Photochemical smog is formed through a sequence of reactions, the first three of which are given bel — Thermodynamics Chemistry Question
Problem Context
Photochemical smog is formed through a sequence of reactions, the first three of which are given below. Smog is formed when the O(g) produced in reaction (3) reacts with organic molecules.
(1) N2(g) + O2(g) → 2NO(g)
(2) 2NO(g) + O2(g) → 2NO2(g)
(3) NO2(g) + hν → NO(g) + O(g)
For reaction (1), ∆Hº = +180.6 kJ·mol–1. Calculate the bond dissociation energy of NO(g).
Model Answer
The overall enthalpy change can be estimated from the bond dissociation energies via the equation,
180.6 kJ = 941 kJ + 498 kJ – 2 × BDENO
so, BDENO = 629 kJ·mol–1
Calculate the entropy change for the first reaction.
Model Answer
Similarly,
∆Sº = 2(210.6) – ((191.5) + (205)) = 24.7 J·mol–1·K–1
Determine the minimum temperature at which reaction (1) becomes spontaneous.
Model Answer
Utilize the equation, ∆Gº = ∆Hº – T∆Sº, and set ∆Gº to zero to find the minimum temperature.
0 = 180.6 kJ·mol–1 – T × (0.0247 kJ·mol–1·K–1), so T = 180.6 kJ·mol–1 / 0.0247 kJ·mol–1·K–1 = 7311 K
For reaction (3), ∆Hº = +306 kJ·mol–1. If the energy for this reaction were provided by sunlight, estimate the wavelength required and specify the region of the spectrum containing this wavelength.
Model Answer
First convert to energy per molecule,
= 5.08×10–19 J / molecule. Now calculate wavelength of light with this energy,
= 3.91×10–7 m (per molecule) = 391 nm (in the ultraviolet).