Calculator Inputs
Decay Plot
The graph updates after calculation and shows concentration decay across time using the selected kinetic model.
Example Data Table
| Case | Reaction Order | [A]₀ | [A]t | Elapsed Time | Estimated k | Half-life |
|---|---|---|---|---|---|---|
| Sample 1 | Zero-order | 1.00 mol/L | 0.52 mol/L | 12 min | 0.0400 mol/L/min | 12.50 min |
| Sample 2 | First-order | 1.00 mol/L | 0.35 mol/L | 12 min | 0.0875 1/min | 7.92 min |
| Sample 3 | Second-order | 0.80 mol/L | 0.32 mol/L | 10 min | 0.1875 1/(mol/L·min) | 6.67 min |
Formula Used
Half-life is the time required for concentration to drop to half of its starting value. The expression depends on the reaction order.
Zero-order kinetics
Integrated law: [A]t = [A]₀ − kt
Half-life: t½ = [A]₀ / (2k)
Zero-order half-life depends directly on the starting concentration.
First-order kinetics
Integrated law: ln([A]₀ / [A]t) = kt
Half-life: t½ = ln(2) / k
First-order half-life stays constant regardless of starting concentration.
Second-order kinetics
Integrated law: (1 / [A]t) − (1 / [A]₀) = kt
Half-life: t½ = 1 / (k[A]₀)
Second-order half-life shortens when the initial concentration rises.
How to Use This Calculator
- Select the reaction order that best matches your chemical system.
- Choose whether to estimate the rate constant from measured data or enter a known value directly.
- Enter the initial concentration and any required observed concentration and elapsed time values.
- Optionally add a prediction time and target concentration for deeper analysis.
- Press Calculate Half Life to show results above the form.
- Review the calculated half-life, rate constant, elapsed half-lives, projected concentration, and graph.
- Use the export buttons to save your current result summary as CSV or PDF.
Frequently Asked Questions
1. What does chemical half-life mean?
Chemical half-life is the time required for a reactant or substance concentration to fall to half of its initial value under defined reaction conditions.
2. Why does reaction order matter here?
Reaction order changes both the integrated rate law and the half-life formula. Zero, first, and second order systems decay differently over time.
3. Does first-order half-life depend on starting concentration?
No. For first-order decay, half-life depends only on the rate constant. That is why radioactive and many decomposition processes show constant fractional decay.
4. Can I estimate the rate constant from lab measurements?
Yes. Choose experimental data mode, then enter initial concentration, observed concentration, and elapsed time. The calculator estimates k using the selected kinetic model.
5. What units should I use?
Use any consistent concentration and time units. The calculator keeps your labels, but the inputs must all follow the same unit system.
6. What is the prediction time field for?
Prediction time estimates how much concentration remains at a future time using the calculated or supplied rate constant and your selected reaction order.
7. Why does zero-order half-life change with initial concentration?
In zero-order kinetics, the substance disappears at a constant rate. Because the rate is fixed, a larger initial amount takes longer to halve.
8. Can this calculator replace experimental validation?
No. It is a fast analytical tool for estimation and planning. Final kinetic decisions should still be checked against controlled laboratory measurements.