Question

After 47.0 min, 20.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?

Answer 1

First calculate rate constant for the reaction following first-order kinetics by using the formula given below:

K = 2.303/t log [A]_o/[A]_o - x

Here [A]_o = initial concentration of the reactant and x = amount of reactant reacted in the time t

K = 2.303/47 log(100/80) = 2.303/47 log(1.25) = 0.0047 min^-1

Now calculate half life. (half life is time in which concentration of reactants reduced to half of initial concentration)

t_1/2 = 2.303/K log[A]_o/([A]_o/2) = 2.303/K log2 = 0.693 / K

t_1/2 = 0.693 / K = 0.693 / 0.0047 = 147 .4 min