2. During long-range atmospheric transport over distances on the order of 1000 km, SO2 emitted from power plants is oxidized to sulfate (SO4 2-) and both compounds undergo dry deposition to the surface. The conversion and removal processes can all be treated as first order, with the rate constant for conversion given as k12, and the rate constants for deposition given as k1d and k2d for SO2 and SO4 2-, respectively. The reaction system is shown in the diagram below. Assume that the air parcel in which SO2 to SO4 2- conversion occurs can be treated as a plug flow reactor with wind velocity u. (a) Write the mass balance equations (differential equations) for SO2 and SO4 2- . (b) Solve for the steady state concentrations of each as a function of distance and write expressions for each of these. (c) Determine the maximum SO4 2- concentration and the distance at which it occurs, given u = 15 km/h, k1d = 0.025 h-1, k2d = 0.015 h-1 and k12 = 0.02 h-1, and that the initial SO4 2- concentration is negligible. Express the maximum as a ratio of SO4 2- to initial SO2 concentration.