The half-life of a reaction, t1/2, is the time it takes for the reactant concentration [A] to decrease by half. For example, after one half-life the concentration falls from the initial concentration [A]0 to [A]0/2, after a second half-life to [A]0/4, after a third half-life to [A]0/8, and so on.
For a first-order reaction, the half-life is constant. It depends only on the rate constant k and not on the reactant concentration. It is expressed as
t1/2=0.693k
For a second-order reaction, the half-life depends on the rate constant and the concentration of the reactant and so is expressed as
t1/2=1k[A]0
1. A certain first-order reaction (A→products ) has a rate constant of 1.00×10-2s-1 at 45 °C. How many minutes does it take for the concentration of the reactant, [A] , to drop to 6.25% of the original concentration? Express your answer with the appropriate units.
2. A certain second-order reaction (B→products ) has a rate constant of 1.25×10-3M-1⋅s-1 at 27 °C and an initial half-life of 286 s . What is the concentration of the reactant B after one half-life?