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JEE MainChemistryChemical Kinetics

For a certain decomposition reaction, the half-life is observed to be independent of the initial concentration of the reactant. If it takes 140 min for 96 % of the reactant to decompose, the half-life of the reaction is: (Given: 2 = 0.30 ; 3 = 0.48 )

Options

  1. A70 min
  2. B73 min
  3. C30 min
  4. D2100 min

Correct answer

C. 30 min

Step-by-step solution

Since the half-life is independent of the initial concentration, the reaction follows first-order kinetics. Let the initial concentration be A₀ = 100 . Since 96 % of the reactant decomposes, the amount remaining at t = 140 min is A_t = 100 - 96 = 4 . Using the first-order integrated rate law: k = 2.303 t ( A₀ A_t ) k = 2.303 140 ( 100 4 ) k = 2.303 140 (25) We can evaluate (25) as 2 (5) . (5) = ( 10 2 ) = 1 - 2 = 1 - 0.30 = 0.70 (25) = 2 0.70 = 1.40 Substituting this back into the rate equation: k = 2.303 140 1.40

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