## 7.27 half life

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

Alex Tchekanov Dis 2k
Posts: 118
Joined: Sat Aug 24, 2019 12:16 am

### 7.27 half life

Is there any formulas or a special way to solve this? I just used random problem solving to get the answer, but is there a specific way to do this with the half-life formula?

Katherine Wu 1H
Posts: 104
Joined: Fri Aug 30, 2019 12:15 am
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### Re: 7.27 half life

use equation for half-life of a first order rxn
t1/2=ln 2/k
k=ln 2/t1/2
k=0.154 h^-1
ln([A]0/[A]t)=kt
[A]/[A]0=e^-kt
after two hours this ratio is,
[A]/[A]0=e^-(0.154 h^-1)(2 h)=0.735
the mass of phenobarbital that remains after 2 hours is 0.735 x 150 mg = 110 mg. to restore the initial amount 40 mg must be re-injected