Reaction Kinetics Calculator — Integrated Rate Laws

Integrated rate laws describe how reactant concentration changes over time, depending on the reaction order.

Zero order: [A] = [A]0 - k*t Concentration drops linearly with time. Half-life t1/2 = [A]0 / (2k). Common in enzyme-saturated reactions and some surface-catalyzed processes.

First order: [A] = [A]0 * e^(-kt), or equivalently ln([A]) = ln([A]0) - kt Concentration falls exponentially. Half-life t1/2 = ln(2) / k = 0.693/k – notably independent of initial concentration. This is the most common order in chemistry: radioactive decay, many drug eliminations, and a large fraction of gas-phase reactions.

Second order: 1/[A] = 1/[A]0 + k*t Half-life t1/2 = 1 / (k * [A]0) – depends on initial concentration. Bimolecular reactions often follow second-order kinetics.

The rate constant k has different units depending on order: zero order: mol/L/s; first order: 1/s; second order: L/mol/s.

The chart shows concentration vs time over 3 half-lives. Notice how first and second order curves both look exponential-ish but differ noticeably at longer times – second order slows down faster initially but has a longer tail.