Consider the following reaction :
\(2 A( g )+ B ( g ) \rightarrow 2 D ( g )\)
\(\Delta U^{\ominus}=-10 kJ mol ^{-1}\) and \(\Delta S^{\ominus}=-44 J K ^{-1}\) at 298 K.
Identify the correct option with \(\Delta G^{\ominus}\) for the reaction and spontaneity of the reaction at 298 K .
(Given : \(R=8.31 J mol ^{-1} K^{-1}\) )

(C) \(+0.63568 kJ mol ^{-1}\), non-spontaneous
The change in the number of moles of gaseous species is:
\(\Delta n_g=n_p-n_r=2-(2+1)=-1\)
The standard enthalpy change \(\Delta H^{\ominus}\) is given by:
\(\Delta H^{\ominus}=\Delta U^{\ominus}+\Delta n_g R T\)
Substituting the given values:
\(\Delta H^{\ominus}=-10+(-1) \times\left(8.31 \times 10^{-3}\right) \times 298\)
\(\Delta H^{\ominus}=-10-2.47638=-12.47638 kJ mol^{-1}\)
The standard Gibbs free energy change \(\Delta G^{\ominus}\) is:
\(\Delta G^{\ominus}=\Delta H^{\ominus}-T \Delta S^{\ominus}\)
\(\Delta G^{\ominus}=-12.47638-298 \times\left(-44 \times 10^{-3}\right)\)
\(\Delta G^{\ominus}=-12.47638+13.112=+0.63562 kJ mol^{-1}\)
Since \(\Delta G^{\ominus}>0\), the reaction is non-spontaneous.