## First Order Reaction Equations

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

Kyra Dingle 1B
Posts: 55
Joined: Fri Sep 29, 2017 7:04 am

### First Order Reaction Equations

How do you know when to use $ln\frac{[A]_{t}}{[A]_{0}}=-kt$
or when to use $ln\frac{[A]_{0}}{[A]_{t}}=kt$ ?
Are there specific instances when we use each?

Priyanka Bhakta 1L
Posts: 50
Joined: Fri Sep 29, 2017 7:04 am

### Re: First Order Reaction Equations

I believe that both those equations are equivalent. I'm not sure where you got the equation with ln( [A]o / [A]t ) and a positive +kt, but they seem to be the same thing. Use them to find the k reaction constant value or t time it takes to get to a certain concentration from a given initial concentration. (all for a first order reaction only)

Tiffany Dao 1A
Posts: 32
Joined: Fri Sep 29, 2017 7:05 am

### Re: First Order Reaction Equations

They are the same equation. The only difference is the way you write the equation that they are derived from. In this case for ln [A]t/[A]o = -kt, it is derived from ln[A]t - ln[A]o = -kt
While the other equation comes from ln[A]o - ln[A]t = kt, which can be rewritten as -ln[A]t +ln[A]o =kt, if you compare this to the above equation, you just multiplied both sides by -1, therefore they are pretty much the same thing and should give you the same answer.

Patricia Macalalag 2E
Posts: 53
Joined: Sat Jul 22, 2017 3:00 am

### Re: First Order Reaction Equations

It's the same thing, you should get the same answer.