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 situation you are to consider is one in which the molar flux of NO2 at ground level, NAo, is known; this flux is attributed to automobile and smokestack emissions. It is also known that the concentration of NO2 at a distance well above ground level is zero and that NO2 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 = −k₁C_A.
(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 a NO2 partial pressure of p_A = 2×10^(−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 k_1 = 0.03 s^(−1), and a NO2−air diffusion coefficient of DAB = 0.15×10^(−4) m^2/s.