## Zero Order Half-Life Relationship

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

edith_escalante_3G
Posts: 10
Joined: Wed Sep 21, 2016 2:57 pm

### Zero Order Half-Life Relationship

Hi, I was reading through the course reader trying to understand half-life reactions. Can someone explain why it says the half-life zero order reaction depends on the initial condition of A. Like what their relationship is?

Michelle_Li_1H
Posts: 32
Joined: Wed Sep 21, 2016 3:00 pm

### Re: Zero Order Half-Life Relationship

Hi!

The half life of the reaction is the time it takes for the reaction to reach half the initial concentration.

For the case of the zeroth order reaction, the integrated rate law is [A]=-kt + [A]o. Therefore the equation for the half life of this zeroth order reaction would mean the concentration of A would have to equal to half the initial concentration, giving you:

0.5 [A]o = -k t1/2 + [A]o

To solve for the time at which the concentration would be half of the initial, you would isolate t1/2 and end up with:

t1/2= [A]o / 2k