Answer to Question #120793 in Inorganic Chemistry for Lontum Rodrique

Question

The common oxidation number for an alkaline earth metal is +2. Using the Born–Mayer equation and a Born–Haber cycle, show that CaCl is an exothermic compound. Use a suitable analogy to estimate an ionic radius for Ca+. The sublimation enthalpy of Ca(s) is 176 kJmol-1. Show that an explanation for the nonexistence of CaCl can be found in the enthalpy change for
the reaction 2 CaCl(s) → Ca(s) + CaCl2(s).

Answer 1

continuation:

$=-782771\frac{J}{mol}\approx-783\frac{kJ}{mol}$

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Then ΔH_f=$534.9\frac{kJ}{mol}​+U_{L}=534.9\frac{kJ}{mol}​-783\frac{kJ}{mol}​\approx-248\frac{kJ}{mol}$ < 0 - an exothermic process

Thus we show that CaCl is an exothermic compound.

for the reaction 2 CaCl(s) → Ca(s) + CaCl2(s).

$\Delta H=\Delta H_{f,CaCl2}-2\cdot \Delta H_{f,CaCl}=-785.8\frac{kJ}{mol}-2\cdot(-248\frac{kJ}{mol})\approx-289.8\frac{kJ}{mol}$ - exotermic. Thus nonexistent CaCl would decompose spontaneously to CaCl2 and Ca.