Two isomers (A and B) of a given compound dimerize as follows: 2A rightarrow A_2

Question

Two isomers (A and B) of a given compound dimerize as follows: 2A rightarrow A_2 2B rightarrow B_2 Both processes are known to be second order in reactant, and k_1 is known to be 0.29 L/mol at 25 degree C, where: Rate = - Delta [A]/Delta t = k_1[A]^2 In a particular experiment, A and B were placed in separate containers at 25 degree C, where [A] = 1.0 times 10^-2 M and [B]_0 = 2.5 times 10^-2 M. It was found that [A] = 3[B] after the reactions progressed for 3.0 minutes. Calculate the half-life for the reaction involving A. A) 3.4 times 10^2 s B) 1.0 times 10^2 s C) 1.8 times 10^2 s D) 2.9 times 10^3 s E) none of these

Explanation / Answer

Half -life of a second order reaction is = 1/k[A0]

where k is the second order rate constant

[A0] is the initial concentration of A

Value of k1 is (for A, it is clear from the rate equation) given as 0.29 L/M.s

half-life of A = 1/(0.29)(1 x 10-2) = 344 s = 3.44 102 s

option B is correct

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