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WB JEE Medical WB JEE Medical Solved Paper-2014

  • question_answer
    The values of \[\Delta H\]and \[\Delta S\]of a certain reaction are  \[-400\,kJ\,mo{{l}^{-1}}\]  and  \[-20\,kJ\,mo{{l}^{-1}}{{K}^{-1}}\] respectively. The temperature below which the reaction is spontaneous, is

    A)  100 K  

    B) \[20{{\,}^{o}}C\]  

    C)  20 K  

    D) \[120{{\,}^{o}}C\]

    Correct Answer: C

    Solution :

     Given,  \[\Delta \Eta =-400\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\] \[\Delta S=-20\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\,{{K}^{-1}}\] Gibbs Helmholtz equation is \[\Delta G=\Delta H-T\Delta S\] For a reaction to be spontaneous, \[\Delta G\]must be less than 0, i.e., negative. \[\therefore \] \[0\ge \Delta H-T\Delta S\] \[T\Delta S\le \Delta H\] \[T\le \frac{\Delta \Eta }{\Delta S}\le \frac{-400}{-20}\le 20\,K\]


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