Q.Write down the Born-Haber cycle for the formation of $CaCl_2$

Step 1. $CaCl_2$ needs a modified cycle from the simple 1:1 $MX$ template (Section 7.9), since $Ca$ loses TWO electrons and TWO $Cl^-$ ions are needed per formula unit.

Step 2. The five (really six, since Ca needs two separate ionisation steps) legs are: sublimation $Ca(s)\rightarrow Ca(g)$; first ionisation $Ca(g)\rightarrow Ca^+(g)+e^-$ ($IE_1$); second ionisation $Ca^+(g)\rightarrow Ca^{2+}(g)+e^-$ ($IE_2$); dissociation $Cl_2(g)\rightarrow2Cl(g)$; electron affinity of BOTH chlorine atoms, $2Cl(g)+2e^-\rightarrow2Cl^-(g)$ (i.e. $2\times EA(Cl)$, since two electrons must be accepted, one per Cl); and finally the lattice enthalpy $U$, $Ca^{2+}(g)+2Cl^-(g)\rightarrow CaCl_2(s)$. …

Adapt the general $MX$ Born-Haber cycle (Section 7.9) to $CaCl_2$'s 1:2 stoichiometry -- doubling BOTH the ionisation step (Ca loses 2 electrons) and …

• Using only ONE ionisation energy for calcium, forgetting Ca$^{2+}$ requires losing TWO electrons in two successive steps ($IE_1$ then $IE_2$, which are numerically different) …