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JEE MainChemistryChemical Kinetics

For a first order reaction A B , the ratio of the initial concentration of the reactant to its concentration at time t = 9.212 min is 100 . If the half-life of the reaction is x 10⁻³ min , the value of x is _____.

Correct answer

1386

Step-by-step solution

For a first order reaction, the rate constant k is given by: k = 2.303 t ( [A]₀ [A]_t ) Given t = 9.212 min and [A]₀ [A]_t = 100 : k = 2.303 9.212 (100) Since 9.212 = 4 2.303 and (100) = 2 : k = 1 4 2 = 0.5 min ⁻¹ The half-life t_ 1/2 is: t_ 1/2 = 0.693 k = 0.693 0.5 = 1.386 min Expressing this in the required format: t_ 1/2 = 1386 10⁻³ min Thus, x = 1386 . Answer: 1386

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