Two atoms that cannot do a deal
The ionic bonding lectures told a story of giving and taking. A sodium atom gives away one electron. A chlorine atom takes it. Both end up with full outer shells, and the opposite charges hold the ions together. The last lecture ended by promising a different way of holding atoms together. Here is the problem that needs it.
Take two chlorine atoms. Each has 7 outer electrons, and each needs one more to reach 8. Which one gives an electron to the other? Neither. They are identical atoms with identical pulls on their electrons. For one of them to lose an electron would cost a lot of energy, and it would gain nothing, because then it would be one short. Transfer is impossible.
Yet chlorine gas is made of pairs of chlorine atoms, Cl₂, held firmly together. Hydrogen is H₂. Oxygen is O₂. Water, sugar, plastics and the DNA in your cells are all made of atoms that hold together without any transfer of electrons. So how?
The answer is that the two atoms share electrons. This lecture shows what sharing means, why it holds atoms together, and how to count shared electrons without mistakes.
What sharing really means
Each chlorine atom puts one of its outer electrons into a pair that sits between the two atoms. That pair now belongs to both atoms at once.
Count the electrons around the left atom. It has three pairs of its own (6 electrons), plus the shared pair (2 electrons). That makes 8: a full outer shell. Now count around the right atom. It also has three pairs of its own and the same shared pair: 8 again. The shared pair is counted twice, once for each atom. That is not cheating. Both atoms really do hold that pair in their outer shells.
But why does sharing hold the atoms together? This is the question students rarely ask, and it is the most important one. The answer is the same force that holds ions together: the attraction between positive and negative charges. The shared pair sits between the two nuclei. Each nucleus is positive, and each attracts the negative pair. So the pair pulls on both nuclei at once, and the nuclei are pulled towards the pair, and so towards each other.
Think of two people both holding the same rope from opposite sides. Neither lets go, so they are tied together through the rope. In a covalent bond, the "rope" is the pair of electrons, and the "hands" are the two nuclei pulling on it.
The atoms do not crash into each other, because the two nuclei repel each other. The bond settles at the distance where attraction and repulsion balance. That distance is the bond length. In H₂, it is about 74 pm (74 × 10⁻¹² m). Pulling the atoms apart needs energy: about 436 kJ for every mole of H–H bonds broken (one table of average values, LibreTexts, from Cotton, Wilkinson and Gaus, 1995). That is it. That is the whole idea. A covalent bond is a shared pair of electrons attracted by two nuclei at once.
A covalent bond is a shared pair of electrons between two atoms. The pair is attracted to both nuclei, and this holds the atoms together.
In most covalent bonds, each atom gives one electron to the pair. A shared pair counts towards the outer shell of both atoms.
Covalent bonds usually form between non-metal atoms. The electronegativity lecture explained why. Non-metals all pull strongly on electrons. When two strong pulls meet, neither atom can take an electron from the other, so they share. When the pulls are very different, as for sodium and chlorine, transfer wins, and the bond is ionic.
How many bonds does an atom make?
Each atom forms enough shared pairs to fill its outer shell. Count how many electrons it is short of 8 (or of 2, for hydrogen). That is the number of bonds it forms. The outer electrons it does not use in bonds stay in pairs on the atom. These are called lone pairs. They belong to that atom alone.
Try it with the atoms of the second period, each bonded to hydrogen.
Choose an atom. The diagram bonds it to as many hydrogen atoms as it needs. Its own electrons are dots and hydrogen's are crosses. Count the bonds and the lone pairs each time. What stays the same?
Each second-period atom bonded to hydrogen. The number of bonds is how many electrons the atom is short of 8.
| Atom | Outer electrons | Bonds | Lone pairs | Molecule |
|---|---|---|---|---|
| C | 4 | 4 | 0 | CH₄ |
| N | 5 | 3 | 1 | NH₃ |
| O | 6 | 2 | 2 | H₂O |
| F | 7 | 1 | 3 | HF |
| Ne | 8 | 0 | 4 | none |
In every row, bonding pairs plus lone pairs make 4 pairs: 8 electrons around the atom. Hydrogen is the exception: its only shell holds 2, so it forms one bond and has no lone pairs.
Did you notice the pattern? From carbon to fluorine, each step adds one outer electron. Each step removes one bond and adds half a lone pair, so every two steps add a lone pair. But the total never changes: 4 pairs, 8 electrons, around every atom. Carbon uses all four pairs for bonding. Fluorine uses only one. Neon needs none, so it forms no bonds at all, which is why the noble gases exist as single atoms.
Water boils at 100 °C, a low temperature. Does that mean the covalent O–H bonds in water are weak?
Show the answer
No. Boiling does not break any O–H bonds. The steam is still made of H₂O molecules. What boiling breaks are the much weaker attractions between separate water molecules. Breaking the O–H bonds themselves needs about 467 kJ for every mole of bonds (the same table), which is far more energy than boiling water. To split water into hydrogen and oxygen, you need a very high temperature or electrolysis. Keep two ideas apart: bonds inside a molecule, which are strong, and forces between molecules, which are much weaker. A later topic is about those forces between molecules.
