When two nonmetal atoms meet
When sodium meets chlorine, sodium hands its electron over. But when a hydrogen atom meets a chlorine atom, both want to gain electrons, and neither will give one up. Their solution: each contributes one electron to a pair that both atoms share. Hydrogen now has 2 electrons around it and chlorine has 8, and both are stable.
Covalent bonds
A covalent bond共价键 is a bond formed when two atoms share a pair of electrons. Covalent bonds usually form between nonmetal atoms, whose electronegativities are too close for either to take the electrons completely.
- A compound held together only by covalent bonds is a covalent compound共价化合物 (or molecular compound), such as H₂O, CO₂, HCl, or CH₄. Most are made of molecules.
- Nonmetal elements such as H₂, Cl₂, and N₂ also contain covalent bonds, though they are not compounds.
There are several ways to draw a covalent molecule. Chinese textbooks use an electron-dot formula电子式, which draws each shared pair as two dots between the atoms, and a structural formula结构式, which draws each shared pair as a line and leaves out all other electrons. The Lewis structure used in American textbooks sits between them: shared pairs are lines, and the lone pairs孤电子对 that aren’t shared are still drawn as dots. For water:
Single, double, and triple bonds
Two atoms can share one, two, or three pairs of electrons, forming a single, double, or triple bond. The number of shared pairs is the bond order键级.
An oxygen atom has 6 valence electrons and needs 2 more, so two oxygen atoms share two pairs; a nitrogen atom needs 3 more, so two nitrogen atoms share three pairs.
Sigma and pi bonds
In terms of orbitals, a covalent bond forms when orbitals on two atoms overlap. They can overlap in two ways:
- A sigma (σ) bondσ 键 forms from head-on overlap along the line between the nuclei, so the electron density sits between them. Every single bond is a σ bond.
- A pi (π) bondπ 键 forms from side-by-side overlap of two p orbitals, so the electron density sits above and below that line. π bonds overlap less and are generally weaker than σ bonds.
A double bond is one σ bond plus one π bond; a triple bond is one σ bond plus two π bonds.
Bond length and bond energy
Two quantities describe a covalent bond:
- Bond length键长: the distance between the nuclei of the two bonded atoms.
- Bond energy键能: the energy needed to break 1 mol of a bond in gaseous molecules into gaseous atoms, in kJ/mol. The larger the bond energy, the stronger the bond and the more stable the molecule.
The higher the bond order, the more electrons are shared and the closer the atoms are pulled: the bond gets shorter and stronger. C–C, C=C, and C≡C bonds are 154, 134, and 120 pm long, with bond energies of 348, 614, and 839 kJ/mol.
Why do two atoms stop at a particular distance? Drag the slider to bring two hydrogen atoms together from far apart and watch the potential energy. Then switch to the second tab to compare several sets of bonds:
The curve is drawn with a Morse function, a standard model for the energy of a bond.
Average bond enthalpies and bond lengths (298 K); different textbooks' tables differ by a few kJ/mol.
Example 1: The nitrogen molecule
Draw the Lewis structure of N₂, and count its σ and π bonds.
- Count electrons. Each nitrogen atom has 5 valence electrons and needs 3 more to complete an octet.
- How many shared pairs? Each nitrogen contributes 3 electrons to 3 shared pairs, leaving one lone pair on each atom.
- Check the electron count. Around each nitrogen: 3 shared pairs + 1 lone pair = 4 pairs = 8 electrons. The molecule has 2 × 5 = 10 valence electrons, exactly 3 shared pairs plus 2 lone pairs.
- Draw it. The Lewis structure is N≡N with one lone pair on each N; the structural formula is just N≡N.
- σ and π. Two atoms share at most one σ bond, and any others are π bonds: a triple bond is 1 σ bond and 2 π bonds. Breaking the N≡N bond takes 941 kJ/mol, which is why nitrogen gas is so unreactive.
Example 2: Reading a potential energy curve
Use the potential energy curve for H₂ above: (1) What are the H–H bond length and bond energy? (2) Why don’t the two atoms keep getting closer?
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Bond length is where the curve bottoms out. The lowest point is at 74 pm, the distance at which the two atoms have the lowest energy and are most stable: bond length 74 pm.
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Bond energy is how deep the well is. The minimum is −436 kJ/mol, and far-apart atoms have potential energy 0:
Breaking 1 mol of H–H bonds absorbs 436 kJ: bond energy 436 kJ/mol.
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Why they stop. Closer than 74 pm, the repulsion between the two positive nuclei rises steeply and the potential energy shoots up. At 74 pm, attraction and repulsion balance.
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Watch the sign. A bond energy is positive (energy absorbed to break the bond); the −436 kJ/mol on the curve is the potential energy of the bonded system.
- H₂
H–H is a single bond: one σ bond.
- N₂
N≡N is a triple bond: one σ and two π bonds.
- O₂
O=O is a double bond: one σ and one π bond.
- CO₂
O=C=O has two double bonds, each with one π bond: 2 in all.
- HCN
H–C≡N: the C≡N triple bond has 2 π bonds.
- C₂H₄
The carbon–carbon double bond has 1 π bond; the C–H bonds are all σ.
- C₂H₂
H–C≡C–H: the carbon–carbon triple bond has 2 π bonds.
- CH₄
All four C–H single bonds are σ bonds.
- CH₂O
The C=O double bond has 1 π bond.
Common mistakes
Mistake 1: “Covalent bonds are found only in covalent compounds.” Elements such as H₂ and Cl₂ contain covalent bonds, and so does the OH⁻ ion inside the ionic compound NaOH. Only a compound with nothing but covalent bonds is called a covalent compound.
Mistake 2: “A double bond is twice as strong as a single bond, and a triple bond three times as strong.” A C=C bond takes 614 kJ/mol to break, less than twice the 348 kJ/mol of C–C. The extra bond in a double bond is a π bond, which is weaker than a σ bond.
Mistake 3: “When water boils, the O–H bonds in the molecules break.” Boiling only separates water molecules from each other; the molecules themselves are unchanged (lesson 2.4.8). Breaking O–H bonds takes temperatures above 2000 °C.
Quick check
Which of these molecules contains a triple bond?
Each nitrogen atom needs 3 more electrons, so the two atoms share three pairs: N≡N. O₂ and CO₂ have double bonds, and H₂O has single bonds.
Which statement about bond length and bond energy is correct?
The H–F bond energy (567 kJ/mol) is much larger than the H–I bond energy (299 kJ/mol), so HF is more stable. Longer bonds are generally weaker; C≡C (839 kJ/mol) is less than three times C–C; and π bonds are generally weaker than σ bonds.
Summary
- A covalent bond is a shared pair of electrons between two atoms, usually nonmetals; a compound with only covalent bonds is a covalent compound.
- Electron-dot formulas draw shared pairs as dots, structural formulas as lines; Lewis structures use lines for shared pairs and dots for lone pairs. Single, double, and triple bonds share one, two, and three pairs.
- A single bond is a σ bond; a double bond is 1 σ + 1 π, and a triple bond is 1 σ + 2 π. The higher the bond order, the shorter and stronger the bond. The minimum of a potential energy curve gives the bond length and bond energy.
On to AP (for later)
AP U2.2 often tests potential energy curves: the distance at the minimum is the bond length, and the depth of the minimum is the bond energy. When you compare curves, larger atoms put the minimum farther right (longer bonds), and higher bond orders make it deeper (stronger bonds). U2.7 asks you to count σ and π bonds just as this lesson does.