Discussion
For the reaction A → B at 298 K, the change in enthalpy is − 7 kJ.mol\(^{-1}\) and the change in entropy is − 25 J.K\(^{-1}\).mol\(^{-1}\). How much is the free energy change and whether the reaction is spontaneous or non-spontaneous ?
Answer: A
\(\Delta G\) is 450 J.mol\(^{-1}\) and the reaction is not spontaneous.
Use \(\Delta G = \Delta H - T\Delta S\), with \(\Delta H\) in joules:
\[ \begin{aligned} \Delta G &= -7000 - 298 \times (-25) \\ &= -7000 + 7450 \\ &= +450\ \text{J mol}^{-1} \end{aligned} \]
A positive \(\Delta G\) means the reaction is not spontaneous at 298 K: the favourable enthalpy change is outweighed by the decrease in entropy. Neither 900 J value follows from these data, and calling the reaction spontaneous ignores the sign of \(\Delta G\).
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