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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

  • question_answer
    A reaction that is of the first order with respect to reactant A has a rate constant \[6\,{{\min }^{-1}}.\]If we start with \[[A]=\text{0}\text{.5}\,\text{mol}\,{{\text{L}}^{-1}},\] when would [A] reach the value \[0.05\,\text{mol}\,{{\text{L}}^{-1}}?\]

    A) \[\text{0}\text{.384 min}\]         

    B) \[\text{0}\text{.15}\,\text{min}\]

    C)  3 min                                   

    D) \[\text{3}\text{.84}\,\text{min}\]

    Correct Answer: A

    Solution :

     We know that for first order kinetics \[K=\frac{2.303}{t}\log \frac{a}{a-x}\] Here\[K=6{{\min }^{-1}},a=0.5\,mol\,{{L}^{-1}}\] \[(a-x)=0.05mol\,{{L}^{-1}}\] \[6=\frac{2.303}{t}\log \frac{0.5}{0.05}\]                 or            \[t=\frac{2.303}{6}\log \frac{0.5}{0.05}=\frac{2.303}{6}=0.384\]


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