The half-life of a zero order reaction A⟶ products, is 0.5 hour. The initial concentration of A is 4‌mol‌L−1. How much time (in hr) does it take for its concentration to come from 2.0‌mol‌L−1 to 1.0‌mol‌L−1 ?
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=‌
[A]0
2k
Given t1∕2=0.5h Initial concentration for half-life, [A]0=4molL−1. First, calculate the rate constant ( k ) 0.5hr‌=‌
4molL−1
2k
k‌=‌
4molL−1
2×0.5hr
=‌
4molL−1
1.0hr
‌=4molL−1hr−1 Next, calculate the time (t) for the concentration to change from 2.0molL−1 to 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=1.0hr ‌t=‌