## Homework question

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

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

### Homework question

On 7B3b, its a first order reaction so how is it ln(A0/At) = kt and not -kt? I thought it was -kt for first order reactions?

If not, how did we get that equation?

Henry Krasner 1C
Posts: 64
Joined: Fri Sep 28, 2018 12:15 am

### Re: Homework question

This is a different way to display the first order reaction equation.
You start with
ln[A]=ln[A(initial)] - kt
Then you move ln[A(initial)] to the other side and use log rules to get
ln([A]/[A(initial)])=-kt.
Then divide by -k or -t depending on what you want to find.

The textbook just organizes it differently, but either method will allow you to obtain the same result.

Lia Inadomi 1I
Posts: 62
Joined: Fri Sep 28, 2018 12:15 am

### Re: Homework question

This is because it is ln([A]0/[A]t) instead of ln([A]t/[A]0) which is when it would be -kt. This is just because of log rules so ln([A]t/[A]0)=-ln([A]0/[A]t) because coefficient of a log can be seen as the exponent inside the log function

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