## First Order- Half life

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

Niyanta Joshi 1F
Posts: 30
Joined: Thu Jul 13, 2017 3:00 am

### First Order- Half life

Why does the first order half life not depend on the initial concentration of reactant? Also, would higher temperature of the reaction lead to a slower half life?

Dylan Davisson 2B
Posts: 50
Joined: Thu Jul 27, 2017 3:00 am
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### Re: First Order- Half life

The half life for a first-order reaction is derived from the integrated rate law for first order reactions. And when manipulating this integrated rate law into a half life equation, the concentration of the reactant [A]t is changed to 1/2[A]0, which allows the initial concentration ([A]0]) to cancel with the 1/2[A]0. So, the initial concentration cancels out and all that is left is the half life= (ln2)/k.

And as far as I know, a higher temperature would make for a shorter half life. The reaction would occur more quickly because more particles collide at higher temperature, and because reactions can only occur when particles collide, more collisions means more (faster) reaction.