Calculate rate, concentration at time t, or half-life for zero, first, and second order reactions.
Select the reaction order, enter three of the four variables ([A]₀, [A]ₜ, k, t), and choose which to solve for. The calculator also shows the half-life and appropriate units for k.
Zero order: [A]ₜ = [A]₀ − kt. Rate is constant and independent of concentration. Half-life: t½ = [A]₀/(2k). k units: M/time.
First order: ln([A]ₜ) = ln([A]₀) − kt, or equivalently [A]ₜ = [A]₀ × e⁻ᵏᵗ. Rate depends linearly on concentration. Half-life: t½ = ln(2)/k = 0.693/k (independent of concentration). k units: 1/time.
Second order: 1/[A]ₜ = 1/[A]₀ + kt. Rate depends on concentration squared. Half-life: t½ = 1/(k[A]₀). k units: 1/(M·time).
How to determine order experimentally: Plot [A] vs t (linear = zero order), ln[A] vs t (linear = first order), or 1/[A] vs t (linear = second order). The plot that gives a straight line reveals the order, and the slope gives k.