• # question_answer 10) For oxidation of iron: $4Fe(s)+3{{O}_{2}}(g)\to 2F{{e}_{2}}{{O}_{3}}(s);$ entropy change is$-549.4J{{K}^{-1}}mo{{l}^{-1}}$ at 298K. Inspite of negative entropy change of this reaction, why is the reaction spontaneous? ${{\Delta }_{r}}{{H}^{{}^\circ }}$for this reaction is$-1648\times {{10}^{3}}J\,mo{{l}^{-1}}$.

Information shadow: $\Delta {{S}_{system}}=-549.4J{{K}^{-1}}mo{{l}^{-1}}$ ${{\Delta }_{r}}{{H}^{{}^\circ }}=-1648\times {{10}^{3}}J\,mo{{l}^{-1}}$ $T=298K$(at standard state) Problem solving strategy: $\Delta {{S}_{Total}}=\Delta {{S}_{System}}+\Delta {{S}_{surroundings}}$ $\Delta {{S}_{Total}}>0$for spontaneous process. Working it out: $\Delta {{S}_{surroundings}}=\frac{\Delta {{H}_{surroundings}}}{T}$ $=\frac{+1648\times {{10}^{3}}}{298}=5530J{{K}^{-1}}mo{{l}^{-1}}$ $\Delta {{S}_{Total}}=-549.4+5530$ $=4980.6J{{K}^{-1}}mo{{l}^{-1}}$ $=+ve$ Hence, the reaction under consideration is spontaneous.