The half-life of a reaction depends on the reaction order.
First order reaction
For a first order reaction the half-life depends only on the rate
constant:
Thus, the half-life of a first order reaction remains constant
throughout the reaction, even though the conentration of the reactant
is decreasing.
Second order reaction
For a second order reaction (of the form: rate=k[A]^2) the half-life
depends on the inverse of the initial concentration of reactant A:
Since the concentration of A is decreasing throughout the reaction,
the half-life increases as the reaction progresses. That is, it takes
less time for the concentration to drop from 1M to 0.5M than it does
for the drop from 0.5 M to 0.25 M.
Plot of concentration vs time shows the difference between 1st
and 2nd order reactions
The plot (below) clearly shows that while the half-life for a first order
reaction is constant throughout the reaction, the half-life for a
second order reaction increases steadily.
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