JEE Main & Advanced Chemistry Chemical Kinetics / रासायनिक बलगतिकी Sample Paper Topic Test - Chemical Kinetics

  • question_answer
    For a first-order homogeneous gaseous reaction \[A\to 2B+C,\] if the total pressure after time t was \[{{P}_{t}}\] and after long time \[(t\to \infty )\] was \[{{P}_{\infty }}\] then k in terms of \[{{P}_{t}},\,{{P}_{\infty }}\] and t is:

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

    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) None of these

    Correct Answer: C

    Solution :

    \[A\] \[\to \] \[2B\] \[+\] \[C\]
    \[t=0\] \[{{p}_{i}}\] 0 0
    \[t\] \[{{p}_{i}}-x\] \[2x\] \[x\]
    \[t\to \infty \] 0 \[2{{p}_{i}}\] \[{{p}_{i}}\]
    \[{{P}_{\infty }}=3{{P}_{i}}\] or \[{{P}_{i}}=\frac{{{P}_{\infty }}}{3};{{P}_{i}}+2x={{P}_{i}}\] As we know \[k=\frac{2.303}{t}\log \left( \frac{{{P}_{i}}}{{{P}_{i}}-x} \right)\] So \[k=\frac{2.303}{t}\log \left( \frac{2{{P}_{\infty }}}{3\left( {{P}_{\infty }}-{{P}_{t}} \right)} \right)\]

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