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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        For the following cell with hydrogen electrodes at two different pressures\[{{p}_{1}}\]and\[{{p}_{2}}\]\[\underset{{{p}_{1}}}{\mathop{pt({{H}_{2}})}}\,|\underset{1\,M}{\mathop{{{H}^{+}}(aq).}}\,|\underset{{{p}_{2}}}{\mathop{Pt({{H}_{2}})}}\,\]emf is given by:

    A)  \[\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}\]                   

    B)  \[\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}\]

    C)  \[\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}\]                   

    D)  \[\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}\]

    Correct Answer: B

    Solution :

                    L.H.S. half Cell: \[\underset{{{p}_{1}}}{\mathop{{{H}_{2}}(g)}}\,\xrightarrow[{}]{{}}2{{H}^{+}}(1M)+2{{e}^{-}}\] R.H.S. half cell:                 \[\begin{align}   & \underline{2{{H}^{+}}(1M)+2{{e}^{-}}\xrightarrow[{}]{{}}\underset{{{p}_{2}}}{\mathop{{{H}_{2}}(g)}}\,} \\  & \underline{\,\,\,\,\,\,\,\,\,\,\,\underset{{{p}_{1}}}{\mathop{{{H}_{2}}(g)}}\,\xrightarrow[{}]{{}}\underset{{{p}_{2}}}{\mathop{{{H}_{2}}(g)}}\,\,\,\,\,\,\,\,\,\,\,\,} \\ \end{align}\] \[E_{cell}^{o}=0.00V,\,K=\frac{{{p}_{2}}}{{{p}_{1}}},n=2\] \[{{E}_{cell}}=E_{cell}^{o}-\frac{RT}{nF}{{\log }_{e}}K\] \[=0-\frac{RT}{2F}{{\log }_{e}}K\] \[{{E}_{cell}}=\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}\]


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