Chemistry - PERIODIC TABLE Question with Solution | TestHub

Question Explanation: Matching thermodynamic properties using a Born-Haber cycle diagram.

Concept: Born-Haber Cycle and Enthalpy.

Solution: Use the energy level diagram to find individual enthalpy changes. Lattice energy is the energy to form a solid from gaseous ions. Hydration energy is the energy change when gaseous ions are dissolved in water.

(1) $\mathrm{Mg}+{\mathrm{Cl}}_2\to {\mathrm{Mg}}^{+2}+2{\mathrm{Cl}}^{-}\Delta \mathrm{H}=1110$

(s) (g) (g) (aq)

(2) $Mg+{\mathrm{Cl}}_2$ $\to {\mathrm{Mg}}^{+2}+2{\mathrm{Cl}}^{-}\Delta \mathrm{H}=-790$

(s)) (g) (aq) (aq)

(2) - (1) ${\mathrm{Mg}}^{+2}$$\to {\mathrm{Mg}}^{+2}$ & $\Delta \mathrm{H}=-790-1110$

(g) (aq) $=-1900\mathrm{KJ}/\mathrm{Mole}$

Mg $\to {\mathrm{Mg}}^{+2}$ $\Delta \mathrm{H}=-790-1110$

(s) (g) $\Delta \mathrm{H}=+2360$

Mg & $\to {\mathrm{Mg}}^{+2}$ $\Delta \mathrm{H}=+2360-1900$

(s) (g) $=+460$

$\begin{array}{rlr}& \Delta {\mathrm{H}}_{\mathrm{f}}\left({\mathrm{Mg}}^{+2}\right)=+460& \end{array}$

$(\mathrm{aq})$

(1) $\mathrm{Mg}+{\mathrm{Cl}}_2\to {\mathrm{Mg}}^{+2}+2{\mathrm{Cl}}^{-}\Delta \mathrm{H}=1110$

$(\mathrm{s})$ $(\mathrm{g})$ $(\mathrm{aq})$ $(\mathrm{aq})$

$(2)\mathrm{Mg}$ $\to$ $\underset{(\mathrm{aq})}{{\mathrm{Mg}}^{+2}}$ $\Delta \mathrm{H}=+460$

$(1)-(2){\mathrm{Cl}}_2\to 2{\mathrm{Cl}}^{-}$

$(\mathrm{g})(\mathrm{aq})$

$\begin{array}{rlr}\Delta \mathrm{H}& =-790-460& =-1250\end{array}$

$\frac{1}{2}{\mathrm{Cl}}_2\to 2{\mathrm{Cl}}^{-}\Delta \mathrm{H}=\frac{-1250}{2}$

$\begin{array}{ccc}(\mathrm{g})& (\mathrm{aq})& =-625\\ {\mathrm{Mg}}^{+2}+2{\mathrm{Cl}}^{-}& \to {\mathrm{MgCl}}_2& \Delta \mathrm{H}=\text{ (L.E.) }{\mathrm{mgcl}}_2\end{array}$

(L.E.) ${\mathrm{MgCl}}_2=+2510$

(s)

Final Answer: Option B