Why do atoms bond? The octet rule
Noble gases like neon and argon hardly react. Their outer shell has 8 electrons (helium has 2). In 1916, Kossel and Lewis said other atoms bond to reach the same stable setup. This is the octet rule: atoms lose, gain or share electrons until the outer shell has 8.
The outer-shell electrons are called valence electrons. Only they take part in bonding.
Limits of the octet rule
- Incomplete octet: the central atom has fewer than 8. Examples: LiCl, BeH₂, BCl₃ (B has only 6).
- Odd-electron molecules: NO and NO₂ have an odd number of electrons, so one atom cannot reach 8.
- Expanded octet: atoms of period 3 and below can use d orbitals and hold more than 8. Examples: PF₅ (10), SF₆ (12), H₂SO₄ (S has 12).
- It does not explain the shape of molecules or the energy of bonds.
- Some noble gases do react (XeF₂, XeF₄, KrF₂), so "8 = cannot react" is not fully true.
Lewis symbols and Lewis structures
A Lewis symbol is the element symbol with its valence electrons as dots: Na has 1 dot, C has 4, N has 5, O has 6, Cl has 7.
A Lewis structure shows how a molecule shares electrons. A shared pair is drawn as a line (a single bond). Two shared pairs = double bond. Three = triple bond. Pairs that are not shared are lone pairs.
How to draw one (5 steps)
- Add all valence electrons. Add one for each minus charge; take one away for each plus charge.
- Pick the central atom: usually the least electronegative one (never H).
- Join each outer atom to the centre with a single bond (2 electrons each).
- Put the rest as lone pairs on the outer atoms first, then on the centre.
- If the centre still lacks 8, turn a lone pair of an outer atom into a double or triple bond.
Example CO₂: 4 + 6 + 6 = 16 electrons. O=C=O with two lone pairs on each O. Every atom has 8.
Formal charge
Sometimes more than one Lewis structure is possible. Formal charge helps choose the best one. It is the charge an atom would have if every shared pair were split equally.
Formal charge = V − L − B/2, where V = valence electrons of the free atom, L = electrons in lone pairs on that atom, B = electrons in bonds around that atom.
Rules: the best structure has the smallest formal charges; any minus formal charge should sit on the more electronegative atom; all formal charges must add up to the charge of the molecule or ion.
Formal charge is only a bookkeeping tool. It is not the real charge on the atom.
Ionic bond and lattice enthalpy
An ionic (electrovalent) bond forms when a metal atom gives electrons to a non-metal atom and the ions attract. It forms easily when:
- the metal has a low ionisation enthalpy (loses electrons easily), and
- the non-metal has a large negative electron gain enthalpy (takes electrons easily).
Making Na⁺ from Na actually costs energy (+496 kJ mol⁻¹), and Cl → Cl⁻ gives back only 349 kJ mol⁻¹. So why does NaCl form? Because packing the ions into a crystal releases a huge amount of energy.
Lattice enthalpy is the energy needed to break 1 mol of a solid ionic compound fully into its gaseous ions. For NaCl it is +788 kJ mol⁻¹. The bigger the lattice enthalpy, the more stable the solid. It is larger when ions are small and highly charged: MgO (≈ 3890) is far above NaCl (788).
Electrovalency
The number of electrons an atom gives or takes is its electrovalency: Na = 1, Mg = 2, O = 2, Cl = 1.
Try it: build ions with coins
Draw a big circle for Na with 1 coin on its edge and a circle for Cl with 7 coins. Move the Na coin to Cl. Count: Cl now has 8. Now try Mg (2 coins) with two Cl circles: each Cl takes 1 coin, so the formula is MgCl₂. Check your answer in the 3D free-play step.
Key formulas and definitions
- Formal charge = V − L − B/2
- Electrons for Lewis structure = Σ valence e⁻ − (positive charge) + (negative charge)
- Lattice enthalpy: MX(s) → M⁺(g) + X⁻(g), ΔH = + (energy needed)
- Lattice enthalpy grows with ion charge and falls with ion size
- Octet = 8 outer electrons (duplet = 2 for H, Li, Be ions)
Worked examples
1. Write the Lewis symbols of N, O and Cl and say how many electrons each needs for an octet.
Step 1: N has 5 valence electrons, O has 6, Cl has 7. Step 2: Needed = 8 − valence: N needs 3, O needs 2, Cl needs 1. Answer: N (5 dots, needs 3), O (6 dots, needs 2), Cl (7 dots, needs 1).
2. Draw the Lewis structure of H₂O.
Step 1: Electrons = 1 + 1 + 6 = 8. Step 2: O is central. Two O–H bonds use 4 electrons. Step 3: 4 left → 2 lone pairs on O. Step 4: O has 2 bonds + 2 lone pairs = 8. Each H has 2. Answer: H–O–H with two lone pairs on O.
3. Draw the Lewis structure of the nitrate ion NO₃⁻ and find the total electrons.
Step 1: 5 + 3 × 6 + 1 = 24 electrons. Step 2: N central with three N–O single bonds (6 used), 18 left. Step 3: Give each O three lone pairs (18 used). N has only 6. Step 4: Turn one O lone pair into a double bond: one N=O and two N–O. Answer: 24 electrons; one N=O, two N–O⁻ (three equivalent resonance forms).
4. Find the formal charge on each atom of O₃ (O=O–O).
Step 1: Left O (double bond): V = 6, L = 4, B = 4 → 6 − 4 − 2 = 0. Step 2: Middle O: V = 6, L = 2, B = 6 → 6 − 2 − 3 = +1. Step 3: Right O (single bond): V = 6, L = 6, B = 2 → 6 − 6 − 1 = −1. Step 4: Check: 0 + 1 − 1 = 0 = charge of O₃. ✓
5. Find the formal charge on N in NH₄⁺.
Step 1: N has V = 5. Step 2: No lone pairs, L = 0. Four N–H bonds, B = 8. Step 3: FC = 5 − 0 − 8/2 = +1. Step 4: Each H: 1 − 0 − 1 = 0. Total = +1 = charge of the ion. ✓
6. Which Lewis structure of CO₂ is better: O=C=O or O≡C–O? Use formal charge.
Step 1: O=C=O: each O: 6 − 4 − 2 = 0; C: 4 − 0 − 4 = 0. All zero. Step 2: O≡C–O: triple-bonded O: 6 − 2 − 3 = +1; C: 0; single-bonded O: 6 − 6 − 1 = −1. Step 3: Smallest formal charges win. Answer: O=C=O is the better structure.
7. Arrange NaCl, MgO and KCl in increasing lattice enthalpy and explain.
Step 1: MgO has ions with charge 2+ and 2−; the others have 1+ and 1−. Higher charge → much larger lattice enthalpy. Step 2: K⁺ is bigger than Na⁺. Bigger ion → ions farther apart → smaller lattice enthalpy. Answer: KCl (717) < NaCl (788) < MgO (≈ 3890 kJ mol⁻¹).
Common mistakes
- Forgetting to add or remove electrons for the charge of an ion when counting electrons for a Lewis structure.
- Thinking formal charge is the real charge on the atom. It is only bookkeeping; real charges come from electronegativity.
- Saying NaCl forms because Na → Na⁺ releases energy. It actually costs energy; the lattice energy makes the overall process favourable.
- Putting H as the central atom. H can form only one bond, so it is always on the outside.