$(i)$ $\quad H_{2} O(\ell) \rightarrow H^{+}(a q .)+O H^{-}(a q .)$

$\Delta H_{r}=57.32 \,k J$

$(ii)$ $\quad H_{2}(g)+\frac{1}{2} O_{2}(g) \rightarrow H_{2} O(\ell)$

$\Delta H_{r}=-286.20 \,k J$

For reaction $(i)$

$\Delta {H_r} = \Delta H_f^o\left( {{H^ + },aq} \right) + \Delta H{\mkern 1mu} _f^o\left( {O{H^ - }.aq} \right) - \Delta H{\mkern 1mu} _f^o\left( {{H_2}O,\ell } \right)$

$57.32 - 0 + \Delta H{\mkern 1mu} _f^o\,\left( {O{H^{ - 1}},aq} \right) - \quad \Delta H_f^o\left( {{H_2}O,\ell } \right)\quad  \ldots (iii)$

For reaction $(ii)$

$\Delta {H_r} = \Delta H_f^o\left( {{H_2}O,l} \right) + \Delta H_f^o\left( {{H_2}O,\,l} \right) - \Delta H_f^o\left( {{H_2},g} \right) - \frac{1}{2}\Delta H_f^o({O_2},g)$

$ - 286.20 = \Delta H_f^o\,({H_2}O,l)$

On replacing this value in equ. $(iii)$ we have

$57.32 = \Delta H_f^o\left( {O{H^ - },aq} \right) - ( - 286.20)$

$\Delta H_f^o =  - 286.20 + 57.32$

$=-228.88 \,k J$