## First Order Integrated Law

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

Tamera Scott 1G
Posts: 65
Joined: Fri Sep 28, 2018 12:27 am

### First Order Integrated Law

Why is the equation ln([A]t[A]0)=−kt also written as ln([A]0[A]t)=kt? Are they the same thing?

Shubham Rai 2C
Posts: 64
Joined: Fri Sep 28, 2018 12:27 am

### Re: First Order Integrated Law

The difference is probably due to what the [A] value is. The - is probably associated with reactants while the equation with the - is associated with products.

Xinyi Zeng 4C
Posts: 63
Joined: Fri Sep 28, 2018 12:18 am

### Re: First Order Integrated Law

They are the same thing!
ln([A]t/[A]0)=−kt can be written as ln([A]t)-ln([A]0)=-kt [ according to the log rule that ln(a/b)=ln(a)-ln(b) ]
multiply both sides of the equation by -1, you will get:
-ln([A]t)+ln([A]0)=kt, hence ln([A]0)-ln([A]t)=kt
applying the log rule again, you will get ln([A]0[A]t)=kt

LeannaPhan14BDis1D
Posts: 57
Joined: Fri Sep 28, 2018 12:16 am

### Re: First Order Integrated Law

Yes they are the same thing.