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]
Calculate First-Order Reaction Kinetics
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Calculate the rate constant (k) using initial and final concentrations
Calculate concentration at any time given initial concentration and rate constant
Calculate the half-life of 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]
The integrated form of the first-order rate law is:
ln[A] = ln[A]₀ - kt
[A] = [A]₀e⁻ᵏᵗ
A unique feature of first-order reactions is that the half-life is independent of initial concentration:
t₁/₂ = ln(2)/k
For a first-order reaction:
Rate = k[A]
ln[A] = ln[A]₀ - kt
t₁/₂ = ln(2)/k ≈ 0.693/k