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Half-Life (Zero Order Reaction) Calculator

Calculates the half-life of a zero-order reaction based on initial concentration and rate constant.

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Half-Life

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Overview

The half-life (t₁/₂) of a zero-order reaction is the time required for the concentration of a reactant to decrease to half its initial value. Unlike higher-order reactions, for a zero-order reaction, the half-life is directly proportional to the initial concentration of the reactant and inversely proportional to the rate constant. This means that as the initial concentration increases, the half-life also increases, which is a unique characteristic of zero-order kinetics.

Symbols

Variables

[A]_0 = Initial Concentration of A, k = Rate Constant, = Half-Life

Initial Concentration of A
mol/L
Rate Constant
Half-Life

Apply it well

When To Use

When to use: Use this equation when analyzing the kinetics of a zero-order reaction and needing to determine the time it takes for half of the initial reactant to be consumed. It's particularly useful in scenarios where the reaction rate is independent of reactant concentration, such as enzyme-catalyzed reactions at saturation or reactions occurring on a surface.

Why it matters: Understanding the half-life of zero-order reactions is crucial in fields like pharmacology (drug degradation), environmental science (pollutant breakdown), and industrial chemistry (catalytic processes). It allows for prediction of reactant depletion over time, aiding in shelf-life determination, process optimization, and understanding reaction mechanisms.

Avoid these traps

Common Mistakes

  • Applying the formula to reactions that are not zero-order.
  • Incorrectly using units for k or [A]₀, leading to incorrect t₁/₂ units.

One free problem

Practice Problem

A drug degrades in the body via a zero-order reaction. If its initial concentration is 0.5 M and the rate constant for its degradation is 0.02 M s⁻¹, what is the half-life of the drug?

Initial Concentration of A0.5 mol/L
Rate Constant0.02 mol L^{-1} s^{-1}

Solve for:

Hint: Remember to use the formula t₁/₂ = [A]₀ / (2k) and ensure units are consistent.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Atkins' Physical Chemistry
  2. Wikipedia: Zero-order reaction
  3. McQuarrie's Physical Chemistry: A Molecular Approach
  4. IUPAC Gold Book
  5. Atkins, P. W., & de Paula, J. (2014). Atkins' Physical Chemistry (10th ed.). Oxford University Press. (Chapter on Chemical Kinetics)
  6. IUPAC Gold Book. (2019). 'Half-life'. Retrieved from https://goldbook.iupac.org/terms/view/H02700
  7. IUPAC Gold Book. (2019). 'Order of reaction'. Retrieved from https://goldbook.iupac.org/terms/view/O04322
  8. Atkins' Physical Chemistry, 11th Edition — Chapter 20: Chemical Kinetics