Hydrogen sulfide, $\mathrm{H}_{2} \mathrm{~S}$, is a poisonous gas with the odor of rotten eggs. The reaction for the formation of $\mathrm{H}_{2} \mathrm{~S}$ from the elements is
$$
\mathrm{H}_{2}(g)+\frac{1}{8} \mathrm{~S}_{8}(\text { rhombic }) \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g)
$$
Use Hess's law to obtain the enthalpy change for this reaction from the following enthalpy changes:
$$
\begin{array}{c}
\mathrm{H}_{2} \mathrm{~S}(g)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{2}(g) ; \Delta H=-518 \mathrm{~kJ} \\
\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H=-242 \mathrm{~kJ} \\
\frac{1}{8} \mathrm{~S}_{8}(\text { rhombic })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) ; \Delta H=-297 \mathrm{~kJ}
\end{array}
$$