Second Order Integrated Rate Law Calculator
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What would you like to calculate?
Concentration at time t ([A]t)
Initial Concentration ([A]0)
Rate Constant (k)
Time elapsed (t)
Half-Life (t½)
Initial Concentration [A]₀ (M)
Concentration at time t [A]ₜ (M)
Rate Constant k (M⁻¹s⁻¹)
Time t (seconds)
Calculate
Understanding the Second Order Integrated Rate Law
In chemical kinetics, a second-order reaction is a reaction where the rate depends either on the concentration of one reactant squared, or on the concentration of two different reactants. This calculator specifically handles the case where the rate depends on a single reactant squared (Rate = k[A]²).
The integrated rate law for a second-order reaction describes how the concentration of a reactant changes over time. It transforms the differential rate law into a linear equation that is easier to use for calculations.
The Formula
The standard equation used in this calculator is:
1 / [A]ₜ = kt + 1 / [A]₀
Where:
[A]ₜ : The concentration of the reactant at time t (Molarity, M).[A]₀ : The initial concentration of the reactant at time t=0 (Molarity, M).k : The second-order rate constant (units typically M⁻¹s⁻¹ or L·mol⁻¹·s⁻¹).t : The time elapsed (seconds, minutes, etc.).
How to Calculate Half-Life
Unlike first-order reactions, the half-life of a second-order reaction depends on the initial concentration. As the reaction proceeds and concentration decreases, each subsequent half-life becomes longer.
t½ = 1 / (k[A]₀)
Example Calculation
Scenario: The decomposition of nitrogen dioxide (NO₂) is a second-order reaction with a rate constant of 0.54 M⁻¹s⁻¹ at 300°C. If the initial concentration is 0.0080 M , what is the concentration after 60 seconds ?
Using the calculator:
Select "Concentration at time t ([A]t)" from the dropdown.
Enter 0.0080 for Initial Concentration [A]₀.
Enter 0.54 for Rate Constant k.
Enter 60 for Time t.
Click Calculate.
Manual Math: 0.00635 M
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