## 7th edition 7B.7

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

Alyssa Bryan 3F
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### 7th edition 7B.7

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) one-eighth of its initial concentration; (b) one-fourth of its initial concentration; (c) 15% of its initial concentration; (d) one-ninth of its initial concentration? How would you approach this question to solve for the different elapsed times?

Srikar_Ramshetty 1K
Posts: 64
Joined: Fri Sep 28, 2018 12:27 am

### Re: 7th edition 7B.7

You are given the reaction is a 1st order. For (a) and (b) you can simply multiply the half life by 2 then 3. For example, if we start off with 10M it takes 355 seconds to get to 5M or 1/2. It would take another 355 seconds to get to 2.5M or 1/4 and another 355 seconds to get to 1.25 or 1/8. For values that aren't divisble by two you can use the rewritten integrated equation.

[A]t=[A]e^-kt

To find k:
.5=1e^-k(355)
k=1.95 x 10^-3

To find time for 15% and 1/9 you can simply set the [A]t value to that number.

.15=1e^-(1.95 x 10^-3)(t)
t=973 seconds

Hope that helps!