Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    For a first order reaction, the concentration changes from 0.8 to 0.4 in 15 min. The time taken for the concentration to change from \[0.01\,\,M\]to\[0.025\,\,M\] is

    A) 30 min                                  

    B) 15 min  

    C)        7.5 min         

    D)        60 min

    Correct Answer: A

    Solution :

                 \[{{T}_{50}}=50\,\,\min \]                  \[k=\frac{2.303\log 2}{{{T}_{50}}}=\frac{2.303\log 2}{15}\]                  \[a=0.1\,\,M\]         \[(a-x)=0.025\,\,M\] For first order reaction,                  \[k=\frac{2.303}{t}\log \left( \frac{a}{a-x} \right)\] \[\frac{2.303\log 2}{15}=\frac{2\times 2.303}{t}.\log \frac{0.1}{0.025}\]                     \[=\frac{2.303}{t}\log 4\] \[\therefore \] \[\frac{2.303\log 2}{15}=\frac{2\times 2.303\log 2}{t}\] \[\therefore \]\[t=30\,\,\min \]


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