CVEN 489-501Special Topics on Mixing and Transport in the EnvironmentProblem Set #8 Physical, Chemical, and Biological TransformationDate distributed : 4.14.2005Date due : 4.20.2005Return your solution in class at the beginning of the lecture period on the date shown above.Please show all your work and follow the rules outlined in the course syllabus.1 Reaction OrderA Chemical reaction is of order 1.5.• What are the units of the rate constant?• What is the solution to the rate equations (i.e. what is C(t))?• Write an expression for the half-life and e-folding time.2 Reaction kineticsIn the atmosphere, N2O5will transform to NO2 due to the chemical reaction:2N2O5→ 4NO2+ O2(1)Experimental data show the concentration of N2O5varies as a function of time. Given themeasured data in the following table, determine• The order of the reaction.• The reaction constant.This problem is taken from Chu, C.R. (2002) Environmental Fluid Mechanics.CIVILCollege Station, Texas 77843-31363136 TAMU (979) 845-4517FAX (979) 862-8162Table 1: Chemical reaction rate data for N2O5in the atmosphere.Time N2O5Concentration[min] [mg/l]0 0.83310 0.62020 0.46530 0.35740 0.26550 0.19660 0.14470 0.1103 Water treatmentIn part of a water treatment plant, a mixing tank is used to remove heavy metals.Untreated water fl ows into the tank where it is rigorously mixed (instantaneously mixed)and brought into contact with other chemicals that remove the metals. A single outlet isinstalled in the tank. Assume the inflow and outflow rates are identical, and assume metalsare removed in a fist-order reaction with a rate constant of k = 0.06 s−1. The tank volume is15 m3. (Hint: write the conservation of mass for the tank volume to obtain an equation thatcan predict the outflow concentration as a function of time. Because the tank is well-mixed,the concentration inside the tank and at the outlet will be identical.)• What is the allowable flow through rate such that the exit stream contains 10% of themetals in the input stream?• How high can the flow through rate be if the reaction rate constant is doubled?4 Bacteria Die-offA Wastewater Tr eatment Plant (WWTP) injects 109bacteria per second into a localstream (width 30 meters, depth 1 meter, flow rate 2 m3/s). Calculate the concentrationof bacteria in #/100 ml downstream of the injection assuming the bacteria die-off rate is1 day−1and the die-off kinetics are first-order. (Hint: solve for the die-off rate as a functionof time and then use the river velocity to convert to distance