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. So the key idea is not just “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. Their electronegativities are usually fairly high, but not different enough for full electron transfer. A covalent substance may be an element, such as $Cl_2$, or a compound, such as $CH_3OH$. Covalent bonding can therefore happen 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 is different. It requires different elements with a substantial electronegativity difference, so electron transfer becomes 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, including C, N, O and F, because 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. “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 $BeCl_2$ and $BF_3$, 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. It can use dots, crosses, dashes, or a mixture. Dots and crosses help when you need to show which atom supplied which electron; dashes are quicker once the bonding is clear.

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, bonding pairs go between atoms. Lone pairs are drawn 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, $NH_4^+$ has no lone pair on nitrogen after bonding, while $NO_2^-$ needs resonance ideas later to describe its bonding fully. Organic examples such as $CH_3Cl$ and $HCN$ are drawn using exactly the same electron-counting logic as inorganic examples such as $OF_2$ and $NH_4^+$.

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 is the number of shared electron pairs between two bonded atoms. Single, double, and triple bonds have bond orders 1, 2, and 3 respectively.

As bond order increases, the atoms are drawn closer and the bond gets stronger. For the same two bonded elements, the pattern is usually:

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 can also affect reactivity. They contain electron density that suitable reagents may attack, and the extra bonding is not simply “more of the same”. In organic chemistry, multiple bonds often act as sites for addition reactions. A stronger multiple bond, though, 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 the name “dative covalent bond”; it refers to the same idea.

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

For example, $NH_3$ can use the lone pair on its nitrogen atom to bond to $H^+$, forming $NH_4^+$. In a Lewis formula, an arrow from the donor atom to the acceptor atom may show the new coordination bond. Once the bond has formed, though, it is not weaker or “half a bond”; the N–H bonds in $NH_4^+$ are equivalent.

A ligand is an ion or molecule that donates a lone pair to a central metal ion, forming a coordination bond. This type of bonding is common in transition element complexes. In $[Co(NH_3)_6]^{3+}$, 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 $H^+$, $BF_3$, $AlCl_3$, or a transition metal ion.

The VSEPR idea

The VSEPR model is a bonding model used to predict molecular shape from the repulsions between electron domains around a central atom. Lewis formulas are flat; real molecules are three-dimensional, so VSEPR gives us a way to move from the drawing to the shape.

An electron domain is a region of high electron density around an atom that repels other regions of high electron density. Each single bond, double bond, triple bond, or lone pair counts as one electron domain. For geometry, a multiple bond still counts as one domain, even though it contains more than one electron pair.

Use the method like this:

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, because a lone pair is held by only one nucleus and takes up more space. So $NH_3$ has a smaller H–N–H angle than $CH_4$, and $H_2O$ has a smaller H–O–H angle than $NH_3$.

Multiple bonds repel more strongly than single bonds too. In a molecule such as $H_2CO$, the $C=O$ domain pushes the C–H domains a little closer together, so the angles are not exactly the ideal trigonal planar value.

VSEPR works very well for quick predictions, especially with small main-group molecules and ions. But it is mainly a shape-prediction model. 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 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. 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 becomes $\delta^-$ and the less electronegative atom becomes $\delta^+$.

A non-polar covalent bond

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

A bond dipole

is a separation of partial positive and partial negative charge across a covalent bond. You can show it using partial charges, $\delta^+$ and $\delta^-$, or as 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 the electronegativity values. A larger difference gives a more polar bond. If the difference is very large, the ionic model becomes more useful; if it is small, the covalent model usually fits better. There is no magical cliff edge. Bonding lies on a continuum.

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

Molecular polarity

is the uneven spread of electron density across a whole molecule or ion, giving a net dipole. Two factors have to be considered together: the polarity of the bonds and the geometry of the species.

A dipole moment is a vector quantity showing the size and direction of charge separation in a bond or molecule.

If a molecule has

, it is non-polar overall; if it has $\mu > 0$, it is polar overall.

Use this routine:

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.

$CO_2$ has polar $C=O$ bonds, but its linear shape makes the two equal bond dipoles cancel. $BF_3$ has polar B–F bonds, although the trigonal planar arrangement cancels the dipoles. In $H_2O$, the O–H bonds are polar and the molecule is bent, so the dipoles do not cancel. $CHCl_3$ 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. Bigger molecules may contain both a polar region and a non-polar region. Surfactants show this clearly, with a polar or ionic head and a long non-polar hydrocarbon tail.

A molecule is infrared active when one of its vibrations changes its dipole moment. This is why molecular polarity and bond polarity matter later in IR spectroscopy. The key question is not just “has polar bonds”, but whether the vibration produces a changing dipole.

