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JEE Main & Advanced AIEEE Solved Paper-2003

  • question_answer
    For the reaction system                 \[2NO(g)+{{O}_{2}}(g)\xrightarrow{{}}2N{{O}_{2}}(g)\]   volume is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to \[{{O}_{2}}\] and second order with respect to NO; the rate of reaction will     AIEEE  Solved  Paper-2003

    A) diminish to one-fourth of its initial value

    B) diminish to one-eighth of its initial value

    C) increase to eight times of its initial value

    D) increase to four times of its initial value

    Correct Answer: C

    Solution :

    Write the rate law equation for both cases and compare them.                                 \[\left( \frac{dx}{dt} \right)=k{{[NO]}^{2}}\,[{{O}_{2}}]\]                                                 \[=k{{\left( \frac{{{n}_{NO}}}{V} \right)}^{2}}\left( \frac{{{n}_{{{O}_{2}}}}}{V} \right)\]                     \[\left( \frac{dx}{dt} \right)=\frac{k}{{{V}^{3}}}{{({{n}_{NO}})}^{2}}({{n}_{{{O}_{2}}}})\]                 ... (i)                     \[\left( \frac{dx}{dt} \right)=\frac{k\,{{({{n}_{NO}})}^{2}}({{n}_{{{O}_{2}}}})}{{{\left( \frac{V}{2} \right)}^{3}}}\]                      ?. (ii) From Eqs. (i) and (ii)                 \[\left( \frac{dx}{dt} \right)'=8\left( \frac{d\,x}{dt} \right)\]


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