## Integrated rate law confusion

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

sarahtang4B
Posts: 132
Joined: Fri Sep 28, 2018 12:27 am

### Integrated rate law confusion

In the homework problems why do we use ln[At]/[A0]=-kt sometimes and other times we use ln[A0]/[At]=kt for first order reactions?
What is the difference?

ThomasLai1D
Posts: 61
Joined: Fri Sep 28, 2018 12:17 am

### Re: Integrated rate law confusion

The difference is the placement of the minus signs. Both will net the same answer, but because of the treatment of the minus signs and properties of natural logs, the equations look different.

Hedi Zappacosta 1E
Posts: 66
Joined: Fri Sep 28, 2018 12:27 am

### Re: Integrated rate law confusion

It just depends which side of the equation you isolate. If you move the ln expressions to the right, then you will end up with the ln[A0] on top

Searra Harding 4I
Posts: 68
Joined: Fri Sep 28, 2018 12:29 am

### Re: Integrated rate law confusion

What is the benefit in using one over the other for a particular problem?

Jennifer Lathrop 1F
Posts: 71
Joined: Sat Dec 02, 2017 3:00 am

### Re: Integrated rate law confusion

^ I have the same question

Nicolette_Canlian_2L
Posts: 77
Joined: Fri Sep 28, 2018 12:25 am
Been upvoted: 1 time

### Re: Integrated rate law confusion

I don't believe there's a gain in using one over the other. It just depends on how you isolate the variables.