Rate constant, K for first order reaction has been found to be 2.54*10 to the power -3 per sec. Calculate its three-fourth life.
The integrated rate equation for a first order reaction is written as
(1)
where k is the reaction constant, t is the time in which reaction has occurred, [A]1 is the initial concentration and [A]2 is the concentration after time t. [A]2 is also written as
[A]2 = [A]1 - x
where x is the amount of reaction that has occurred.
Three fourth life means that 3/4 of the reaction has taken occurred. Let us assume that for the given reaction the initial concentration of the reactant is [A]1. Let t be the time in which the concentration is reduced by 3/4. So [A]2 = 1/4 [A]1 = 0.25 [A]1. We are given that k =2.54 X 10-3 s-1. Substituting these values in equation (1), we get
t = {2.303 / (2.54 X 10-3)} log {[A]1 / 0.25 [A]1}
Solving the above, we get
t = 546 s
Therefore the 3/4 life of the reaction is 546 seconds.