Half-life and the rate constant
Half-life and the rate constant
- The half-life is the time for a concentration to halve.
- For a first-order reaction it is constant.
- That lets you find the rate constant.
Constant half-life
- For a first-order reaction, the half-life does not depend on concentration.
- So the concentration halves in the same time, again and again — a useful way to spot first order.
Practice
A reaction whose half-life stays the same as it proceeds is:
A constant half-life (independent of concentration) is the signature of a first-order reaction.
Practice
A constant half-life can be used to identify a first-order reaction.
Only first-order reactions have a half-life that is independent of the concentration.
Finding k
$$k = \frac{0.693}{t_{\frac{1}{2}}}$$
- You can also find $k$ by putting initial-rate data into the rate equation.
Practice
For a first-order reaction, the rate constant is:
k = 0.693 / t½ for a first-order reaction.
Practice
A first-order reaction has a half-life of 100 s. What is k? (k = 0.693/t½)
k = 0.693 / 100 = 0.00693 (per second).
You've got it
Key idea
- half-life = time for the concentration to halve
- a first-order reaction has a constant half-life (independent of concentration)
- $k = \dfrac{0.693}{t_{1/2}}$ — or find $k$ from initial-rate data in the rate equation