## Half life for second order reaction

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

Briana Yik 1H
Posts: 30
Joined: Fri Sep 28, 2018 12:20 am

### Half life for second order reaction

What is the formula for half life for a second order reaction? Thank you

megansardina2G
Posts: 61
Joined: Fri Sep 28, 2018 12:23 am
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### Re: Half life for second order reaction

The half life equation for a second order reaction is: t(1/2) = 1/(K)([A]o)

This can be derived from some of the equations that we got in class:

t=1/K (1/[A] - 1/[A]o) to get K= 1/(t(1/2))([A]o) and then switch the K and t(1/2)

you can also solve for the time it takes for decay that isn't to the half life (ex: 1/5) by combining these equations to get:
t = t(1/2) ([A]/[A]o - 1)