A treatise on atmospheric chemistry lists the following rate constants for the decomposition of PAN described in the Integrative Example on page 965: 0 °C, k = 5.6 x 10^-6 s^-1; 10 °C, 3.2 x 10^-5 s^-1; 20 °C, 1.6 x 10^-4 s^-1; 30 °C, 7.6 x 10^-4 s^-1.

(a) Construct a graph of ln k versus 1/T.

(b) What is the activation energy, of the reaction?

(c) Calculate the half–life of the decomposition reaction at 40 °C.

Integrative Example

Peroxyacetyl nitrate (PAN) is an air pollutant produced in photochemical smog by the reaction of hydrocarbons, oxides of nitrogen, and sunlight. PAN is unstable and dissociates into peroxyacetyl radicals and NO₂(g). Its presence in polluted air is like a reservoir for NO₂ storage.

The first-order decomposition of PAN has a half-life of 35 hours at 0 °C and 30.0 min at 25 °C. At what temperature will a sample of air containing 5.0 x 10¹⁴ PAN molecules per liter decompose at the rate of 1.0 x 10¹² PAN molecules per liter per minute?

Transcribed Image Text:

O CH3COONO2 PAN CH3COO+NO₂ Peroxyacetyl radical