Calculate the standard free energy change, \(\triangle\)G\(^\circ\), for the following reaction. Is the reaction spontaneous?
CH\(_4\) (g) + 2 O\(_2\) (g) \(\longrightarrow\) CO\(_2\) (g) + 2 H\(_2\)O (l)
Values of standard molar entropy, S\(_{f}^\circ\) are as follows: CH\(_4\) (g), 186 J/(K*mol); O\(_2\) (g), 205 J/(K*mol); CO\(_2\) (g), 213.6 J/(K*mol); 2 H\(_2\)O (l), 69.9 J/(K*mol)
\(\triangle\)H\(^\circ\) for this reaction is -890.3 kJ