Chapter 21, Problem 74AP

Peroxyacetyl nitrate (PAN) undergoes thermal decomposition as follows:

${\text{CH}}_{\text{3}}{\text{(CO)OONO}}_{\text{2}}\underset{}{\to }{\text{CH}}_{\text{3}}{\text{(CO)OO+NO}}_{\text{2}}$

The rate constant is $\text{3}\text{.0}\times {\text{10}}^{-4}{s}^{-1}$ at $\text{25°C}$. At the boundary between the troposphere and stratosphere, where the temperature is about $\text{-40°C}$, the rate constant is reduced to $\text{2}{\text{.6×10}}^{\text{-7}}{\text{s}}^{\text{-1}}$. (a) Calculate the activation energy for the decomposition of PAN. (b) What is the half-life of the reaction (in min) at $\text{25°C}$ ?