Chapter 21, Problem 21.74QP

Peroxyacetyl nitrate (PAN) undergoes thermal decomposition as follows:

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

The rate constant is 3.0 × 10⁻⁴s⁻¹ at 25°C. At the boundary between the troposphere and stratosphere, where the temperature is about −40°C, the rate constant is reduced to 2.6 × 10⁻⁷ s⁻¹. (a) Calculate the activation energy for the decomposition of PAN. (b) What is the half-life of the reaction (in min) at 25°C?