The (\(\mathrm{S^\circ}\)) of the following substances are: \(\mathrm{CH_4}\)(g) \(186.2\,\mathrm{JK^{-1}mol^{-1}}\), \(\mathrm{O_2}\)(g) \(205.2\,\mathrm{JK^{-1}mol^{-1}}\), \(\mathrm{CO_2}\)(g) \(213.6\,\mathrm{JK^{-1}mol^{-1}}\), \(\mathrm{H_2O}\)(g) \(69.9\,\mathrm{JK^{-1}mol^{-1}}\). The entropy change (\(\Delta S^\circ\)) for the reaction \(\mathrm{CH_4(g)+2O_2(g)\to CO_2(g)+2H_2O(l)}\) is: