Second-Order Reaction Calculator
Use the second-order integrated rate law to find half-life and the concentration of a reactant at any time.
L/mol·s
mol/L
s
Concentration remaining after the chosen time
- 1
1 ÷ [A]₀
1 ÷ 1 = 1 L/mol - 2
k × t
0.05 × 20 = 1 - 3
1 ÷ [A]t = 1/[A]₀ + k·t
1 + 1 = 2 L/molA linear plot of 1/[A] vs t identifies second-order kinetics — the slope equals k. - 4
[A] at time t
1 ÷ 2 = 0.5000
How does this calculator work?
For a second-order reaction, 1/[A]t = 1/[A]0 + k·t and the half-life is t½ = 1/(k·[A]0). Enter the rate constant, initial concentration, and optionally a time; the tool returns the half-life, the remaining concentration, and a 1/[A] versus time line whose slope equals k.
Formula
How this is calculated
A second-order reaction has a rate that depends on the square of one reactant concentration (or the product of two). Integrating the rate law −d[A]/dt = k[A]² gives the linear form 1/[A]t = 1/[A]0 + k·t. This calculator takes the rate constant k (in L/mol·s), the initial concentration [A]0 (in mol/L), and an optional elapsed time t (in seconds).
The half-life is computed as t½ = 1/(k·[A]0). Unlike first-order reactions, the second-order half-life depends on the starting concentration: more concentrated solutions react faster initially, so the half-life is shorter. If a time t is supplied, the concentration at that moment is [A]t = 1/(1/[A]0 + k·t).
The plot shows 1/[A] versus t, which is a straight line with slope k and intercept 1/[A]0 — the hallmark used to identify second-order kinetics from experimental data. Inputs must be positive; k or [A]0 of zero (or negative) is rejected because it produces an undefined half-life. Ensure k is expressed in L/mol·s so the units stay consistent with concentrations in mol/L and time in seconds.
Frequently asked questions
For a second-order reaction t½ = 1/(k·[A]0), so doubling the starting concentration halves the half-life. Each successive half-life is twice as long as the previous one.
Plot 1/[A] against time. If the data fall on a straight line, the reaction is second-order in that reactant and the slope equals the rate constant k.
A second-order rate constant has units of L/mol·s (equivalently M⁻¹·s⁻¹), so that k·[A]² has units of mol/(L·s), a rate of concentration change.
Also known as
TG we-Calculate Editorial Team. (2026). Second-Order Reaction Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/second-order-reaction-calculator
TG we-Calculate Editorial Team. "Second-Order Reaction Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/second-order-reaction-calculator.
TG we-Calculate Editorial Team, "Second-Order Reaction Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/second-order-reaction-calculator
@misc{wecalculate_second_order_reaction_calculator, title = {Second-Order Reaction Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/second-order-reaction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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