Integrated Rate Law Calculator (1st Order)
Use this calculator to determine the concentration, time, or rate constant for a first-order chemical reaction. Enter any three values to calculate the fourth.
Understanding First-Order Kinetics
In chemical kinetics, a first-order reaction is a reaction whose rate depends linearly on the concentration of only one reactant. The integrated rate law provides a mathematical relationship between the concentration of a reactant and the time elapsed.
The Mathematical Formula
ln([A]ₜ) = -kt + ln([A]₀)
or
[A]ₜ = [A]₀ * e-kt
Where:
- [A]₀: Initial concentration of the reactant at time zero.
- [A]ₜ: Concentration of the reactant after time t has passed.
- k: The first-order rate constant (units: 1/time).
- t: The time interval over which the reaction occurs.
Key Characteristics
First-order reactions are unique because the half-life (t₁/₂) is independent of the initial concentration. It is calculated using the formula: t₁/₂ = 0.693 / k. Common examples include radioactive decay and many metabolic drug elimination processes in the body.
Example Calculation
Suppose you have a reactant with an initial concentration of 2.0 M and a rate constant of 0.1 s⁻¹. How much concentration will remain after 5 seconds?
- 1. [A]₀ = 2.0
- 2. k = 0.1
- 3. t = 5
- 4. Calculation: [A]ₜ = 2.0 * e-(0.1 * 5)
- 5. Result: [A]ₜ ≈ 1.213 M