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:
$$\begin{gathered}\mathrm{H}_{2} \mathrm{~S}(g)+{ }_{2}^{3} \mathrm{O}_{2}(g)
\longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{2}(g) ; \Delta
H=-518 \mathrm{~kJ} \\\\\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)
\longrightarrow \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H=-242 \mathrm{~kJ}
\\\\\frac{1}{8} \mathrm{~S}_{8}(\text { rhombic })+\mathrm{O}_{2}(g)
\longrightarrow \mathrm{SO}_{2}(g) ; \Delta H=-297
\mathrm{~kJ}\end{gathered}$$