5.1.4 Comparing Lattice Enthalpies

How accurate are lattice enthalpies?

• It is possible to calculate a theoretical value for the lattice enthalpy of an ionic solid. To do this you need to know
  • the geometry of the ionic solid
  • the charge on the ions
  • the distance between the ions

• This has been calculated for a number of ionic solids and allows a comparison between theoretical lattice enthalpies and experimental lattice enthalpies obtained from Born-Haber cycles

Table comparing theoretical and experimental lattice enthalpies

• You can see from the table that there is quite close agreement between the two values for the lattice enthalpy of sodium chloride
• The calculation of the theoretical value is based on an assumption that the substance is a highly ionic compound with only electrostatic attraction between cations and anions

The ionic model for sodium chloride

• However, the difference between theoretical and experimental lattice enthalpy increases for zinc sulfide
• This suggests that the bonding is not purely ionic and some covalent character is present
• This can be explained as follows:
  • Zinc is a smaller ion with a greater charge(+2) than sodium(+1)
  • Zinc ions attract electron density towards themselves, distorting the electron cloud and making the bonding slightly covalent
  • Sulfide ions are larger ions than chloride ions(-1) with a greater negative charge(-2)
  • The electron cloud around sulfide ions is more easily distorted than in chloride ions leading to further covalent character

Covalent character in ionic compounds

• As you move left to right across the period table the lattices become less ionic and more covalent leading to a discrepancy in the lattice enthalpy values
• The result of these analyses provides strong evidence that supports the ionic model for some compounds like sodium chloride

Factors affecting lattice enthalpy

• The two key factors which affect lattice energy, ΔH_latt^ꝋ, are the charge and radius of the ions that make up the crystalline lattice

Ionic radius

• The lattice energy becomes less exothermic as the ionic radius of the ions increases
• This is because the charge on the ions is more spread out over the ion when the ions are larger
• The ions are also further apart from each other in the lattice
  • The attraction between ions is between the centres of the ions involved, so the bigger the ions the bigger the distance between the centre of the ions

• Therefore, the electrostatic forces of attraction between the oppositely charged ions in the lattice are weaker
• For example, the lattice energy of caesium fluoride (CsF) is less exothermic than the lattice energy of potassium fluoride (KF)
  • Since both compounds contain a fluoride (F^-) ion, the difference in lattice energy must be due to the caesium (Cs⁺) ion in CsF and potassium (K⁺) ion in KF
  • Potassium is a Group 1 and Period 4 element
  • Caesium is a Group 1 and Period 6 element
  • This means that the Cs⁺ ion is larger than the K⁺ ion
  • There are weaker electrostatic forces of attraction between the Cs⁺ and F^- ions compared to K⁺ and F^- ions
  • As a result, the lattice energy of CsF is less exothermic than that of KF

The lattice energies get less exothermic as the ionic radius of the ions increases

Ionic charge

• The lattice energy gets more exothermic as the ionic charge of the ions increases
• The greater the ionic charge, the higher the charge density
• This results in stronger electrostatic attraction between the oppositely charged ions in the lattice
• As a result, the lattice energy is more exothermic
• For example, the lattice energy of calcium oxide (CaO) is more exothermic than the lattice energy of potassium chloride (KCl)
  • Calcium oxide is an ionic compound which consists of calcium (Ca²⁺) and oxide (O^2-) ions
  • Potassium chloride is formed from potassium (K⁺) and chloride (Cl^-) ions
  • The ions in calcium oxide have a greater ionic charge than the ions in potassium chloride
  • This means that the electrostatic forces of attraction are stronger between the Ca²⁺ and O^2- compared to the forces between K⁺ and Cl^-
  • Therefore, the lattice energy of calcium oxide is more exothermic, as more energy is released upon its formation from its gaseous ions
  • Ca²⁺ and O^2- are also smaller ions than K⁺ and Cl^-, so this also adds to the value for the lattice energy being more exothermic