Born-Haber versus theoretical lattice enthalpy of silver chloride
A student is investigating the bonding in silver chloride. She has the following data: standard enthalpy of formation of AgCl(s) = -127 kJ mol-1; enthalpy of atomisation of Ag(s) = +285 kJ mol-1; first ionisation energy of Ag(g) = +731 kJ mol-1; bond dissociation enthalpy of Cl2(g) = +242 kJ mol-1; electron affinity of Cl(g) = -349 kJ mol-1. A theoretical lattice enthalpy of -833 kJ mol-1 is calculated from a simple electrostatic model using ionic radii. The student's Born-Haber cycle gives a different value. She claims this proves AgCl is not ionic at all. Her teacher says the discrepancy is evidence of polarisation, not a complete absence of ionic bonding. The student must decide whether to describe AgCl as ionic, covalent, or intermediate, and how to justify the choice using the data.
1. Use the Born-Haber data to calculate the lattice enthalpy of AgCl and compare it with the theoretical value.
Read the worked answer
Write the Born-Haber cycle for AgCl(s):
ΔHf = ΔHatom(Ag) + IE1(Ag) + 1/2 BDE(Cl2) + EA(Cl) + ΔHlatt
Substitute the values:
-127 = 285 + 731 + (242/2) + (-349) + ΔHlatt
-127 = 285 + 731 + 121 - 349 + ΔHlatt
-127 = 788 + ΔHlatt
ΔHlatt = -127 - 788 = -915 kJ mol-1
The experimental lattice enthalpy is -915 kJ mol-1, whereas the theoretical electrostatic value is -833 kJ mol-1. The experimental value is more exothermic by 82 kJ mol-1. This difference is too large to ignore and suggests that the simple ionic model is incomplete, but it does not mean the compound has no ionic character.
2. Explain, using polarisation and Fajans' rules, why the experimental lattice enthalpy is more exothermic than the theoretical value.
Read the worked answer
The theoretical value assumes point charges separated by a fixed ionic distance. In reality, the Ag+ ion is small and has a high charge density, so it strongly attracts the electron cloud of the Cl- ion. Cl- is polarisable, meaning its electron cloud can be distorted toward Ag+. This polarisation increases electron density between the nuclei, adding a covalent contribution to the ionic attraction. Because the ions are pulled closer together than the rigid-sphere model predicts, the actual lattice is more stable and more energy is released when it forms. Hence the Born-Haber lattice enthalpy is more exothermic than the theoretical value. The correct description is therefore intermediate: predominantly ionic with significant covalent character, not purely ionic and not purely covalent.
3. Predict whether the discrepancy between experimental and theoretical lattice enthalpy will be larger or smaller for AgBr, and justify your answer.
Read the worked answer
The discrepancy should be larger for AgBr. Br- is larger than Cl- and has a more polarisable electron cloud, so it is more strongly distorted by the polarising Ag+ ion. This gives greater covalent character. At the same time, the larger internuclear distance lowers the purely electrostatic lattice enthalpy, so the theoretical ionic value becomes less exothermic. The experimental value will therefore be more exothermic than the theoretical value by a larger margin than for AgCl. The prediction is that the experimental-theoretical gap increases from AgCl to AgBr, consistent with greater polarisation and covalent character.