## 15.21 SOS!!!!!

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

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Frenz Cabison 1B
Posts: 54
Joined: Fri Sep 29, 2017 7:07 am

### 15.21 SOS!!!!!

Where did ln [A]t / [A]o = -kt come from? I was looking at the formula sheet thinking it was an original formula, but I think it is derived???

Lena Nguyen 2H
Posts: 51
Joined: Fri Sep 29, 2017 7:06 am
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### Re: 15.21 SOS!!!!!

The equation is [A]t / [A]0 = e^-kt. From ln [A]t = -kt + ln [A]0,

ln[A]t - ln [A]0 = -kt
ln [A]t / [A]0 = -kt
[A]t / [A]0 = e^-kt (Exponentiate both sides)

torieoishi1A
Posts: 32
Joined: Sat Jul 22, 2017 3:00 am

### Re: 15.21 SOS!!!!!

It is a property of natural logs. When you subtract two natural logs, you can use division.
For example, lnA-lnB= ln(A/B)
So we are given lnA=-kt+lnA(initial)
Then you can change it depending on what you are solving for:
So lnA-lnA(initial)=-kt which is converted to ln(A/A(initial))=-kt

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