2nd-Order Reaction Half-Life Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
A 2nd-order chemical reaction's half-life is calculated with t½ = 1 ÷ (k × [A]₀), where k is the rate constant and [A]₀ the reactant's initial concentration. For k = 0.1 L/(mol·s) and an initial concentration of 2 mol/L, the half-life is 5 seconds.
Explanation
A chemical reaction's half-life is the time needed for the reactant's concentration to be reduced by half. For a 2nd-order reaction, whose rate depends on the square of the reactant's concentration, this half-life is NOT constant: it depends directly on the starting concentration, unlike the half-life of a 1st-order reaction, which stays the same regardless of the initial concentration. Concretely, halving the initial concentration doubles a 2nd-order reaction's half-life — a direct consequence of the formula, since [A]₀ sits in the denominator: the less reactant there is to start with, the rarer the collisions between molecules (which govern a 2nd-order reaction's rate), and the longer the reaction takes to consume half of that reactant. This distinction between reaction orders shows up, in a different form, in radioactive decay, which always follows 1st-order kinetics (an atomic nucleus's decay is a random process independent of the amount of matter remaining) — a 2nd-order chemical reaction, by contrast, generally involves a collision between two molecules of the same reactant, which explains why its kinetics depend on the square of the concentration.
Example: k = 0.1 L/(mol·s), initial concentration of 2 mol/L
Inputs
Rate constant (k): 0.1 L/(mol·s). Initial concentration ([A]₀): 2 mol/L.
Calculation
t½ = 1 ÷ (0.1 × 2) = 1 ÷ 0.2 = 5 s.
Result
This reaction's half-life is 5 seconds.
Frequently asked questions
How do you tell a reaction is 2nd order rather than 1st order?
Experimentally, by plotting the inverse of concentration against time: a 2nd-order reaction gives a straight line (1÷[A] varies linearly with time), while a 1st-order reaction gives a straight line if you instead plot the logarithm of concentration. It's this experimental signature, not a property visible to the naked eye, that lets you determine a reaction's actual order.
Do the rate constant's units change depending on the reaction's order?
Yes, and it's an important difference: for a 1st-order reaction, k is expressed in s⁻¹ (the inverse of a time), while for a 2nd-order reaction, k is expressed in L/(mol·s) (the inverse of a concentration multiplied by a time) — the two quantities are neither interchangeable nor directly comparable to each other.
What happens if the initial concentration is very high?
The half-life decreases proportionally: the more reactant there is to start with, the more frequent the collisions between molecules, and the faster the reaction consumes half of that reactant. This is the opposite effect of a low initial concentration, which lengthens the half-life — a sensitivity to concentration that doesn't exist at all for a 1st-order reaction.