Half-Life Calculator (Second Order)

Computes the half-life (t_½) for second-order reactions from the rate constant (k) and initial concentration ([A]₀). Built for students, researchers, and lab technicians. Supports units M, mM, µM, s⁻¹, min⁻¹, and h⁻¹. Fully offline, no data leaves your browser.

Educational only. Follow your lab SOPs and SDS.

Result

Half‑Life (t_½)

200.00

seconds

Rate constant (k) in base units 0.05 M⁻¹·s⁻¹

[A]₀ in base units 0.1000 M

Calculation check t_½ = 1/(k·[A]₀) ✓

Understanding Second‑Order Half‑Life

In second‑order kinetics, the half‑life depends on both the rate constant and the initial concentration, unlike first‑order reactions. This tool helps you quickly compute t_½ for reaction planning, data analysis, and educational verification.

Step‑by‑Step Usage

Enter the rate constant (k) with its appropriate unit. For example, if your textbook gives k = 0.05 M⁻¹·s⁻¹, enter 0.05 and select "M⁻¹·s⁻¹".
Enter the initial concentration ([A]₀) in molar, millimolar, or micromolar. The tool automatically converts to M (mol/L).
Click "Calculate Half‑Life" (or press Enter in any field). The result updates immediately.
Use the "Find k from t_½" button if you know the half‑life and concentration and want to back‑calculate the rate constant.

Realistic Examples

Scenario	k (unit)	[A]₀	t_½ (approx)
Aqueous dimerization at 25°C	0.05 M⁻¹·s⁻¹	0.10 M	200 s
Enzyme‑substrate (simplified)	1.2×10³ M⁻¹·min⁻¹	5.0 µM	0.278 min
Gas‑phase reaction	2.5e‑4 M⁻¹·h⁻¹	0.5 M	8000 h

Common Mistakes Checklist

❌ Unit mismatches

Using k in M⁻¹·min⁻¹ with [A]₀ in µM but forgetting to convert µM → M (10⁻⁶).

❌ Zero or negative concentration

[A]₀ must be positive; t_½ is undefined for [A]₀ ≤ 0.

❌ Misapplying first‑order formula

Using t_½ = ln(2)/k for second‑order data gives incorrect results.

❌ Ignoring temperature dependence

k varies with T (Arrhenius). Verify your k is for the reaction temperature.

Frequently Asked Questions

How accurate is this calculator?

It uses the exact second‑order formula t_½ = 1/(k·[A]₀). Accuracy depends on your input precision and correct unit selection. The tool does not account for non‑ideality, activity coefficients, or changing concentration during measurement.

When does the second‑order approximation fail?

If the reaction is not truly second‑order (e.g., pseudo‑first‑order conditions), or if [A]₀ is not constant (flow reactors, continuous feeding). Also, very low concentrations may be affected by diffusion limits.

What are common unit pitfalls?

Mixing time units (e.g., k in M⁻¹·h⁻¹ but expecting t_½ in seconds). Forgetting that mM = 10⁻³ M. Using concentration in g/L without converting to molarity via molecular weight.

Any measurement tips for k and [A]₀?

Use calibrated pipettes and volumetric flasks for [A]₀. For k, use multiple timepoints and verify linearity of 1/[A] vs t. Record temperature and control it if possible. Use appropriate analytical techniques (UV‑Vis, titration, etc.) with known molar absorptivity.

Safety notes for kinetic studies?

Always review SDS for reactants and products. Use proper PPE (gloves, goggles). Perform reactions in appropriate containment (fume hood if volatile/toxic). Plan for waste disposal. Start with small concentrations to avoid rapid heat/ gas release.

Formulas & Assumptions

Primary Equation

t_½ = 1 / (k · [A]₀)

Valid for elementary second‑order reactions A + A → products or A + B → products with [A]₀ = [B]₀.

Constants & Conversions

1 M⁻¹·min⁻¹ = 60 M⁻¹·s⁻¹
1 M⁻¹·h⁻¹ = 3600 M⁻¹·s⁻¹
1 mM = 10⁻³ M; 1 µM = 10⁻⁶ M
Time conversions: 1 min = 60 s, 1 h = 3600 s, 1 d = 86400 s
No activity corrections; ideal dilute solution assumed.

Rounding policy: Results are shown to the selected decimal places (2–6). Intermediate calculations use full JavaScript double precision (≈15 decimal digits).

Half-Life Calculator (Second Order)

Result

Quick Rate‑Constant Converter

Understanding Second‑Order Half‑Life

Step‑by‑Step Usage

Realistic Examples

Common Mistakes Checklist

❌ Unit mismatches

❌ Zero or negative concentration

❌ Misapplying first‑order formula

❌ Ignoring temperature dependence

Frequently Asked Questions

How accurate is this calculator?

When does the second‑order approximation fail?

What are common unit pitfalls?

Any measurement tips for k and [A]₀?

Safety notes for kinetic studies?

Formulas & Assumptions

Primary Equation

Constants & Conversions

Disclaimer

Sources & References

Half-Life Calculator (Second Order)

Result

Quick Rate‑Constant Converter

Understanding Second‑Order Half‑Life

Step‑by‑Step Usage

Realistic Examples

Common Mistakes Checklist

❌ Unit mismatches

❌ Zero or negative concentration

❌ Misapplying first‑order formula

❌ Ignoring temperature dependence

Frequently Asked Questions

How accurate is this calculator?

When does the second‑order approximation fail?

What are common unit pitfalls?

Any measurement tips for k and [A]0?

Safety notes for kinetic studies?

Formulas & Assumptions

Primary Equation

Constants & Conversions

Disclaimer

Sources & References

Any measurement tips for k and [A]₀?

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Half Life Calculator Second Order

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