Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 10 / b / ii

The large positive sum of ionization energies and large negative hydration enthalpy dominate, with a smaller but significant positive atomization term. Ionization depends on effective nuclear attraction, orbital energies and the stability of successive gas-ion electron configurations; removing the third electron may require disruption of a particularly stable divalent f configuration. Atomization depends on the metal's cohesive bonding and valence participation, and need not vary perfectly smoothly.

Hydration becomes more favourable for higher charge density. All the compared ions have charge $+3$, so smaller effective ionic radius generally gives more negative hydration enthalpy. Incomplete shielding by the 4f shell produces the lanthanide contraction and strengthens ion–water attraction along the series. A Born-type electrostatic estimate has a stabilization scale proportional to $-z^2/r$, but hydration-shell structure, water polarization and temperature dependence prevent treating that crude scale as an exact enthalpy formula. The hydration trend is smoother than the sharp configuration-dependent ionization anomalies. The measured formation enthalpy reflects cancellation of large terms, so comparison of just one term can give a misleading prediction.