Chemistry - Thermochemistry 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) $=+460$

$\Delta {\mathrm{H}}_{\mathrm{f}}\left({\mathrm{Mg}}^{+2}\right)=+460$

(aq)

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

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

(s) (aq)

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

(g) (aq)

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

$\frac{1}{2}{\mathrm{Cl}}_2\to 2{\mathrm{Cl}}^{-}\Delta \mathrm{H}=\frac{-1250}{2}=-625$

(g) (aq)

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

(s)

Final Answer: Option B