## 15.27 C & D

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

Cassidy 1G
Posts: 54
Joined: Fri Sep 29, 2017 7:07 am

### 15.27 C & D

Could someone explain question 15.27 parts c and d? I understand for parts a and b we can multiply the half-lives by 3 and 2 respectively but I don't think that method will work for c and d.
A substance A decomposes in a first-order reaction and its half life is 355 s. How much time must elapse for the concentration of A to decrease to (c) 15% of its initial concentration; (d) one-ninth of its initial concentration?

Janine Chan 2K
Posts: 71
Joined: Fri Sep 29, 2017 7:04 am

### Re: 15.27 C & D

Since 15% isn't a multiple of 1/2, we have to do more calculations. We first solve for k using the 1st-order equation t1/2=0.693/k.
If we end up with 15% of the initial concentration, we can say that [A]t=.15, and [A]0=1. By rearranging the equation ln[A]t = -kt + ln[A]0, we can solve for t.

We can do the same for part d by assuming [A]t=1, and [A]0=9.