Setup of Born-Haber cycle; calculate lattice energy of ${\mathrm{MgO}}_{\left(\mathrm{s}\right)}.$ The given that enthalpy of formation of ${\mathrm{MgO}}_{\left(\mathrm{s}\right)}=-602,$ sublimation of ${\mathrm{Mg}}_{\left(\mathrm{s}\right)}=148;1^{\mathrm{st}}$ and $2^{\text{nd }}$ ionization energy of $\mathrm{Mg}=738$ and $1450$ respectively. For Oxygen bond dissociation energy $=498; 1^{\text{st }}$ $2^{\text{nd }}$ and electron gain enthalpy $=-141$ and $844$ respectively (all unit in $\mathrm{kJ} {\mathrm{mole}}^{-1}$).

Determine which of the following reactions, at constant pressure represent surrounding that does work on the system?

$\left(\mathrm{I}\right) 4{\mathrm{NH}}_3\left(\mathrm{g}\right)+7{\mathrm{O}}_2\left(\mathrm{g}\right)⟶4{\mathrm{NO}}_2\left(\mathrm{g}\right)+6{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

$\left(\mathrm{II}\right) \mathrm{CO}\left(\mathrm{g}\right)+2{\mathrm{H}}_2\left(\mathrm{g}\right)⟶{\mathrm{CH}}_3\mathrm{OH}\left(\mathrm{l}\right)$

$\left(\mathrm{III}\right) \mathrm{C}\left(\mathrm{s}, \text{graphite}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)⟶\mathrm{CO}\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$

$\left(\mathrm{IV}\right) {\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)⟶{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$

Consider the reaction at $300 \mathrm{K}$

${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)⟶2 \mathrm{HCl}\left(\mathrm{g}\right); △\mathrm{H}°=-185 \mathrm{kJ}$

If $2$ moles of ${\mathrm{H}}_2$ completely react with $2$ mole of ${\mathrm{Cl}}_2$ to form $\mathrm{HCl}$, what is $△\mathrm{U}°$ for this reaction.