Question

A certain first order reaction proceeds through t first order kinetics. The half-life of the reaction is 180 s. What percent of the initial concentration remains after 900s?

Answer 1

Answer: 3.12%
From the integrated rate law for a first order reaction, [A]=[A]0e−kt[A]=[A]0e−kt.
The half life t1/2=ln2kt1/2=ln2k=0.693k=0.693k. Given t1/2=180s→k=0.693180st1/2=180s→k=0.693180s =0.00385s−1=0.00385s−1
The fraction remaining is the concentration divided by the initial concentration =[A][A0]=[A][A0]=ekt=e0.00385s−1×900s=ekt=e0.00385s−1×900s=0.0312=3.12%