# First-order reactions - 2 | Chemical Kinetics: Rate Laws

The half-life for a first order reaction is 22.0 s.

What was the original concentration if, after 2.00 minutes, the reactant concentration is 0.0840 ?

First-order reaction:

t1/2 = ln(2)/k

⇒ k = ln(2)/ t1/2

⇒ k = ln(2)/22.0 = 3.15 x 10-2 s-1

$\frac{\left[\mathrm{A}\right]}{{\left[\mathrm{A}\right]}_{0}}$ = e-kt

⇒ [A]0 = [A] x ekt

At t = 2.0 min = 120 s: [A]0 = 0.0840 x e0.0315 x 120 = 3.68 M