Half-Life by Reaction Order | Online Free Tool | Elysia Tools
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Half-Life by Reaction Order
t½ = a₀/(2k), ln 2/k or 1/(k·a₀) for zero-, first- and second-order reactions, with timelines and depletion time.
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Key facts
Category
Science & Education
Input types
select, number
Output type
text
Sample coverage
4
API ready
Yes
Overview
The Half-Life by Reaction Order calculator computes the half-life and concentration depletion timelines for zero-, first-, and second-order chemical reactions. By selecting the reaction order and providing the rate constant alongside initial reactant concentrations when required, you can instantly determine half-life values, evaluate decay profiles, and analyze how reaction rates evolve over time.
When to use
Determining half-life durations and total depletion times for zero-order, surface-catalyzed, or enzyme-saturated processes.
Evaluating first-order exponential decay constants and half-lives for radioactive isotopes or unimolecular decomposition reactions.
Calculating concentration-dependent half-lives for second-order dimerization or bimolecular kinetics.
How it works
1Select the reaction order (zero order, first order, or second order) corresponding to the kinetic model.
2Enter the reaction rate constant k in units matching your timeframe and concentration dimensions.
3Input the initial concentration [A]₀ for zero-order (t½ = a₀/(2k)) or second-order (t½ = 1/(k·a₀)) reactions; this field is omitted for first-order kinetics (t½ = ln 2/k).
4View the computed half-life value alongside a step-by-step timeline of remaining reactant concentrations or fractions over multiple half-life intervals.
Use cases
Chemistry students verifying chemical kinetics homework problems and plotting reactant concentration decay curves.
Researchers calculating radioactive dating benchmarks such as Carbon-14 decay intervals.
Process engineers estimating batch reaction completion times and reactant consumption rates in industrial reactors.
Examples
1. Radiocarbon Dating Calculation
Archaeology Researcher
Background
An archaeologist needs to confirm the theoretical half-life of Carbon-14 using its known decay rate constant.
Problem
Calculate the half-life of C-14 given a decay constant k = 1.21 × 10⁻⁴ yr⁻¹.
How to use
Select 'First order' as the reaction order and enter 0.000121 into the rate constant k field.
order: first, k: 0.000121
Outcome
Returns a half-life of approximately 5,728.49 years with an exponential decay timeline showing remaining fractions of 1/2, 1/4, and 1/8.
2. Bimolecular Dimerization Kinetics
Chemical Engineer
Background
A chemical engineer is modeling a second-order dimerization reaction in a batch reactor.
Problem
Determine the initial half-life and progressive concentration depletion for a starting concentration of 0.4 M with k = 0.5 M⁻¹·min⁻¹.
How to use
Select 'Second order', set rate constant k to 0.5, and set initial concentration [A]₀ to 0.4.
FAQ
Why is the initial concentration not required for first-order reactions?
First-order half-life depends exclusively on the rate constant (t½ = ln 2 / k), meaning the time required to halve the reactant remains constant regardless of starting concentration.
How does half-life change over time in a second-order reaction?
In second-order kinetics, half-life is inversely proportional to concentration (t½ = 1 / (k·[A]₀)), causing each successive half-life period to double in duration as the reactant is consumed.
When does a zero-order reaction reach complete depletion?
A zero-order reaction reaches full depletion at time t = [A]₀ / k, which is exactly twice its half-life value.
What units should be used for rate constant k and initial concentration?
Units must be consistent: zero-order k uses concentration/time, first-order k uses 1/time, and second-order k uses 1/(concentration·time). The resulting half-life matches the time unit of k.
Can this tool calculate radioactive decay half-lives?
Calculates an initial half-life of 5.0 minutes and demonstrates the slowdown with remaining concentrations of 0.2 M, 0.133 M, and 0.1 M after successive intervals.
3. Zero-Order Catalytic Depletion
Laboratory Analyst
Background
An analyst is studying a surface-catalyzed decomposition where the reaction rate is independent of reactant concentration.
Problem
Find the half-life and total time to zero concentration for an initial reactant level of 0.5 M with k = 0.02 M·min⁻¹.
How to use
Select 'Zero order', enter 0.02 for rate constant k, and enter 0.5 for initial concentration [A]₀.
order: zero, k: 0.02, a0: 0.5
Outcome
Yields a half-life of 12.5 minutes and a total depletion time of 25.0 minutes.
Yes. Radioactive decay follows first-order kinetics, allowing you to compute isotope half-lives directly from the decay constant k.