## Half life of 1st-Order Reaction

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

Fionna Shue 4L
Posts: 59
Joined: Fri Sep 28, 2018 12:18 am

### Half life of 1st-Order Reaction

Conceptually, why does the half life of a first order reaction not depend on the initial concentration?

Danielle_Gallandt3I
Posts: 70
Joined: Fri Sep 28, 2018 12:24 am

### Re: Half life of 1st-Order Reaction

I think it is because it is actually proportional to the rate constant k (so it is dependent on the environment, temp activation energy, etc). Another way to think about this is that a second half life takes the same amount of time as the first half life would, even though there is half the original concentration.

dgerges 4H
Posts: 65
Joined: Fri Sep 28, 2018 12:24 am

### Re: Half life of 1st-Order Reaction

because half life of any quantity of a first order reaction is the same, it'll take the same time to halve no matter how much it started with