This problem involves a zero-order reaction, where the rate of reaction is independent of the reactant's concentration.
The integrated rate law for a zero-order reaction is given by
[A]t=[A]0−kt where,
[A]t is the concentration at time
t.
[A]0 is the initial concentration.
k is the rate constant.
t is time.
The half-life (
t1∕2 ) for a zero-order reaction is related to the initial concentration and rate constant by the expression
t1∕2=‌Given
t1∕2=0.5hInitial concentration for half-life,
[A]0=4molL−1.
First, calculate the rate constant (
k )
0.5hr‌=‌k‌=‌=‌‌=4molL−1hr−1Next, calculate the time
(t) for the concentration to change from
2.0molL−1to
1.0molL−1;
Using the integrated rate law
‌1.0molL−1=2.0molL−1‌−(4molL−1hr−1)t Rearrange to solve for
t‌(4molL−1hr−1t=2.0molL−1−1.0molL−1)‌4t=1.0hr‌t=‌hr‌t=1∕4h‌ or ‌0.25h.
