# 5.1.4 Comparing Lattice Enthalpies

### 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

#### Exam Tip

The distortion of the electron clouds is known as polarisation and illustrates that bonding is not either pure ionic or covalent, but rather a continuum between the two extremes.

#### Factors affecting lattice enthalpy

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

• 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 (O2-) 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 O2- 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 O2- are also smaller ions than K+ and Cl, so this also adds to the value for the lattice energy being more exothermic
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