Advertisement Remove all ads

Derive the Relation Between Half Life and Rate Constant for a First Order Reaction - Chemistry

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Derive the relation between half life and rate constant for a first order reaction

Advertisement Remove all ads

Solution

The integrated rate law for the first order reaction is given by the equation

`k= 2.303/t log_10"[A]_o/[A]_t`

Where [A]0 = initial concentration of the reactant at t = 0

The concentration falls to [A]t at time t from the start of the reaction.

The concentration of the reactant falls to [A]0/2 at time t1/2.
Therefore, t = t1/2
[A]t = [A]0/2
So, the equation can be written as

`k= 2.303/t_(1/2) log_10"[A]_o /([A]_o/2)`

     `=2.303/(t_1/2)log_10 2`

     `=2.303/(t_1/2)*0.301=0.693/(t_1/2)`

`t_(1/2)=0.693/k`

 

Concept: Integrated Rate Equations - Half-life of a Reaction
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×