Topic 12 · page 13 of 17
Covalent character in ionic bonds
A lattice energy from a Born-Haber cycle is the real value. One from electrostatic theory assumes pure ionic bonding. The gap between them measures covalent character, which arises when a cation polarises an anion.
Read first: Born-Haber calculations
Experimental and theoretical values 12.14
There are two ways to get a lattice energy.
- The experimental value comes from a Born-Haber cycle (pages 11 and 12). It reflects the real compound, whatever its bonding.
- The theoretical value comes from electrostatic theory. It assumes that the compound is 100% ionic: perfectly spherical ions with their charges treated as points at their centres.
If a compound really is purely ionic, the two values should agree. If the two disagree, the compound is not purely ionic.
| Compound | Experimental / kJ mol⁻¹ | Theoretical / kJ mol⁻¹ | Difference / kJ mol⁻¹ | Difference as % |
|---|---|---|---|---|
| NaCl | −787 | −770 | 17 | 2% |
| NaBr | −747 | −735 | 12 | 2% |
| NaI | −704 | −687 | 17 | 2% |
| AgCl | −915 | −833 | 82 | 9% |
| AgBr | −904 | −816 | 88 | 10% |
| AgI | −889 | −778 | 111 | 12% |
The difference is the size of (experimental − theoretical), as a percentage of the size of the experimental value.
The extra attraction is why the real value is more exothermic: electrons shared between the ions give an additional bonding contribution on top of the electrostatic attraction.
Polarisation of the anion 12.15
Why do some compounds have covalent character? Because a cation can distort, or polarise, the electron cloud of a nearby anion. The positive charge pulls electron density from the anion towards itself, so some of it sits between the two ions. Electrons shared between the nuclei make the bond partly covalent.
Two features make polarisation larger:
- A cation that is small and highly charged has a high charge density, so it pulls the electron cloud strongly.
- An anion that is large is easily polarised, because its outer electrons are far from its nucleus and held weakly. A higher negative charge also helps.
The silver halides show the anion effect: the gap grows from chloride (9%) to bromide (10%) to iodide (12%) as the anion gets larger and more polarisable. The sodium halides stay at about 2% because Na⁺ is a large cation with only a 1+ charge, a weak polariser.
Check yourself
- State the assumptions made when a theoretical lattice energy is calculated from electrostatic theory.
- A compound MX has an experimental lattice energy of −640 kJ mol⁻¹ and a theoretical value of −580 kJ mol⁻¹ (illustrative values). Calculate the percentage difference and say what it shows.
- Which compound in the table has the most covalent character, and which the least? Explain how you know.
- Describe what polarisation of an anion means.
- Which would you expect to be polarised more by the same cation, I⁻ or Cl⁻? Explain.
- A student writes: "The theoretical lattice energy of AgCl is wrong because it does not match the experimental one." Explain what the difference really shows.
Answers cover these until you have tried the questions
- The compound is 100% ionic: the ions are perfectly spherical and their charges act as point charges at the centres of the ions.
- Difference = 640 − 580 = 60 kJ mol⁻¹. As a percentage: 60 ÷ 640 × 100 = 9% (9.4%). The experimental value is more exothermic than the theoretical one, so the bonding has some covalent character.
- Most covalent: AgI (12% difference). Least covalent: the sodium halides, NaCl, NaBr and NaI, all about 2%. The larger the difference between experimental and theoretical values, the more covalent character.
- A cation attracts the electron cloud of a neighbouring anion and distorts it towards the cation, so there is electron density between the two nuclei and the bond is partly covalent.
- I⁻ is polarised more. It is a larger ion, so its outer electrons are further from the nucleus and more weakly held, and are easier to pull towards the cation.
- The theoretical value is the correct figure for a purely ionic model. The difference shows that the real bonding in AgCl is not purely ionic: silver ions polarise chloride ions, giving covalent character and extra attraction.