Question #44180

The Born-Haber cycle for a hypothetical alkaline earth metal halide $\ce{MX2(s)}$ involves the following thermodynamic parameters (in $\text{kJ mol}^{-1}$): Standard enthalpy of formation ($\Delta H_f^\circ$) = $-795$ Enthalpy of sublimation of $\ce{M(s)}$ = $155$ Sum of first and second ionization enthalpies of $\ce{M(g)}$ = $2180$ Bond dissociation enthalpy of $\ce{X2(g)}$ = $240$ Electron gain enthalpy of $\ce{X(g)}$ = $-340$

A $1.0 \text{ molal}$ aqueous solution of $\ce{MX2}$ is prepared. In concentrated solutions, $\ce{MX2}$ deviates from ideal colligative behavior due to partial ion-pairing according to the equilibrium: $\ce{M^{2+}(aq) + X^{-}(aq) \rightleftharpoons MX^{+}(aq)}$ The ion-pair formation constant $K_c$ is $2.4 \text{ kg mol}^{-1}$.

Assuming ideal behavior of the individual dissolved species, determine the magnitude of the lattice enthalpy ($U_L$ in $\text{kJ mol}^{-1}$) of $\ce{MX2(s)}$ and the boiling point of the $1.0 \text{ m}$ solution. (Given: $K_b$ for water = $0.52 \text{ K kg mol}^{-1}$, boiling point of pure water = $100.00^\circ\text{C}$)