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NEET AIPMT SOLVED PAPER SCREENING 2004

  • question_answer
    The rate of first order reaction is \[\text{1}.\text{5}\times \text{1}{{0}^{-\text{2}}}\]\[\text{mol}{{\text{L}}^{-1}}\]\[\text{mi}{{\text{n}}^{-\text{1}}}\] at 0.5 M concentration of the reactant. The half-life of the reaction is:                                                                                                                                       

    A) 0.383mm                    

    B) 23.1mm

    C) 8.73mm                                       

    D) 7.53mm

    Correct Answer: B

    Solution :

                            For the first order reaction Rate\[\left( \frac{dx}{dt} \right)=k[A]\] \[[A]\to \]concentration of reactant \[k\to \]rate constant Given that \[\frac{dx}{dt}=1.5\times {{10}^{-2}}\,mol\,\,{{L}^{-1}}\] \[k=?\]and\[[A]=0.5\,M\] \[\therefore \]          \[1.5\times {{10}^{-2}}=k\times 0.5\] \[\therefore \]          \[k=\frac{1.5\times {{10}^{-2}}}{0.5}=3\times {{10}^{-2}}{{\min }^{-1}}\] For first order reaction Half-life period \[{{t}_{1/2}}=\frac{0.693}{k}=\frac{0.693}{3\times {{10}^{-2}}}\] \[=23.1\,\,\min \]


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