## 15.23 b

$aR \to bP, Rate = -\frac{1}{a} \frac{d[R]}{dt} = \frac{1}{b}\frac{d[P]}{dt}$

Andrea Grigsby 1I
Posts: 60
Joined: Fri Sep 29, 2017 7:03 am

### 15.23 b

Why is the formula used for this question ln[A]0 / [A]t , instead of ln [A]t/[A]0?

Angela 1K
Posts: 80
Joined: Fri Sep 29, 2017 7:05 am

### Re: 15.23 b

I used the equation $ln\frac{[A]t}{[A]0} = -kt$ and got the same answer as the solutions manual. I think the two equations are equivalent because of the negative sign I used in my answer, when transferred to the other side, would flip the two concentrations.

David Zhou 1L
Posts: 61
Joined: Fri Sep 29, 2017 7:04 am

### Re: 15.23 b

It's just algebraic manipulation; flipping the numerator and denominator will give you the negative log value.

Jenny Cheng 2K
Posts: 30
Joined: Fri Sep 29, 2017 7:05 am
Been upvoted: 1 time

### Re: 15.23 b

If you make both sides of the equation ln([A]t/[A]0) = -kt negative, you will have: ln([A]0/[A]t) = kt. Making the natural log negative flips the content because:
ln([A]t/[A]0) = ln[A]t - ln[A]0