## Half Life

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

Selena_Wong_1I
Posts: 13
Joined: Wed Sep 21, 2016 2:56 pm

### Half Life

Why is the half-life of a first order reaction independent of the initial concentration?

nicoleclarke_lec1M
Posts: 25
Joined: Sat Jul 09, 2016 3:00 am

### Re: Half Life

When you look at the 1st order integrated rate law, you see that ln[A]=-kt+ln[A]o. At the half life, [A]=1/2 of [A]o. When you plug this value into the equation, you will get ln(1/2([A]o/[A]o)). The [A]o values cancel so you are left with simply ln 1/2. This is why the half life is independent of [A]o.