Reaction Kinetics Calculator
Determine reactant concentration at any point in time for zero, first, or second-order reactions. Enter the rate constant, initial concentration, and reaction time to get [A] instantly.
About this calculator
The integrated rate law describes how reactant concentration [A] changes with time, and its form depends on the reaction order. For a zero-order reaction: [A] = [A₀] − k·t. For a first-order reaction: [A] = [A₀] × e^(−k·t). For a second-order reaction: [A] = 1 / (1/[A₀] + k·t). Here [A₀] is the initial concentration (M), k is the rate constant (s⁻¹ for first-order), and t is the elapsed time (s). The half-life — time for [A] to reach [A₀]/2 — equals t½ = [A₀]/(2k) for zero-order, ln(2)/k for first-order, and 1/(k·[A₀]) for second-order reactions. These equations are foundational in pharmacokinetics, environmental chemistry, and industrial process design.
How to use
For a first-order reaction with [A₀] = 0.80 M, k = 0.05 s⁻¹, and t = 20 s: [A] = 0.80 × e^(−0.05 × 20) = 0.80 × e^(−1.0) = 0.80 × 0.3679 ≈ 0.294 M. Enter 0.80 in Initial Concentration, 0.05 in Rate Constant, 20 in Reaction Time, and select order = 1. The calculator returns approximately 0.294 M. To find the half-life: t½ = ln(2) / 0.05 = 0.693 / 0.05 = 13.86 s.
Frequently asked questions
How do I determine the order of a reaction from experimental concentration-time data?
Plot concentration vs. time for zero-order, ln[A] vs. time for first-order, and 1/[A] vs. time for second-order. The plot that yields a straight line reveals the reaction order, and the slope of that line equals −k (zero and first order) or +k (second order). Alternatively, measure the half-life at different initial concentrations: if t½ is constant, the reaction is first-order; if t½ is proportional to 1/[A₀], it is second-order; if t½ is proportional to [A₀], it is zero-order.
What units does the rate constant k have for zero, first, and second-order reactions?
The units of k depend on the reaction order because the integrated rate law must produce units of concentration (M) on both sides. For zero-order reactions, k has units of M·s⁻¹. For first-order reactions, k is in s⁻¹ (or any reciprocal time unit). For second-order reactions, k has units of M⁻¹·s⁻¹. Always check that your k value carries the correct units before entering it into this calculator, especially when mixing literature values that may use minutes or hours instead of seconds.
How is reaction kinetics used in pharmacokinetics to calculate drug half-life?
Most drugs are eliminated from the body following first-order kinetics, meaning the rate of elimination is proportional to the current drug concentration in plasma. The half-life t½ = ln(2)/k tells clinicians how long it takes for the drug concentration to halve, which determines dosing intervals. After approximately 5 half-lives, the drug is considered fully eliminated (< 3% remaining). Drugs with short half-lives (minutes to hours) require more frequent dosing or continuous infusion, while those with long half-lives (days) accumulate with repeated dosing and require careful loading-dose calculations.