For a cell reaction $2{\mathrm{H}}_{2\left(\mathrm{g}\right)}+{\mathrm{O}}_{2\left(\mathrm{g}\right)}\to 2{\mathrm{H}}_2{\mathrm{O}}_{\left(\ell \right)};{\mathrm{\Delta S}}_{298}^0=-0.32\mathrm{kJ}/\mathrm{K}.$ What is the value ${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}_{298}^0\left({\mathrm{H}}_2\mathrm{O},\mathrm{\ell }\right)?$
Given : ${\mathrm{O}}_{2\left(\mathrm{g}\right)}+4{\mathrm{H}}_{\left(\mathrm{aq}\right)}^{+}+4{\mathrm{e}}^{-}\to 2{\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{\ell }\right)};{\mathrm{E}}^0=1.23\mathrm{V}$

$\begin{array}{l}\mathrm{\Delta G}=\mathrm{\Delta H}-{\mathrm{T\Delta S}}^0\\ -\mathrm{nFE}=\mathrm{\Delta H}-\mathrm{T\Delta S}\\ -4\times 1.23\times 96,500=\mathrm{\Delta H}-298\times (-0.32)\\ {\mathrm{\Delta H}}_{\text{for }2\text{ moles }}=-(4\times 1.23\times 96,500)-(298\times 0.32) =-570.14\\ {\mathrm{\Delta H}}_{{\mathrm{H}}_2\mathrm{O}}\text{ for }1\text{ mole }=-285.07\mathrm{KJ}/\mathrm{mole}\end{array}$