2   mol of Hg g is combusted in a fixed volume bomb calorimeter with excess of O 2 at 298   K and…

$2\mathrm{Hg}\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)⟶2\mathrm{HgO}\left(\mathrm{s}\right)$

Heat capacity of calorimeter $=20 \mathrm{kJ} {\mathrm{K}}^{-1}$

Rise in temperature $=14.8 \mathrm{K}$

Heat evolved $=20\times 14.8=296 \mathrm{kJ}$

$\mathrm{\Delta H}°=\mathrm{\Delta U}°+{\mathrm{\Delta n}}_{\mathrm{g}}\mathrm{RT}$

$=-296-3\times 8.3\times 298\times {10}^{-3}$

$=-303.42 \mathrm{kJ}$

$\mathrm{\Delta H}°=2{\mathrm{\Delta H}}_{\mathrm{f}}°\left(\mathrm{HgO}\left(\mathrm{s}\right)\right)-2{\mathrm{\Delta H}}_{\mathrm{f}}°\left(\mathrm{Hg}\left(\mathrm{g}\right)\right)$

$-303.42=2{\mathrm{\Delta H}}_{\mathrm{f}}°\left(\mathrm{HgO}\left(\mathrm{s}\right)\right)-2\times 61.32$

$2{\mathrm{\Delta H}}_{\mathrm{f}}°\left(\mathrm{HgO}\left(\mathrm{s}\right)\right)=-180.78 \mathrm{kJ}$

$\left|{\mathrm{\Delta H}}_{\mathrm{f}}°\left(\mathrm{HgO}\left(\mathrm{s}\right)\right)\right|=90.39 \mathrm{kJ} {\mathrm{mol}}^{-1}$