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### Problem 15.35 (half life)

Posted: Wed Mar 13, 2019 7:06 pm
given the half-life, how do we calculate the time needed for a certain amount of the reactant's concentration to decrease using the half-life equation

for example : (problem 15.35)
The half-life for the second-order reaction of a substance A is 50.5 s when [A]0 = 0.84 mol/L. Calculate the time needed for the concentration of A to decrease to (a) one-sixteenth; (b) one-fourth; (c) one-fifth of its original value.

is there a way to calculate these values more quickly using only the half-life equation? or do we have to solve for k using the half-life equation and then solve for time using the integrated rate law

### Re: Problem 15.35 (half life)

Posted: Thu Mar 14, 2019 1:33 am
first you solve for k then you use the formula to solve for t and you get t = (1/[A]t - 1/[A]o)/k to solve for t in which [A]t can be replaced by (1/16)[A]o , (1/4)[A]o , and (1/5)[A]o which gives you something like for 1/16th : t = (16/[A]o - 1/[A]o)/k