Answer:
a) 79.66 seconds is the half-life of the reaction.
b) It will take
seconds for 34% of a sample of an acetone to decompose.
c) It will take
seconds for 89% of a sample of an acetone to decompose.
Explanation:
The decomposition of acetone follows first order kinetics
The rate constant of the reaction = k = 
a)
Half life of the reaction = 
For the first order kinetic half life is related to k by :


79.66 seconds is the half-life of the reaction.
b)
Let the initial concentration of acetone be = ![[A_o]](https://tex.z-dn.net/?f=%5BA_o%5D)
Final concentration of acetone left after t time = [A]
![A=(100\%-34\%)[A_o]=66\%[A_o]=0.66[A_o]](https://tex.z-dn.net/?f=A%3D%28100%5C%25-34%5C%25%29%5BA_o%5D%3D66%5C%25%5BA_o%5D%3D0.66%5BA_o%5D)
For the first order kinetic :
![[A]=[A_o]\times e^{-kt}](https://tex.z-dn.net/?f=%5BA%5D%3D%5BA_o%5D%5Ctimes%20e%5E%7B-kt%7D)
![0.66[A_o]=[A_o]\times e^{-8.7\times 10^{-3} s^{-1}\times t}](https://tex.z-dn.net/?f=0.66%5BA_o%5D%3D%5BA_o%5D%5Ctimes%20e%5E%7B-8.7%5Ctimes%2010%5E%7B-3%7D%20s%5E%7B-1%7D%5Ctimes%20t%7D)
Solving for t;

It will take 47.76 seconds for 34% of a sample of an acetone to decompose.
c)
Let the initial concentration of acetone be = ![[A_o]](https://tex.z-dn.net/?f=%5BA_o%5D)
Final concentration of acetone left after t time = [A]
![A=(100\%-89\%)[A-o]=11\%[A_o]=0.11[A_o]](https://tex.z-dn.net/?f=A%3D%28100%5C%25-89%5C%25%29%5BA-o%5D%3D11%5C%25%5BA_o%5D%3D0.11%5BA_o%5D)
For the first order kinetic :
![[A]=[A_o]\times e^{-kt}](https://tex.z-dn.net/?f=%5BA%5D%3D%5BA_o%5D%5Ctimes%20e%5E%7B-kt%7D)
![0.11[A_o]=[A_o]\times e^{-8.7\times 10^{-3} s^{-1}\times t}](https://tex.z-dn.net/?f=0.11%5BA_o%5D%3D%5BA_o%5D%5Ctimes%20e%5E%7B-8.7%5Ctimes%2010%5E%7B-3%7D%20s%5E%7B-1%7D%5Ctimes%20t%7D)
Solving for t;

It will take
seconds for 89% of a sample of an acetone to decompose.