## 15.27

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

Naomi Jennings 2H
Posts: 21
Joined: Thu Jul 13, 2017 3:00 am

### 15.27

15.27 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 (a) 1/8 [A] ; (b) one-fourth of its 80
initial concentration; (c) 15% of its initial concentration; (d) one-ninth of its initial concentration?

How would you set up this question?

RyanS2J
Posts: 32
Joined: Thu Jul 27, 2017 3:00 am

### Re: 15.27

Since the reaction is first order, I used ln[A]t = ln[A]o - kt, where [A]t is the concentration of A after some time and [A]o is the initial concentration of A, and plugged in the fraction of A remaining after some time for [A]t and 1 for [A]o.

Kayla Ikemiya 1E
Posts: 56
Joined: Fri Sep 29, 2017 7:04 am

### Re: 15.27

For part c, shouldn’t you get on (0.15) when subtracting the natural log of the concentrations instead of ln (1/0.15)?

Kayla Ikemiya 1E
Posts: 56
Joined: Fri Sep 29, 2017 7:04 am

### Re: 15.27

Never mind I see that there’s different ways to add/subtract things to both sides. I’m a brick

Audrey Goodman 1F
Posts: 31
Joined: Fri Sep 29, 2017 7:06 am

### Re: 15.27

For parts a) and b), you can also multiply the half-life by 3 for a) and 2 for b) since when 1/8 is remaining is the time elapsed for 3 half-lives ( (1/2)^3) and since 1/4 remaining is the time elapsed for 2 half-lives ( (1/2)^2). However, for parts c) and d), you must solve using the equations.

Caitlin Mispagel 1D
Posts: 47
Joined: Tue Oct 10, 2017 7:13 am

### Re: 15.27

What happens to the k when you rearrange the equation?

Alysa Rallistan 2G
Posts: 32
Joined: Thu Jan 17, 2019 12:16 am

### Re: 15.27

Do you neglect k in the equations? and do you have to solve for regular t or can you use t(1/2) in the equation?