1/[A] = 1/[A]₀ + k × t
Integrated Rate Law
t₁/₂ = 1 / (k × [A]₀)
Half-Life Formula
[A]₀ = Initial concentration
[A] = Concentration at time t
k = Rate constant (M⁻¹·time⁻¹)
t = Time elapsed
t₁/₂ = Half-life (depends on [A]₀)
What is a Second-Order Reaction?
A second-order reaction is one where the rate depends on the concentration of one reactant squared (Rate = k[A]²) or on two reactants (Rate = k[A][B]).
Variable Half-Life
Unlike first-order reactions, the half-life of a second-order reaction depends on the initial concentration. Higher initial concentrations lead to shorter half-lives.
Common Examples
Dimerization reactions, many bimolecular reactions, enzyme-substrate interactions at high substrate concentrations, and some decomposition reactions follow second-order kinetics.
Important Note
Second-order kinetics assume rate depends on the concentration of one or two reactants. Deviations may occur for complex reaction mechanisms or under non-ideal conditions.
Second-order reaction kinetics describes chemical reactions where the rate is proportional to either the square of one reactant's concentration or the product of two reactants' concentrations. For a reaction involving a single reactant A, the rate law is Rate = k[A]². For reactions involving two reactants, the rate law is Rate = k[A][B]. This type of kinetics is commonly observed in bimolecular reactions where two molecules must collide for the reaction to occur.
The integrated rate law for second-order reactions, 1/[A] = 1/[A]₀ + kt, allows us to calculate concentration changes over time, determine how long a reaction will take to reach a certain point, or find the rate constant from experimental data. A plot of 1/[A] versus time will yield a straight line with a slope equal to k for a true second-order reaction, which is used to confirm reaction order.
Second-order kinetics plays a crucial role in many chemical and biochemical processes. In organic chemistry, many bimolecular reactions such as SN2 substitutions and E2 eliminations follow second-order kinetics. Understanding these kinetics helps chemists predict reaction rates and design efficient synthetic routes for pharmaceutical and industrial chemical production.
In biochemistry, enzyme kinetics at high substrate concentrations can exhibit second-order behavior. The study of protein-protein interactions, antigen-antibody binding, and drug-receptor interactions often involves second-order kinetics. Environmental scientists also use second-order models to predict the degradation of pollutants when two species react together or when a single pollutant undergoes dimerization.