In which of the following chemical reactions is the standard reaction entropy change ($\Delta S^\cir

Question

In which of the following chemical reactions is the standard reaction entropy change ($\Delta S^\circ$) definitively positive, causing the standard Gibbs energy change ($\Delta G^\circ$) to become increasingly negative (more spontaneous) as temperature rises?

Professor PC Thomas Classes · Answer

(b) : The defining factor for a significant positive entropy change ($\Delta S^\circ > 0$) in a reaction is an increase in the number of moles of gaseous species ($\Delta n_g > 0$). Let's evaluate: (a) $\Delta n_g = 2 - (1+1) = 0$. (b) $\Delta n_g = 2 - 1 = +1$. (c) $\Delta n_g = 2 - (1+3) = -2$. (d) $\Delta n_g = 0 - (2+1) = -3$. Only reaction (b) has a positive $\Delta n_g$, hence $\Delta S^\circ > 0$. From $\Delta G = \Delta H - T\Delta S$, a positive $\Delta S$ ensures that as $T$ increases, the $-T\Delta S$ term becomes more negative, making $\Delta G$ decrease sharply.