The
half life for a reaction is the time taken for half of a given quantity of reactant to be consumed by the reaction.
It can be shown that for a first-order reaction,
- the half life does NOT depend on concentration.
Therefore the time taken for the concentration to fall from 1 to 0.5 is the same as for it to fall from 0.5 to 0.25. - the rate constant can be calculated from the half life.
The relationship between half life and the rate constant for a first order reaction can be derived from the integrated rate equation by substituting for
t and [A] as shown below.
At t = t
1/2, [A] = [A]
0/2
Because ln
1/
2 is equal to -ln 2, this simplfies to the relationship below.