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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 21

  • question_answer
    Ethylene is produced by \[{{C}_{4}}{{H}_{8}}\xrightarrow{\Delta }2{{C}_{2}}{{H}_{4}}\] The rate constant is \[2.3\times {{10}^{-4}}{{s}^{-1}}\]. Approximately in what time will the molar ratio of ethylene to cyclobutane in mixture attain the value equal to one? \[(\log \,2=0.3,\,\,\log 3=0.47)\]

    A) \[1700\,s\]                     

    B) \[1600\,s\]

    C) \[2000\,s\]              

    D)        \[1200\,s\]

    Correct Answer: A

    Solution :

    \[{{C}_{4}}{{H}_{8}}\xrightarrow{{}}2{{C}_{2}}{{H}_{4}}\]
    Moles at \[t=0\] a 0
    Moles at \[t=t\] \[(a-x)\] 2x
    when \[\frac{2x}{a-x}=1\] then \[x=\frac{a}{3}\] \[\therefore \,\,\,t=\frac{2.303}{k}\log \frac{a}{(a-x)}\] \[=\frac{2.303}{2.3\times {{10}^{-4}}}\log \frac{a}{a-\frac{a}{3}}=1700s\]


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