First Order Rate Constant Calculator
Seconds (s)
Minutes (min)
Hours (h)
Days (d)
First Order Rate Constant (k):
About the First Order Rate Constant
This calculator determines the rate constant (k) for a first-order chemical reaction. In first-order kinetics, the reaction rate is directly proportional to the concentration of a single reactant. This behavior is common in radioactive decay, drug metabolism (pharmacokinetics), and unimolecular decomposition reactions.
Formulas Used
Depending on the data available, there are two primary ways to calculate the rate constant:
1. Using Integrated Rate Law
If you know the initial concentration and the concentration after a specific time interval, the formula is:
k = (1 / t) × ln([A]₀ / [A]ₜ)
- [A]₀: Initial concentration of the reactant.
- [A]ₜ: Concentration remaining at time t.
- t: Time elapsed.
- ln: Natural logarithm.
2. Using Half-Life
If the half-life of the substance is known, the rate constant relates directly to it via a constant value derived from the natural log of 2:
k = 0.693 / t½
In a first-order reaction, the half-life is constant and independent of the initial concentration.
Understanding the Units
The units for a first-order rate constant are always inverse time (time⁻¹). Common units include:
- s⁻¹ (per second)
- min⁻¹ (per minute)
- h⁻¹ (per hour)
Unlike zero or second-order reactions, the unit for k in first-order kinetics does not include concentration terms (like Molarity).
Application in Real World
Radioactive Decay: All radioactive decay processes follow first-order kinetics. This calculator can determine the decay constant if the half-life of the isotope is known.
Pharmacokinetics: Most drugs are eliminated from the body via first-order kinetics, meaning a constant fraction of the drug is removed per unit of time.