CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

  • question_answer
    A reaction was observed for 15 days and the percentage of the reactant remaining after the days indicated was recorded in the following table
    Time (days) % Reactant remaining
    0 100
    2 50
    4 39
    6 25
    8 21
    10 18
    12 15
    14 12.5
    15 10
    Which one of the following best describes the order and the half-life of the reaction?

    A)
    Reaction order Half-life (days)
    First 2

    B)
    Reaction order Half-life (days)
    First 6

    C)
    Reaction order Half-life (days)
    Second 2

    D)
    Reaction order Half-life (days)
    Zero 6

    E)
    Reaction order Half-life (days)
    Third 2

    Correct Answer: C

    Solution :

    \[100\xrightarrow[{}]{2\,days}50\] \[50\xrightarrow[{}]{4\,days}25\] \[25\xrightarrow[{}]{8\,days}12.5\] Hence, the order of reaction is second. For second order reaction, \[k=\frac{1}{t}\left[ \frac{x}{a(a-x)} \right]=\frac{1}{2}\left[ \frac{50}{100\times 50} \right]\]                 \[=\frac{1}{200}\]                 \[{{t}_{1/2}}=\frac{1}{k.a}\] \[\Rightarrow \]               \[=\frac{1}{1/200.100}\]                 \[=\frac{200}{100}=2\,days\]


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