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how does the time required for a first order reaction to go to 99% completion related to the half life of the reaction?

how does the time required for a first order reaction to go to 99% completion related to the half life of the reaction?


 

Grade:12th Pass

1 Answers

Aman Bansal
592 Points
9 years ago

Dear Sajid,

The integrated rate law of first oder order reaction, which gives the change of concentration with time, is:
ln[A] = -k·t + ln[A]0
where [A]0 is the initial concentration.
Since ln(a) - ln(b) = ln(a/b) you can write
ln( [A]/[A]0 ) = -k·t

Next introduce the the fractional completion of the reaction
X = ( [A] - [A]0)/[A]0 = 1 - [A]/[A]0
So the integrated rate law in term of completion is:
ln(1 - X) = -k·t

From the given completion data you can calculate the rate constant:

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