First-order reaction kinetics

For an irreversible reaction $A\rightarrow B$, the first-order rate law is

$$-\frac{d[A]}{dt}=k[A],\qquad [A](t)=[A]_0e^{-kt}.$$

With no product initially, $[B](t)=[A]_0-[A](t)$ and $t_{1/2}=\ln(2)/k$. This model assumes constant temperature and volume, a 1:1 reaction, and no reverse or side reactions.

Try this: double the rate constant. What happens to the half-life? Then double the initial concentration while keeping the rate constant fixed. Does the half-life change?

Python version: download the file below and run python3 first_order.py. It creates kinetics.csv without extra packages. Change inputs with --rate 0.2 --initial 2 --duration 60. For a plot, install Matplotlib and add --plot.

A → BFirst-order reaction

Adjust the parameters to see how reactant and product concentrations change over time.

Rate constant k (s⁻¹)

0.10

Initial concentration [A]₀ (mol/L)

1.00

Duration (s)

60

━ [A] Reactant┄ [B] Product

Inspect time (s)

30.0

[A] = mol/L[B] = mol/Lt½ = s

ResetDownload CSV

The interactive version runs in your browser. Download the Python version below to run the same model on your computer.

Download Python source (.py)