2mol of Hg(g) is combusted in a fixed volume bomb calorimeter with...

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

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

Rise in temperature $= 14 . 8K$

Heat evolved $= 20 \times 14 . 8 = 296kJ$

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

$= - 296 - 3 \times 8 . 3 \times 298 \times {10}^{- 3}$

$= - 303 . 42kJ$

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

$- 303 . 42 = 2{\Delta H}_{f} ° \left(HgO\left(s\right)\right) - 2 \times 61 . 32$

$2{\Delta H}_{f} ° \left(HgO\left(s\right)\right) = - 180 . 78kJ$

\left|{\Delta H}_{f} ° \left(HgO\left(s\right)\right)\right| = 90 . 39kJ{mol}^{- 1}