First-Order Reaction Calculator

Calculate First-Order Reaction Kinetics

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Rate Constant Calculator

Calculate the rate constant (k) using initial and final concentrations

Rate Constant: - s⁻¹

Concentration Calculator

Calculate concentration at any time given initial concentration and rate constant

Concentration: - M

Half-Life Calculator

Calculate the half-life of a first-order reaction

Half-Life: - s

Understanding First-Order Reactions

What is a First-Order Reaction?

A first-order reaction is a reaction where the rate depends on the concentration of a single reactant raised to the first power. The rate law is:

Rate = -d[A]/dt = k[A]

Integrated Rate Law

The integrated form of the first-order rate law is:

ln[A] = ln[A]₀ - kt

[A] = [A]₀e⁻ᵏᵗ

Half-Life

A unique feature of first-order reactions is that the half-life is independent of initial concentration:

t₁/₂ = ln(2)/k

Examples of First-Order Reactions

  • Radioactive decay
  • Many decomposition reactions
  • Hydrolysis of esters
  • Some enzyme-catalyzed reactions

Graphical Analysis

For a first-order reaction:

  • Plot of ln[A] vs. time gives a straight line
  • Slope = -k (rate constant)
  • y-intercept = ln[A]₀

Essential First-Order Reaction Formulas

Rate Law

Rate = k[A]

Integrated Rate Law

ln[A] = ln[A]₀ - kt

Half-Life

t₁/₂ = ln(2)/k ≈ 0.693/k