A covalent network structure is a giant structure where atoms are joined by covalent bonds in one continuous lattice. These substances aren’t made from separate small molecules, so their properties come from the covalent lattice, not 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 dramatically different.

Carbon allotropes

Diamond is a covalent network. Each carbon atom forms four covalent bonds in a tetrahedral arrangement, giving a rigid three-dimensional 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 is a layered covalent network. Each carbon atom bonds to three others in a trigonal planar hexagonal sheet, with one electron per carbon delocalized across the layer. Graphite conducts electricity along the layers because these electrons can move. The layers 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 a single layer of graphite. It is one atom thick, strong, flexible and electrically conducting because the same delocalized electron system runs through the sheet.

Fullerenes are carbon allotropes made from closed cages or tubes containing rings of carbon atoms. Buckminsterfullerene, $C_{60}$, is molecular rather than giant covalent: individual $C_{60}$ molecules are held together by intermolecular forces. Carbon nanotubes have strong covalent bonding within the tube and can conduct because of delocalized electrons.

Silicon and silicon dioxide

Silicon forms a covalent network similar in broad outline to diamond: each silicon atom bonds tetrahedrally to four other silicon atoms. It 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.

Silicon dioxide, $SiO_2$, is a covalent network where each silicon atom is bonded to four oxygen atoms, and each oxygen atom bridges two silicon atoms. 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 difference clear: when iodine sublimes or water boils, the intermolecular forces are overcome; the covalent bonds inside the molecules stay intact.

We use the term “bond” for strong attractions that define particles such as molecules, lattices or metallic structures. “Force” is broader and covers attractions between particles. Hydrogen bonding is historically called a “bond”, but in this topic it is treated 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 treated separately because it has a more specific structural requirement 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 become 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 matters 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 explains 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 produces an open network; in liquid water the arrangement is more disordered and 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 evolve 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 automatically when the 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 evaporating them only requires the 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. To vaporize or melt them, strong covalent bonds must be disrupted 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, since they have no mobile ions or delocalized electrons. Most covalent networks do not 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, and a solvent is the substance that does the dissolving.

A useful rule is “like dissolves like”: polar solutes tend to dissolve in polar solvents, while 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 used to identify properties of covalent substances include 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 in which components of a mixture move at different rates because they have different relative attractions to a mobile phase and a stationary phase. These attractions involve intermolecular forces.

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

A correctly measured $R_F$ value 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 the use of locating agents. For this topic, focus on paper chromatography and TLC as practical methods, and on explaining separation through intermolecular attractions.

A resonance structure is one of two or more valid Lewis formulas for the same arrangement of atoms, differing only in where the electrons are placed. You usually see resonance when a double bond, or a lone-pair/$\pi$-electron arrangement, could be drawn in more than one position.

Delocalization means electrons spread over more than two atoms instead of staying confined between one pair of atoms. The actual species does not rapidly flip between resonance structures. Its real structure is a resonance hybrid with delocalized electron density.

Ozone, $O_3$, is the classic first example. You can draw two Lewis formulas, each with one $O-O$ single bond and one $O=O$ double bond. Experimentally, 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 $NO_2^-$ and $CO_3^{2-}$. In carbonate, the $\pi$ bonding is delocalized over three $C-O$ regions, so each $C-O$ bond has bond order $1\frac{1}{3}$. The $C-O$ bonds are therefore equal, with lengths and strengths between typical single and double $C-O$ bonds.

Resonance also connects to ultraviolet absorption by oxygen allotropes. $O_2$ has an $O=O$ bond with higher bond order than the $O-O$ bonds in $O_3$, so dissociating them requires different photon energies, and therefore different wavelengths. That is why oxygen and ozone absorb different parts of ultraviolet radiation in the atmosphere.

Benzene, $C_6H_6$, is a planar cyclic molecule made up 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^^\circ.

One Lewis formula for benzene draws alternating $C-C$ single bonds and $C=C$ double bonds in a six-membered ring. The second equivalent resonance structure puts the double bonds in the alternate positions. A more accurate way to show benzene is a hexagon with a circle inside it, representing delocalized $\pi$ electrons spread around the ring.

Physical evidence supports this delocalized structure. X-ray diffraction shows that benzene is a regular hexagon, with all six $C-C$ bonds equal in length. The $C-C$ bond length in benzene lies between a typical $C-C$ single bond and a typical $C-C$ double bond. Bond strength data give intermediate values too, just as expected when the electrons are delocalized.

