2. A lake with a single inflow stream has the following characteristics: Mean depth = 5.0 m; Surface area = 10 x 106 m2; Hydraulic residence time = 4 yr An industrial plant present discharges the pesticide atrazine (W= 2.1 x 106 kg/yr) to the lake. In addition, the inflowing stream also contains atrazine (Cin = 9.3 mg/L). Note that the volumetric rate of inflow and outflow are equal. Assuming that a first-order reaction can be used to characterize atrazine decay (k= 0.13/yr) (a) Develop the mass balance equation for atrazine for this system. Include a system diagram showing each process that adds or removes mass from the lake. (b) If the lake is at steady-state, compute the in-lake atrazine concentration. (c) If the lake is at steady-state, what industrial plant loading rate must be maintained to lower the lake's concentration to 25 ppm? Express your result as a percent reduction. (d) At steady-state, is it possible to lower the lake's concentration to 5 ppm by lowering the plant loading (assume extreme scenario of no loading [W] into the lake at all)? Explain. (e) Evaluate each of the following engineering options to determine which is the most effective for lowering the steady-state concentration: (i) Reduce the present loading rate of the industrial plant by building a waste treatment facility that will remove 50% of the atrazine from the plant's effluent (ii) Double the lake's depth by dredging (iii) Double the lake's outflow rate Q by diverting atrazine-free water from a nearby unpolluted stream into the lake