## 15.23 [ENDORSED]

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

Sammy Thatipelli 1B
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### 15.23

For 15.23, I am confused on why we use the equation ln[A]o/[A]t=kt, because I thought that the equation for first order half life reaction is used when it is written as: [A]t-[A]0=-kt. Can someone explain when we have to use this equation in our homework versus the other equation in our homework?

I am confused on if the two equations are equivalent and both work for solving for K in a first order reaction?

Thank you!

Hena Sihota 1L
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### Re: 15.23  [ENDORSED]

The equations ln[A]0/ln[A]t=kt and ln[A]t-ln[A]0=-kt are equivalent. If you divide both sides of the second equation by -1 then you get -[A]t+[A]0=kt which can be rewritten as [A]0-[A]t=kt. According to log rules, this equation can be rewritten as ln[A]0/ln[A]t=kt which is the first equation.