First Order Rate Constant Calculator
Calculate the reaction rate constant (k) using concentration data or half-life.
By Concentration
By Half-Life
Molarity (M)
Millimolar (mM)
Moles (mol)
Seconds (s)
Minutes (min)
Hours (h)
Seconds (s)
Minutes (min)
Hours (h)
First Order Rate Constant (k):
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Calculated Half-Life (t₁/₂):
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About First Order Rate Constants
In chemical kinetics, a first-order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration. Common examples include radioactive decay and certain decomposition reactions.
The Integrated Rate Law Formula
To calculate the rate constant ($k$) using concentration data over time, we use the integrated rate law for first-order reactions:
ln([A]ₜ / [A]₀) = -kt
Where:
- [A]₀: Initial concentration of the reactant.
- [A]ₜ: Concentration of the reactant at time t.
- k: The rate constant (units of time⁻¹).
- t: The time elapsed.
Rearranging this formula to solve for k gives:
k = (ln([A]₀) – ln([A]ₜ)) / t
Calculating via Half-Life
For first-order reactions, the half-life (t₁/₂) is constant and independent of the initial concentration. The relationship between the rate constant and half-life is:
k = ln(2) / t₁/₂ ≈ 0.693 / t₁/₂
Units of Measurement
The rate constant k for a first-order reaction has units of reciprocal time. Depending on the time unit used in your calculation, k will be expressed in:
- s⁻¹ (per second)
- min⁻¹ (per minute)
- h⁻¹ (per hour)
Example Calculation
Suppose a reactant starts with a concentration of 1.0 M. After 60 seconds, the concentration drops to 0.25 M. To find the rate constant:
- Calculate natural log of ratio: ln(1.0/0.25) = ln(4) ≈ 1.386
- Divide by time: 1.386 / 60 ≈ 0.0231
- Result: k ≈ 0.0231 s⁻¹