Second-Order Integrated Rate Law
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
When two molecules of the same reactant must find each other, the rate goes as [A]², and integrating gives a straight line only if you plot the reciprocal concentration against time. The slope of that line is k, in L/(mol·s). Starting at 0.100 M with k = 0.500 L/(mol·s), after 10 s the reciprocal has climbed from 10 to 10 + 5 = 15, so [A] = 0.0667 M.
The three integrated laws form the standard diagnostic kit: plot [A] versus t, ln[A] versus t, and 1/[A] versus t, and whichever comes out straight tells you the order. Second-order kinetics has a distinctive personality — it starts fast and then drags, because losing reactant hurts the rate twice over. Gas-phase NO₂ decomposition and many radical recombinations follow it. Be careful with the "pseudo" cases: a reaction that is genuinely second order overall but run with a huge excess of one partner behaves like first order in the other, which is exactly how kineticists tame a two-variable problem into a one-variable measurement.
- = Concentration at time t
- = Initial concentration
- = Rate constant in L/(mol·s)
- = Elapsed time
- Concentration at time t — Zero-Order Integrated Rate Law, First-Order Integrated Rate Law
- Initial concentration — Dilution Equation (C1V1 = C2V2), Zero-Order Integrated Rate Law
- Rate constant in L/(mol·s) — Zero-Order Integrated Rate Law, Half-Life of a Second-Order Reaction
- Elapsed time — Half-Life Decay, Zero-Order Integrated Rate Law