Thermodynamics

For complete combustion of ethene.

\(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

the amount of heat produced as measured in bomb calorimeter is \(1406 \mathrm{~kJ} \mathrm{~mol}^{-1}\) at \(300 \mathrm{~K}\). The minimum value of \(\mathrm{T} \Delta \mathrm{S}\) needed to reach equilibrium is (\(-\)) _________ \(\mathrm{kJ}\). (Nearest integer)

Given : \(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\)