As an employee of the Los Angeles Air Quality Commission, you have been asked to develop a model for computing the distribution of NO₂ in the atmosphere. The molar flux of NO₂ at ground level, N''_A2, is presumed known. This flux is attributed to automobile and smoke stack emissions. It is also known that the concentration of NO₂ at a distance well above ground level is zero and that N O₂ reacts chemically in the atmosphere. In particular, NO₂ reacts with unburned hydrocarbons (in a process that is activated by sunlight) to produce PAN (peroxyacetylnitrate), the final product of photochemical smog. The reaction is first order, and the local rate at which it occurs may be expressed as N_A = –k₁ CA.

(a) Assuming steady-state conditions and a stagnant atmosphere, obtain an expression for the vertical distribution C_A (x) of the molar concentration of NO₂ in the atmosphere.

(b) If an NO₂ partial pressure of PA = 2 x 10^-6 bar is sufficient to cause pulmonary damage, what is the value of the ground level molar flux for which you would issue a smog alert? You may assume an isothermal atmosphere at T = 300 K, a reaction coefficient of k₁ = 0.03 S^–1, and an NO_2-air diffusion coefficient of D_AB = 0.15 x 10^-4 m²/s.