Half-life
The half-life (t½) is the time for a reactant's concentration to fall to half. For a first-order reaction, t½ = 0.693/k, and it is the same no matter how much you start with. Zero and second order half-lives do change.
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Analogy
Like a bar of chocolate you eat half of each hour: half the remaining chocolate is gone every time.
Example
k = 0.0231 min⁻¹t½ = 0.693 / 0.0231 = 30.0 minAfter 90 min: 3 half-livesFraction left = (½)³ = 1/8
In practice
Carbon-14 has a half-life of about 5730 years, which archaeologists use to date old wood and bone.
Practice
Flashcards
- Half-life formula for first order?t½ = 0.693/k.
Questions people ask
Why is first-order half-life constant?
In first-order decay, the rate is proportional to the amount left. Halving the amount halves the rate, so the time to lose the next half stays the same. This is why t½ = 0.693/k does not depend on the starting concentration.
How many half-lives until a reaction is basically over?
After 5 half-lives, about 3 percent of the reactant remains, and after 7, less than 1 percent. Chemists often treat a first-order reaction as complete after 7 to 10 half-lives. The reactant never reaches exactly zero, because each half-life removes only half.