### Homework, 6th edition, 15.35

Posted:

**Mon Mar 11, 2019 10:32 pm**Hi, I was wondering how I would use the second-order reaction (after I found k by using the half-life equation)?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=149&t=44218

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Posted: **Mon Mar 11, 2019 10:32 pm**

Hi, I was wondering how I would use the second-order reaction (after I found k by using the half-life equation)?

Posted: **Tue Mar 12, 2019 12:02 am**

You are given the [A]0 and you have k, from solving the half-life equation. You are trying to find time and you actually are given [A] as well. For example, in part a) you want to find how long it takes to decrease to one-sixteenth of the original which is [A] and you can figure that out by multiplying 1/16 by the [A]0 to give you [A]. Now you plug everything in to solve for t.

Posted: **Tue Mar 12, 2019 12:04 am**

Use the formula t1/2= [A]/2k to solve for k, then modify the formula for the other proportions.

eg.

t1/16= 15[A]/16k

t1/4= 3[A]/4k

etc

eg.

t1/16= 15[A]/16k

t1/4= 3[A]/4k

etc

Posted: **Tue Mar 12, 2019 12:46 am**

You know the half-life equation for a second-order reaction is: t_{1/2} = 1 / k [A]_{o}

Therefore, after finding k, you can use the integrated rate law 1/[A] = kt + 1/[A]_{o} for a second-order reaction to find t.

Therefore, after finding k, you can use the integrated rate law 1/[A] = kt + 1/[A]