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JEE Main & Advanced Sample Paper JEE Main Sample Paper-28

  • question_answer
    \[A\to 2B+C\]. The above first order reaction has total pressure \[{{P}_{t}}\] after time t and after long time \[(t\to \infty )\] was\[{{P}_{\infty }}\], then k in terms of \[{{P}_{t}}\], \[{{P}_{\infty }}\] and t is

    A)  \[k=\frac{2.303}{t}\log \frac{{{P}_{\infty }}}{({{P}_{{{\infty }^{-}}}}{{P}_{t}})}\]  

    B)  \[k=\frac{2.303}{t}\log \left( \frac{2{{P}_{\infty }}}{({{P}_{{{\infty }^{-}}}}{{P}_{t}})} \right)\]

    C)  \[k=\frac{2.303}{t}\log \left( \frac{2{{P}_{\infty }}}{3\left( {{P}_{{{\infty }^{-}}}}{{P}_{t}} \right)} \right)\]             

    D)  \[k=\frac{2.303}{t}\log \left( \frac{{{P}_{\infty }}}{{{P}_{t}}} \right)\]

    Correct Answer: C

    Solution :

    \[A\xrightarrow{{}}2B+C\]
    \[t=0\] \[{{P}_{i}}\] \[0\] \[0\]
    \[t=t\] \[({{P}_{i}}-x)\] \[2x\] \[x\]
    \[t=\infty \] \[0\] \[2{{P}_{i}}\] \[{{P}_{i}}\]
    \[{{P}_{\infty }}=3{{P}_{i}}\Rightarrow {{P}_{i}}=\frac{{{P}_{\infty }}}{3}\] \[P+2x={{P}_{i}}\] \[x=\frac{{{P}_{t}}-{{P}_{i}}}{2}\] \[k=\frac{2.303}{t}\log \left( \frac{{{P}_{i}}}{{{P}_{i}}-x} \right)\] \[=\frac{2.303}{t}\log \left( \frac{2{{P}_{\infty }}}{3({{P}_{\infty }}-{{P}_{t}})} \right)\]


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