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 


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.  

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