Chapter 14, Problem 14.38P

As an employee of the Los Angeles Air Quality Commission, you have been asked to develop a model for computing the distribution of ${\text{NO}}_2$ , in the atmosphere. The molar flux of ${\text{NO}}_2$ , at ground level, $N_{A,0}^{"}$ , is presumed known. This flux is attributed to automobile and smoke stack emissions. It is also known that the concentration of ${\text{NO}}_2$ at a distance well above ground level is zero and that NO, reacts chemically in the atmosphere. In particular, ${\text{NO}}_2$ 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 $N_A=-k_1{C}_A$ .
(a) Assuming steady-state conditions and a stagnant atmosphere, obtain an expression for the vertical distribution $C_A\left(x\right)$ of the molar concentration of ${\text{NO}}_2$ in the atmosphere.
(b) If an ${\text{NO}}_2$ partial pressure of $p_A=2\times {10}^{-6}$ 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 $k_1=0.03s^{-1}$ , and an NO₂-air diffusion coefficient of $D_{AB}=0.15\times {10}^{-4}$
$m^2/s$ .