$\frac{1}{2}{\mathrm{H}}_{2\left(\mathrm{ }\mathrm{g}\right)}+\frac{1}{2}{\mathrm{Cl}}_{2\left(g\right)}\to {\mathrm{HCl}}_{\left(\mathrm{g}\right)};\Delta {\mathrm{H}}^0=-92.4\mathrm{ }\mathrm{k}\mathrm{J}/\mathrm{mole}$ ${\mathrm{HCl}}_{\left(\mathrm{g}\right)}+{\mathrm{nH}}_2\mathrm{O}\to {\mathrm{H}}_{\left(aq\right)}^{+}+\mathrm{Cl}{ }_{\left(\text{aqq }\right)}$; ${\mathrm{\Delta H}}^0=-74.8 \mathrm{kJ}/\mathrm{mole}. {\mathrm{\Delta H}}_{\mathrm{f}}^0$ for ${\mathrm{Cl}}_{\left(\text{aq }\right)}$ is

$$\begin{gathered} \text{ Given, }\frac{1}{2}{\mathrm{H}}_2\left(\mathrm{g}\right)+\mathrm{aq}.\to {\mathrm{H}}_{\mathrm{aq}}^{+}+{\mathrm{e}}^{-} \\ {\mathrm{\Delta H}}^0=0\dots .\text{ (i) } \\ \frac{1}{2}{\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to \mathrm{HCl}\left(\mathrm{g}\right) \\ {\mathrm{\Delta H}}^0=-92.4\mathrm{kJ}\dots .\left(\text{ ii }\right) \\ \mathrm{HCl}\left(\mathrm{g}\right)+{\mathrm{nH}}_2\mathrm{O}\left(\mathrm{l}\right)\to {\mathrm{H}}_{\left(\mathrm{aq}\right)}^{+}+{\mathrm{Cl}}_{\left(\mathrm{aq}\right)}^{-} \\ {\mathrm{\Delta H}}^0=-74.8\mathrm{kJ}\dots .\text{ (iii)} \\ \mathrm{A}\text{dd. eq. (ii) and (iii) } \\ \frac{1}{2}{\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{Cl}}_2\left(\mathrm{g}\right)+{\mathrm{nH}}_2\mathrm{O}\to {\mathrm{H}}_{\left(\mathrm{aq}\right)}^{+}+{\mathrm{Cl}}_{\left(\mathrm{aq}\right)}^{-} \\ {\mathrm{\Delta H}}^0=-167.2\mathrm{kJ}\dots \dots \text{ (iv)} \\ \mathrm{S}\text{ubtract eq. (i) from (iv) } \\ \therefore \frac{1}{2}{\mathrm{Cl}}_2\left(\mathrm{g}\right)+{\mathrm{e}}^{-}\to {\mathrm{Cl}}_{\left(\mathrm{aq}\right)}^{-},\mathrm{\Delta H}=-167.2\mathrm{kJ} \end{gathered}$$

Hence option B  is the correct answer.