Half-Life (1st Order) Calculator
Time for concentration to halve.
Formula first
Overview
The half-life of a first-order reaction represents the time required for a reactant's concentration to decrease to half of its initial value. Uniquely, for first-order kinetics, this time interval remains constant regardless of the starting concentration, as it depends solely on the reaction's rate constant.
Symbols
Variables
= Half-Life, k = Rate Constant
Apply it well
When To Use
When to use: Apply this equation when analyzing radioactive decay or chemical reactions where the rate is directly proportional to the concentration of one reactant. It is specifically used for systems confirmed to follow first-order integrated rate laws where the concentration-time relationship is logarithmic.
Why it matters: This principle is critical for determining the shelf-life of pharmaceuticals and calculating the dosage intervals for medications in the body. It also forms the scientific basis for carbon dating and assessing the safety of nuclear waste storage over long durations.
Avoid these traps
Common Mistakes
- Applying this formula to non-first-order reactions.
- Confusing with 2nd order half-life.
One free problem
Practice Problem
A radioactive isotope decays with a first-order rate constant of 0.0347 per year. Calculate the half-life of this isotope in years.
Solve for:
Hint: Divide the natural log of 2 by the rate constant.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Atkins Physical Chemistry
- IUPAC Gold Book
- Wikipedia: First-order reaction
- Atkins' Physical Chemistry
- NIST Chemistry WebBook
- Atkins' Physical Chemistry, 11th Edition
- IUPAC Gold Book: Half-life (t1/2)
- Wikipedia: Half-life