Enter your **Initial Concentration [A]₀**, **Rate Constant (k)**, and **Time (t)** into the **Second-Order Reaction Calculator**, then hit **Calculate** to find the **Final Concentration [A]ₜ** along with the **Half-Life (t₁/₂)**, **Fraction Remaining**, and **Fraction Consumed** — everything you need to track how your reactant depletes over time.
Final Concentration [A]ₜ
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Half-Life (t₁/₂)
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Fraction Remaining
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Fraction Consumed
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A second-order reaction is one where the rate is proportional to the square of the concentration of one reactant, or proportional to the product of two reactant concentrations. The rate law is rate = k[A]² or rate = k[A][B].
For a second-order reaction, the rate constant k can be calculated using the integrated rate law: 1/[A]ₜ - 1/[A]₀ = kt. Rearranging gives k = (1/[A]ₜ - 1/[A]₀)/t, where [A]₀ is initial concentration, [A]ₜ is final concentration, and t is time.
For second-order reactions, the half-life is t₁/₂ = 1/(k[A]₀), where k is the rate constant and [A]₀ is the initial concentration. Unlike first-order reactions, the half-life depends on the initial concentration.
In second-order kinetics, the rate depends on concentration squared, the half-life varies with initial concentration, and the integrated rate law is 1/[A]ₜ = 1/[A]₀ + kt. First-order reactions have constant half-life and exponential decay.
The units of a second-order rate constant are L/(mol·s) or M⁻¹s⁻¹. This ensures that when multiplied by concentration squared (mol²/L²), the result has units of concentration/time (mol/(L·s)).
The rate constant depends primarily on temperature (following the Arrhenius equation), the presence of catalysts, and the nature of the reactants. Higher temperatures generally increase the rate constant exponentially.