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

Aman Bansal
592 Points
12 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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Aman Bansal