Question

Which one of the following is spontaneous at all temperatures?

• A. $ {{H}_{2}}_{(g)}\xrightarrow{{}}2{{H}_{\text{atom}}} $ $ \Delta {{H}^{o}}=436\,kJ, mol^{-1} \Delta {{S}^{o}}=90.7\,mol/K $
• B. $ \frac{1}{2}{{N}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}NO(g); $ $ \Delta {{H}^{o}}=90.3\,kJ,\Delta {{S}^{o}}=3.0 \,kJ/mol/K $
• C. $ 2N{{O}_{2}}(g)\xrightarrow{{}}{{N}_{2}}{{O}_{4}}(g) $ $ \Delta {{H}^{o}}=-56.0\,kJ\,, \Delta {{S}^{o}}=-17.7\text{eu} $
• D. $ {{H}_{2}}{{O}_{2}}_{(g)}\xrightarrow{{}}{{H}_{2}}O_{(l)}+\frac{1}{2}{{O}_{2}}_{(g)} $ $ \Delta {{H}^{o}}=-98.3\,kJ, \Delta {{S}^{o}}=80.0\,kJ/mol/K $

Answer 1

Answer: (D)

For a spontaneous process, $ \Delta G $ must be negative.
$ \Rightarrow $ $ \Delta G=\Delta H-T\Delta S $
$ \therefore $ For negative value of $ \Delta G $ at all temperatures,
$ \Delta H=-ve $ $ \Delta S=+\,ve $