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
- A70 min
- B73 min
- C30 min
- 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