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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 38

  • question_answer
    Assume that the decomposition of \[HN{{O}_{3}}\] can be represented by the following equation \[4NH{{O}_{3}}(g)\rightleftharpoons 4N{{O}_{2}}(g)+2{{H}_{2}}O(g)+{{O}_{2}}(g)\] and the reaction approaches equilibrium at 400 K temperature  and 30  atm pressure. At equilibrium partial pressure of \[HN{{O}_{3}}\] is 2 atm- Calculate \[{{K}_{c}}\]in \[{{\left( mol/L \right)}^{3}}\] at 400 K: \[(Use:R=0.08\text{ }atm-L/mol-K)\]

    A) 4     

    B)                    8   

    C) 16                    

    D)        32

    Correct Answer: D

    Solution :

    [d] \[{{P}_{total}}={{P}_{HN{{O}_{3}}}}+{{P}_{N{{O}_{2}}}}+{{P}_{{{H}_{2}}O}}+{{P}_{{{O}_{2}}}}\] \[\therefore {{P}_{N{{O}_{2}}}}=4{{P}_{{{O}_{2}}}}\,and\,{{P}_{{{H}_{2}}O}}=2{{P}_{{{O}_{2}}}}\] \[\therefore \text{ }{{P}_{total}}={{P}_{HN{{O}_{3}}}}+7P{{o}_{2}}\] \[\Rightarrow 30-2=P{{o}_{2}}\times 7\] \[{{K}_{p}}=\frac{P_{N{{O}_{2}}}^{4}.{{P}_{{{H}_{2}}O}}.P{{O}_{2}}}{P_{HN{{O}_{3}}}^{4}}\] \[={{\frac{{{(4\times 4)}^{4}}\times {{(2\times 4)}^{2}}\times 4}{{{2}^{4}}}}^{3}}={{2}^{20}}\] \[{{K}_{p}}={{K}_{c}}{{(RT)}^{\Delta {{n}_{g}}}}={{K}_{c}}{{(0.08\times 400)}^{3}}\] \[\Rightarrow {{K}_{c}}=\frac{{{2}^{20}}}{{{(32)}^{3}}}=32\]


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