(Solved): For a decomposition reaction:2CH \( \mathrm{CH}_{4}(g)+\mathrm{S}_{8}(g) \rightarrow 2 \mathrm{CS} ...

For a decomposition reaction:2CH \( \mathrm{CH}_{4}(g)+\mathrm{S}_{8}(g) \rightarrow 2 \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) \), What is the value of the equilibrium constant Kc for this reaction at \( 298 \mathrm{~K} \) ? Given that Gibbs free energy of formation at \( 298 \mathrm{~K} \mathrm{for} \mathrm{CH}_{4}(\mathrm{~g}) \) is \( -50.768 \mathrm{~kJ} / \mathrm{mol} \), for \( \mathrm{CS}_{2}(\mathrm{~g}) \) is \( 66.902 \mathrm{~kJ} / \mathrm{mol} \), for \( \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) \) is \( -33.054 \mathrm{~kJ} / \mathrm{mol} \) and for \( \mathrm{S}_{8}(\mathrm{~g}) \) is \( 49.162 \mathrm{~kJ} / \mathrm{mol} \)