hexagon, with all six C–C bonds equal in length. The C–C bond length in benzene sits between a typical C–C single bond and a typical C=C double bond. Bond strength data also give intermediate values, just as delocalization would predict.

The chemical evidence matters too. Benzene is unsaturated, but it doesn’t react like a normal alkene. Alkenes readily undergo addition reactions that break the π bond. Benzene tends to undergo substitution reactions instead, because addition would destroy the stable delocalized ring.

Resonance energy is the extra stability of a delocalized species compared with a hypothetical localized structure. When benzene is hydrogenated, it is much less exothermic than the theoretical molecule with three isolated double bonds would be. That energy difference shows that delocalization stabilizes benzene, which helps explain why it is relatively unreactive in addition reactions.

Evidence for benzene delocalization from bond data and hydrogenation energy.

The structural features that favour electrophilic substitution are the electron-rich delocalized π system above and below the plane of the ring, plus the stability gained when aromatic delocalization is restored after substitution. Benzene attracts electrophiles, but it resists reactions that permanently remove its delocalized ring.

An expanded octet is a valence-shell arrangement where the central atom has more than eight electrons around it in a Lewis formula. For this syllabus, focus on species with five or six electron domains around the central atom.

When you draw these Lewis formulas, count the valence electrons, then place bonds and lone pairs as usual. Don’t force the central atom back to eight electrons when a valid expanded-octet structure is expected. Expanded octets are linked with atoms in period 3 and below; small period 2 atoms such as C, N, O and F do not expand their octets in this course model.

Five electron domains

Five electron domains produce a trigonal bipyramidal electron domain geometry. The positions are not all the same: equatorial positions lie in the triangular plane, while axial positions sit above and below that plane. Lone pairs usually take equatorial positions, as this minimizes 90° repulsions.

Six electron domains

Six electron domains produce an octahedral electron domain geometry. The common molecular geometries are:

Typical examples are PF₅ for trigonal bipyramidal, SF₄ for seesaw, ClF₃ for T-shaped, I₃⁻ for linear with five domains, SF₆ for octahedral, BrF₅ for square pyramidal and XeF₄ for square planar. As in the smaller VSEPR shapes, lone pairs compress bond angles because they repel more strongly than bonding domains.

Formal charge is the hypothetical charge given to an atom in a Lewis formula when bonding electrons are shared equally, while lone-pair electrons are treated as belonging completely to the atom they are drawn on. It’s a bookkeeping tool, not a measured charge map.

Use this expression to calculate formal charge:

FC = VE − (NBE + ½BE), where FC is formal charge (dimensionless charge number), VE is the number of valence electrons in the free atom (dimensionless electron count), NBE is the number of non-bonding electrons assigned to the atom in the Lewis formula (dimensionless electron count), and BE is the number of bonding electrons around the atom in the Lewis formula (dimensionless electron count).

The formal charges must add up to the overall charge of the species. So, if a neutral molecule has formal charges adding to +1, the Lewis formula or the arithmetic is wrong.

When more than one Lewis formula can be drawn, the preferred formula usually has:

• formal charges as close to zero as possible;
• the smallest separation of positive and negative formal charges;
• negative formal charge on the more electronegative atom, if a negative formal charge is unavoidable.

In many oxoanions, for instance, structures with expanded octets on a period 3 or heavier central atom can lower the formal charge values. Resonance still matters: several equivalent formal-charge-minimized structures may contribute to the actual ion.

Formal charge and oxidation state are based on different assumptions. Formal charge treats bonding electrons as shared equally. Oxidation state is a formal electron-accounting value assigned by assuming bonding electrons belong to the more electronegative atom. For the same atom in the same species, the two numbers often differ.

A sigma bond is a covalent bond made when atomic orbitals overlap head-on, so the electron density lies along the bond axis. The bond axis is the imaginary line joining the nuclei of the bonded atoms.

A pi bond is a covalent bond made by sideways overlap of parallel p orbitals, with electron density on opposite sides of the bond axis.

Every single bond is one sigma bond. A double bond has one sigma bond and one pi bond. A triple bond has one sigma bond and two pi bonds. Use this counting rule; it’s the simplest one in the topic.

For organic examples, CH₂=CH₂ contains five sigma bonds and one pi bond. CH₃C≡N contains five sigma bonds and two pi bonds. For inorganic ions, a Lewis formula of NO₃⁻ with one N=O and two N–O bonds contains three sigma bonds and one pi bond in that resonance structure; the real ion is delocalized, but the sigma/pi count comes from the displayed Lewis formula.

Sigma bonds are usually stronger than pi bonds because head-on overlap works better than sideways overlap. Two s orbitals cannot form a pi bond because s orbitals are spherical, so they cannot give the side-by-side, above-and-below overlap pattern needed for π electron density.