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 M ?

Question

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 M ?

| General Chemistry 2

Accepted Answer

First-order reaction:

t_1/2 = ln(2)/k

⇒ k = ln(2)/ t_1/2

⇒ k = ln(2)/22.0 = 3.15 x 10^-2 s^-1

$\frac{[A]}{{[A]}_{0}}$ = e^-kt

⇒ [A]₀ = [A] x e^kt

At t = 2.0 min = 120 s: [A]₀ = 0.0840 x e^{0.0315 x 120} = 3.68 M

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