Sharing more than one pair
Sometimes one shared pair is not enough to fill both shells. Then two atoms share two or three pairs between them.
An oxygen atom has 6 outer electrons and needs 2 more. In O₂, the two atoms share two pairs. This is a double bond, written O=O. Each oxygen then has its two lone pairs plus the two shared pairs: 4 + 4 = 8.
A nitrogen atom has 5 outer electrons and needs 3 more. In N₂, the two atoms share three pairs: a triple bond, N≡N. Each nitrogen keeps one lone pair. Count around each atom: 2 + 6 = 8.
The number of shared pairs between two atoms is called the bond order: 1 for a single bond, 2 for a double bond, 3 for a triple bond. More shared pairs means more negative charge between the two nuclei. That pulls the nuclei closer together and holds them more strongly. So the prediction is clear: as bond order rises, bonds should get shorter and stronger. Measurements agree.
| Bond | Bond order | Length (pm) | Energy to break (kJ/mol) |
|---|---|---|---|
| C–C | 1 | 154 | 346 |
| C=C | 2 | 134 | 598 |
| C≡C | 3 | 121 | 813 |
| N–N | 1 | 140 | 160 |
| N=N | 2 | 120 | 418 |
| N≡N | 3 | 110 | 946 |
These are average values from one table (LibreTexts, using Cotton, Wilkinson and Gaus, 1995). Other books give slightly different numbers, because each bond's energy changes a little from one molecule to another. The pattern is the same in every table. Notice also that a double bond is not twice as strong as a single bond. The second and third pairs add strength, but each one adds a different amount.
Drawing dot-and-cross diagrams: worked examples
The method is the same every time. Count the outer electrons of each atom. Work out how many bonds each atom needs. Join the atoms with that many shared pairs. Put the leftover electrons in lone pairs. Then check: every atom has 8 around it, except hydrogen, which has 2.
Count. Nitrogen has 5 outer electrons. Each hydrogen has 1.
Bonds. Nitrogen needs 3 more electrons, so it forms 3 bonds, one to each hydrogen. Each N–H bond is one shared pair: one electron from nitrogen and one from hydrogen.
Lone pairs. Nitrogen used 3 of its 5 electrons in bonds. The other 2 form one lone pair.
Check. Around nitrogen: 3 shared pairs + 1 lone pair = 4 pairs = 8 electrons. Around each hydrogen: 1 shared pair = 2 electrons. Total outer electrons in the molecule: , and the diagram shows 4 pairs, which is 8. They match.
Count. Carbon has 4 outer electrons. Each oxygen has 6. Total: .
Bonds. Carbon needs 4 more electrons, so it must form 4 bonds. Each oxygen needs 2 more, so each forms 2 bonds. The only way to fit both: carbon forms a double bond to each oxygen, O=C=O.
Lone pairs. Carbon uses all 4 of its electrons in bonds, so it has no lone pairs. Each oxygen uses 2 of its 6, leaving 2 lone pairs.
Check. Around carbon: 4 shared pairs = 8. Around each oxygen: 2 shared pairs + 2 lone pairs = 8. Total pairs: 4 shared + 4 lone = 8 pairs = 16 electrons, as counted.
The most common mistake with CO₂ is to draw single bonds. Find it in this student's working.
A student draws CO₂ as O–C–O, with one shared pair between carbon and each oxygen. Exactly one line of the reasoning is wrong. Tap it.
A student's reasoning for CO₂ drawn with single bonds. Line 4 is wrong.
- Line 1. Carbon has 4 outer electrons and each oxygen has 6. Correct.
- Line 2. With single bonds, carbon shares one pair with each oxygen. Correct as a description of the drawing.
- Line 3. Carbon then has 2 shared pairs and its other 2 electrons: 6 around it. Each oxygen has 1 shared pair and its other 5 electrons: 7 around it. Correct counting.
- Line 4. So every atom has a full outer shell. Wrong: line 3 shows 6 and 7, not 8. The single-bond drawing fails.
- Line 5. The fix: two double bonds, O=C=O, giving 8 around every atom. Correct.
Count. Hydrogen has 1 outer electron, carbon 4 and nitrogen 5. Total: 10.
Bonds. Hydrogen forms 1 bond. Carbon needs 4 bonds and nitrogen needs 3. Carbon sits in the middle. It uses 1 bond for hydrogen, so its other 3 must go to nitrogen: a triple bond. The molecule is H–C≡N.
Lone pairs. Carbon uses all 4 electrons, so it has none. Nitrogen uses 3 of its 5, leaving one lone pair.
Check. Around carbon: 1 + 3 = 4 shared pairs = 8. Around nitrogen: 3 shared pairs + 1 lone pair = 8. Around hydrogen: 2. Total: 4 shared pairs + 1 lone pair = 5 pairs = 10 electrons. One molecule can contain bonds of different orders.
The strongest bond in the air
The triple bond in N₂ is one of the strongest bonds between two atoms: about 946 kJ/mol in the table above. Air is about four-fifths nitrogen, yet that nitrogen hardly reacts with anything. The triple bond is the reason. Breaking it costs so much energy that most reactions cannot start.
