question_answer 1)

For the reaction; \[2A(g)+B(g)\to 2D(g)\] \[\Delta {{U}^{{}^\circ }}_{298\,K}=-10.5kJ\] and \[\Delta {{S}^{{}^\circ }}=-44.1J{{K}^{-1}}\] Calculate \[\Delta {{G}^{{}^\circ }}_{298K}\] for the reaction and predict whether the reaction is spontaneous or not.  

Answer:

\[\Delta {{H}^{{}^\circ }}=\Delta {{U}^{{}^\circ }}+\Delta {{n}_{g}}RT\] \[=-10.5+(-1)\times 8.314\times {{10}^{-3}}\times 298\] \[=-12.978kJ\] According to Gibbs-Helmholtz equation: \[\Delta {{G}^{{}^\circ }}=\Delta {{H}^{{}^\circ }}-T\Delta {{S}^{{}^\circ }}\] \[=-12.978-298(-44.1\times {{10}^{-3}})\] \[=+0.164kJ\] Since, \[\Delta G{}^\circ \text{ }=+ve\], hence the reaction is non-spontaneous.