## Half life

$\frac{d[R]}{dt}=-k[R]^{2}; \frac{1}{[R]}=kt + \frac{1}{[R]_{0}}; t_{\frac{1}{2}}=\frac{1}{k[R]_{0}}$

DamianW
Posts: 35
Joined: Fri Sep 29, 2017 7:06 am

### Half life

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

Alyssa Pelak 1J
Posts: 72
Joined: Fri Sep 29, 2017 7:04 am
Been upvoted: 1 time

### Re: Half life

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!

Joanne Guan 1B
Posts: 30
Joined: Sat Jul 22, 2017 3:01 am

### Re: Half life

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.

Salman Azfar 1K
Posts: 50
Joined: Thu Jul 13, 2017 3:00 am

### Re: Half life

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.

Timothy Kim 1B
Posts: 62
Joined: Fri Sep 29, 2017 7:04 am

### Re: Half life

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.

Christina Bedrosian 1B
Posts: 33
Joined: Fri Sep 29, 2017 7:05 am

### Re: Half life

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

Jennie Fox 1D
Posts: 66
Joined: Sat Jul 22, 2017 3:01 am

### Re: Half life

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