HSC Science (General) 12th Board ExamMaharashtra State Board
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Solution - Derive the Relation Between Half Life and Rate Constant for a First Order Reaction - HSC Science (General) 12th Board Exam - Chemistry

Question

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

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`

 

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Reference Material

Solution for question: Derive the Relation Between Half Life and Rate Constant for a First Order Reaction concept: null - Half-life of a Reaction. For the courses HSC Science (General) , HSC Science (Electronics), HSC Science (Computer Science)
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