This matters for food. Plants need nitrogen atoms to build proteins, but they cannot use N₂ from the air directly. In the Haber process, factories make ammonia from nitrogen and hydrogen at about 400–450 °C and about 200 atmospheres, with an iron catalyst. Even then, only about 15% of the gases react on each pass through the reactor (Chemguide, Haber process). Much of that ammonia becomes fertiliser. Some bacteria do the same job at ordinary temperatures, using an enzyme called nitrogenase. Chemists are still studying exactly how this enzyme breaks such a strong bond so gently.
Three classic mistakes
A shared pair counts towards the outer shell of both atoms. In Cl₂, each atom has 3 lone pairs plus the shared pair: 8. If you count the shared pair for one atom only, the other atom seems to have 6, and you will add bonds that are not there.
Not every molecule is joined by single bonds. Always finish with the count. If an atom has fewer than 8 electrons around it (or fewer than 2 for hydrogen), turn a lone pair into an extra shared pair. CO₂ needs two double bonds, and N₂ needs a triple bond.
When a simple molecular substance such as water melts or boils, the molecules separate from each other, but they stay whole. The covalent bonds inside them are not broken. Low boiling points tell you that the forces between molecules are weak, not that covalent bonds are weak.
Work each one on paper first. Draw the dot-and-cross diagram before you open a hint.
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Draw a dot-and-cross diagram for methane, CH₄. How many lone pairs does it have?
Hint 1
Carbon has 4 outer electrons and needs 4 more.
Hint 2
Each hydrogen shares one pair with carbon.
Full answer
Carbon forms 4 single bonds, one to each hydrogen. Each bond has one dot (from carbon) and one cross (from hydrogen). Carbon uses all 4 electrons, so there are no lone pairs. Check: carbon has 4 shared pairs = 8; each hydrogen has 2. Total outer electrons: = 4 pairs.
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Draw a dot-and-cross diagram for oxygen, O₂. State the bond order and the number of lone pairs on each atom.
Hint 1
Each oxygen has 6 outer electrons and needs 2 more.
Hint 2
One shared pair gives each atom only 7. Try two.
Full answer
The atoms share two pairs: a double bond, bond order 2. Each oxygen keeps 2 lone pairs. Check around each atom: 4 lone-pair electrons + 4 shared electrons = 8. Total: 12 outer electrons = 2 shared pairs + 4 lone pairs = 6 pairs.
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Phosphorus is in Group 15, below nitrogen. Predict the formula of the simplest compound of phosphorus and hydrogen, and the number of lone pairs on phosphorus.
Hint 1
Phosphorus has the same number of outer electrons as nitrogen.
Hint 2
Think of ammonia, NH₃.
Full answer
Phosphorus has 5 outer electrons and needs 3 more, so it forms 3 bonds: PH₃. Like nitrogen in NH₃, it keeps one lone pair. Check: 3 shared pairs + 1 lone pair = 8 around phosphorus. Atoms in the same group form the same number of bonds, because they have the same number of outer electrons.
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Ethyne, C₂H₂, is the gas burned in welding torches. Each carbon is bonded to one hydrogen and to the other carbon. Draw its dot-and-cross diagram. Then use the table in this lecture to predict how its carbon–carbon bond compares with the one in ethane, C₂H₆, where each carbon has three hydrogens.
Hint 1
Each carbon needs 4 bonds. One goes to hydrogen. How many are left for the other carbon?
Hint 2
In ethane, each carbon uses 3 bonds for hydrogens, so only one is left for the other carbon.
Full answer
In ethyne, each carbon uses 1 bond for its hydrogen, so 3 are left: a triple bond, H–C≡C–H. No lone pairs. Check: each carbon has 1 + 3 = 4 shared pairs = 8; total electrons = 5 shared pairs. In ethane, each carbon has 3 hydrogens and one single C–C bond. From the table, the triple bond should be shorter (about 121 pm against 154 pm) and need more energy to break (about 813 against 346 kJ/mol). A triple bond needs less than three times the energy of a single bond: , more than 813.
Ionic and covalent bonding are not two unrelated ideas. Both are the attraction between positive nuclei and negative electrons. In ionic bonding, electrons move completely and the ions attract. In covalent bonding, electrons are shared and both nuclei attract the same pair. The electronegativity lecture showed that most real bonds lie somewhere between: the pair is shared, but not always equally. The lecture on bond polarity returns to that idea.
Lone pairs matter too, even though they make no bonds. They take up space around an atom and push the bonds away. The next lecture uses every pair, bonding and lone, to predict the three-dimensional shape of a molecule.
- A covalent bond is a shared pair of electrons, held between two atoms because both nuclei attract it.
- A shared pair counts towards the outer shell of both atoms, so sharing lets non-metal atoms reach 8 outer electrons (2 for hydrogen).
- An atom forms as many bonds as it is short of a full shell, and its unused outer electrons form lone pairs.
- Atoms can share one, two or three pairs, and higher bond order gives shorter, stronger bonds.
- Boiling a molecular substance separates molecules without breaking the covalent bonds inside them.