Question

Determine the first half-life of the reaction. Determine the second and third half-lives. aA - bВ Time [A] (S) 0 0.0100 0.0071 8 0.0055 112 0.0045 16 0.0038

Answer 1

Expression for therate constant 1t or der Kineti cs: (1) 4 ] 1 Expres sion for therate constant 2nd order Kinetics: (2) The given reacti on belongs to that order which ever expression gives the constnat values of k. If the 1st expression gives the constant values of k, then the reaction is of 1st or der If the 2d expressi on gives the constant values of k, then the reacti on is of 2nd order. Initi al concentrati on of A,A 0.0100 M Concentrati on of A after 4 s, [A] 0.0071 M According to the lst order kinetics 0.0100 M 1 =0.0856 s , In = [A] Concentrati on of A after 8 s, A0.0055 M 0.0071 M 4 s According to the 1st order kinetics 0.0100 M 0.0055 M 1 2In [A] = 0.0747 s 8 s Concentrati on of A after 12 s, A = 0.0045 M According to the 1st order kinetics 0.0100 M 1 k=-ln [A] = 0.0665 s 0.0045 M 12 s Since the values of k does not comes out to be constant, this reacti on is not of the 1st order. Initi al concentrati on of A, A=0.0100 M Concentrati on of A after 4 s, A = 0.0071 M According to the 2nd order kinetics 1 1 1 1 1 = 10.2 M1 4 s0.0071M 0.0100 M Concentrati on of A after 8 s, A0.0055 M According to the 2nd order kinetics 1 1 1 1 = 10.2 M k 0.0100 M 8 s 0.0055M Concentrati on of A after 12 s, A]0.0045 M According to the 2nd order kinetics 1 1 1 1 =10.2 M [A [A 12 s 0.0045M 0.0100 M, Concentrati on of A after 16 s, [A] = 0.0038 M According to the 2nd order kinetics, -ा) 1 1 1 =10.2 M = 16 s0.0038M 0.0100 M Since the values of k comes out to be constant, this reaction is of the 2nd order Rate law Rate k[A Rate constant of the reaction, k 4 (10.2 4)+(10.2 A1)+(10.2 M) +(102.4 ) = 10.2 M1 = 4

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Rate law Rate k[A Rate constant of the reacti on,k=10.2 M1 Initi al concentrati on of the reactant A, [A 0.0100 M 1 Half-life of the 2nd order reaction [A) 1 (10.2 M's1) (0.0100 M) 1 0.102 s =9.80 s First half-life 9.80 s Second half-life = 2 x 9.80 s 19.6 s Third half-life 3x 9.80 s29.4 s =