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, ΔHlatt?, 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 (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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