Chapter 12, Problem 108CP

The decomposition of NO₂(g) occurs by the following bimolecular elementary reaction:

$2{\text{NO}}_{{}_{\text{2}}}\left(g\right)\to 2\text{NO}\left(g\right)+{\text{O}}_{\text{2}}\left(g\right)$

The rate constant at 273 K is 2.3 × 10⁻¹² L/mol · s, and the activation energy is 111 kJ/mol. How long will it take for the concentration of NO₂(g) to decrease from an initial partial pressure of 2.5 atm to 1.5 atm at 500. K? Assume ideal gas behavior.