JEE Main & Advanced Chemistry Chemical Kinetics / रासायनिक बलगतिकी Sample Paper Topic Test - Chemical Kinetics

  • question_answer
    Consider the following case of completing 1st order reactions.
    After the start of the reaction at t = 0 with only A, the [C] is equal to the [D] at all times. The time in which all three concentrations will be equal is given by -

    A) \[t=\frac{1}{2{{k}_{1}}}\ell n3\]                       

    B) \[t=\frac{1}{2{{k}_{2}}}\ell n\,3\]

    C) \[t=\frac{1}{3{{k}_{1}}}\ell n2\]                       

    D) \[t=\frac{1}{3{{k}_{1}}}\ell n2\]

    Correct Answer: B

    Solution :

    \[{{k}_{1}}={{k}_{2}}\Rightarrow \frac{2}{3}rd\] of A has r exacted for \[\left[ A \right]=\left[ C \right]=\left[ D \right]\] \[\therefore \]      \[{{k}_{1}}+{{k}_{2}}=\frac{1}{t}\text{ }\ln \text{ }\frac{{{\left[ A \right]}_{0}}}{\frac{1}{3}{{\left[ A \right]}_{0}}}\] \[\Rightarrow \]   \[t=\frac{1}{{{k}_{1}}+{{k}_{2}}}\ln \text{ }3=\frac{1}{2{{k}_{1}}}\ln \text{ }3=\frac{1}{2{{k}_{2}}}\ln \text{ }3\]

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