The chemical evidence points the same way. Benzene is unsaturated, but it doesn’t react like a normal alkene. Alkenes readily undergo addition reactions, where the $\pi$ bond is broken. Benzene usually undergoes substitution reactions instead, because addition would disrupt 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 releases much less energy than the theoretical molecule with three isolated double bonds would release. That energy difference shows the stabilizing effect of delocalization, and helps explain why benzene 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 $\pi$ system above and below the plane of the ring, and the stability gained when aromatic delocalization is restored after substitution. Benzene therefore attracts electrophiles, but 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 if the expected structure has an expanded octet. Expanded octets are associated 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. There are two kinds of position: equatorial positions, which lie in the triangular plane, and axial positions, which sit above and below that plane. Lone pairs prefer equatorial positions because this minimizes $90^\circ$ repulsions.

Six electron domains

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

Examples include $PF_5$ for trigonal bipyramidal, $SF_4$ for seesaw, $ClF_3$ for T-shaped, $I_3^-$ for linear with five domains, $SF_6$ for octahedral, $BrF_5$ for square pyramidal and $XeF_4$ for square planar. As with 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 split equally, while lone-pair electrons are counted entirely on the atom where they are drawn. Treat it as a bookkeeping method, not a measured charge map.

Formal charge is calculated using:

The sum of the formal charges must match the overall charge of the species. For instance, if a neutral molecule has formal charges adding to $+1$, the Lewis formula or the arithmetic is wrong.

When several Lewis formulas are possible, the preferred one 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 example, using expanded octets on a period 3 or heavier central atom can lower the formal charge values. Remember, though, that resonance may mean several equivalent formal-charge-minimized structures contribute to the actual ion.

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

A sigma bond is a covalent bond formed by head-on overlap of atomic orbitals, with electron density concentrated 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 formed by sideways overlap of parallel $p$ orbitals, with electron density concentrated on opposite sides of the bond axis.

Every single bond counts as 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 rule first — it’s the simplest one in this topic.

For organic examples, $CH_2=CH_2$ contains five sigma bonds and one pi bond. $CH_3C\equiv N$ contains five sigma bonds and two pi bonds. For inorganic ions, a Lewis formula of $NO_3^-$ 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 is more effective than sideways overlap. Two s orbitals cannot form a pi bond, since s orbitals are spherical and cannot give the side-by-side, above-and-below overlap pattern needed for $\pi$ electron density.

Hybridization is a bonding model where atomic orbitals on the same atom mix to make new hybrid orbitals. These orbitals are used for sigma bonding and lone pairs. In this syllabus you only need $sp$, $sp^2$ and $sp^3$ hybridization.

A hybrid orbital is an orbital made by mixing atomic orbitals on one atom, producing orbitals with new shapes and orientations. The number of hybrid orbitals formed equals the number of atomic orbitals mixed. In these cases, it also matches the number of electron domains used for VSEPR.

The three hybridization patterns

An $sp^3$ atom has four hybrid orbitals in a tetrahedral arrangement. In $CH_4$, carbon uses four $sp^3$ orbitals to make four sigma bonds. Nitrogen in $NH_3$ has four electron domains: three N–H sigma bonds and one lone pair, so it is $sp^3$ and trigonal pyramidal. Oxygen in $H_2O$ has two O–H sigma bonds and two lone pairs, so it is $sp^3$ and bent.

An $sp^2$ atom has three hybrid orbitals arranged trigonal planar, with one unhybridized $p$ orbital left over. The hybrid orbitals form sigma bonds or hold lone pairs. The unhybridized $p$ orbital can form a $\pi$ bond or take part in delocalization. In ethene, each carbon is $sp^2$: the C–C sigma bond and C–H sigma bonds use hybrid orbitals, while the $p$ orbitals overlap sideways to form the $\pi$ bond.

An $sp$ atom has two hybrid orbitals arranged in a straight line, plus two unhybridized $p$ orbitals. In ethyne, each carbon is $sp$: one C–C sigma bond and one C–H sigma bond use $sp$ orbitals, while two pairs of $p$ orbitals form two $\pi$ bonds.

Lewis formulas, electron domains, molecular geometry and hybridization fit together. Draw the Lewis formula, count domains around the atom, use VSEPR to find the electron domain geometry, then assign hybridization. Multiple bonds count as one domain because the $\pi$ bond does not use an additional hybrid orbital for the central atom’s basic geometry.

Hybridization also explains delocalization. In an ion such as $CH_3COO^-$, the carbon and both oxygens in the carboxylate group are $sp^2$. That gives parallel $p$ orbitals, allowing $\pi$ electrons to spread over the O–C–O system. This is why the two C–O bonds become equivalent in the delocalized ion.