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CMC Medical CMC-Medical VELLORE Solved Paper-2008

  • question_answer
    For the homogeneous reaction\[xA+yB\rightleftharpoons lY+mZ\]\[\Delta H{}^\circ =-30\,kJ\,mo{{l}^{-1}}\]and                 \[\Delta S=-100\,JK\,mo{{l}^{-1}}\] At what temperature the reaction is at equilibrium?

    A)  \[50{}^\circ C\]                                

    B)  \[250{}^\circ C\]

    C)  \[100K\]                             

    D)  \[27{}^\circ C\]

    E)  \[500K\]

    Correct Answer: D

    Solution :

                    For the homogeneous reaction \[xA+yB\rightleftharpoons lY+mZ\] \[\Delta H{}^\circ =-\,30\,kJ\,\text{mo}{{\text{l}}^{-1}},\]\[\Delta S=-\,100\,J\,\text{mo}{{\text{l}}^{-1}}{{K}^{-1}}\] By using     \[\Delta G=\Delta H-T\cdot \Delta S\] At equilibrium: \[\Delta G=0\] \[\therefore \]                  \[\Delta H=T\cdot \Delta S\]                                 \[T=\frac{\Delta H}{\Delta S}=\frac{-30\times {{10}^{3}}J\,mo{{l}^{-1}}}{-100\,J\,mo{{l}^{-1}}\,{{K}^{-1}}}\]                                 \[T=300\,K\]                                     \[=300-273=27{}^\circ C\]


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