### Half life

Posted:

**Sun Mar 11, 2018 5:20 pm**for a second order reaction, when given something like 1/16 why do you flip it in the equation and write 16-1?

Created by Dr. Laurence Lavelle

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

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=149&t=29409

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Posted: **Sun Mar 11, 2018 5:20 pm**

for a second order reaction, when given something like 1/16 why do you flip it in the equation and write 16-1?

Posted: **Sun Mar 11, 2018 5:58 pm**

you would use the integrated rate law for this question.

1/[A]=kt+1[A]0

1/[A]-1/[A]0=kt

You know that 1/[A] is 1/16[A]0 so you sub that into the equation:

1/(1[A]0/16)-1/[A]0=kt

In order to remove the fraction in the denominator you get

16/[A]0-1/[A]0=kt

Hope this helps!

1/[A]=kt+1[A]0

1/[A]-1/[A]0=kt

You know that 1/[A] is 1/16[A]0 so you sub that into the equation:

1/(1[A]0/16)-1/[A]0=kt

In order to remove the fraction in the denominator you get

16/[A]0-1/[A]0=kt

Hope this helps!

Posted: **Sun Mar 11, 2018 10:14 pm**

If you're talking about finding the time for when the concentration is 1/16 of the initial concentration, you would use the integrated second-order rate law which is:

1/{A] = 1/[A]_{0} + kt

[A] = (1/16)[A]_{0}

Subbing that into the 1/[A] part would give you 1/((1/16)[A]_{0}), and if you reorganize it, you have 16[A]_{0}.

1/{A] = 1/[A]

[A] = (1/16)[A]

Subbing that into the 1/[A] part would give you 1/((1/16)[A]

Posted: **Mon Mar 12, 2018 10:14 am**

The key is that when you put them into the formula (integrated second order rate law) I believe you end up using reciprocals due to the way the law is formatted. Just remember that half life problems for second order problems usually require use of the rate law; they aren't usually as simple as adding together multiple half lives for first order.

Posted: **Mon Mar 12, 2018 4:08 pm**

Since it is a fraction, the value would appear flipped when it is used in the second-order reaction. take a look at the respective equations and you will see that the values correspond to each other.

Posted: **Tue Mar 13, 2018 11:16 am**

it is 1/(1/16) making it 16/1 (it flips); just plug it into the equation and you should be fine

Posted: **Tue Mar 13, 2018 4:23 pm**

If you plug it in to the equation, you should get the correct answer. 1/(1/16) is 16.