Half‑Life Calculator: Zero‑Order Kinetics

Compute the half‑life (t_½) for zero‑order reactions directly in the browser. This tool is for students, researchers, and lab technicians. Supports molar (M, mM, µM) and time (s, min, h, d) units. No data leaves your device—runs entirely offline.

Note: Educational only. Follow your lab SOPs and SDS.

Inputs

Initial Concentration [A]₀

Enter a number (dots or commas accepted).

Rate Constant k

Units: concentration per time.

Output Time Unit

Results

Half‑life (zero‑order)

0.00 s

t_½ = [A]₀ / (2k)

Intermediate Values

[A]₀ (in M): 0.5000

k (in M/s): 0.0025

Half‑life (in s): 100.00

Export for Notebook

Half‑life (zero‑order) calculation:
[A]₀ = 0.5000 M, k = 0.0025 M/s
t½ = 100.00 s

Scenario Comparison

Adjust the slider to change the initial concentration and see how t_½ changes for your fixed k.

[A]₀ Multiplier: 1.0×

Scenario	[A]₀ (M)	t_½ (s)	t_½ (min)

Understanding Zero‑Order Half‑Life

In zero‑order kinetics, the reaction rate is independent of reactant concentration. The half‑life is directly proportional to the initial concentration and inversely proportional to the rate constant. This is common in surface‑catalyzed reactions or when an enzyme is saturated.

Step‑by‑Step Usage

Enter the initial concentration [A]₀ and select its unit.
Enter the zero‑order rate constant k (concentration per time) and choose its concentration and time units.
Select your desired output time unit (seconds, minutes, etc.).
Click Calculate t_½; results appear instantly.
Use the scenario slider to explore how changing [A]₀ affects half‑life.

Realistic Examples

Example 1: Decolorization of a dye on a catalyst

[A]₀ = 0.200 M, k = 1.0×10^‑3 M/s → t_½ = 100 s (1.67 min).

Example 2: Enzyme‑catalyzed reaction at saturation

[A]₀ = 5.0 mM, k = 0.05 mM/min → t_½ = 50 min.

Common Mistakes Checklist

Using the wrong rate‑constant units (ensure concentration/time matches [A]₀ unit).
Applying zero‑order formulas when the reaction is actually first‑ or second‑order.
Forgetting that zero‑order half‑life depends on initial concentration (unlike first‑order).
Not checking that [A] remains ≫ k·t throughout the reaction (otherwise order may change).

Frequently Asked Questions

When is zero‑order kinetics observed?

Zero‑order kinetics typically occur when a catalyst or enzyme is saturated, or in surface‑limited reactions. The rate is constant until reactant is nearly exhausted.

What are the limits of this approximation?

The zero‑order model fails when [A] drops close to zero, or if the reaction mechanism changes with concentration. Always verify linearity of [A] vs. time plot.

How do I measure k experimentally?

Plot concentration vs. time; the slope of the linear decrease is –k (in concentration per time). Use replicates and error bars for reliable k.

What safety considerations apply?

Zero‑order reactions can accelerate if temperature rises. Always monitor temperature, use appropriate containment, and follow SDS for all chemicals.

Formulas & Assumptions

Equation Used

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Half Life Calculator Zero Order

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