Develop the expressions for the mole fractions of reacting species as functions of the reaction coordinate for a system initially containing \(3 \mathrm{~mol} \mathrm{H}_{2} \mathrm{~S}\) and \(5 \mathrm{~mol} \mathrm{O}_{2}\) undergoing the following reaction:

\[ 2 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+2 \mathrm{SO}_{2}(\mathrm{~g}) \]