Lake silbersee is located in the German city of Nuernberg. The lak's water quality has been diminishedbecause of high hydrogen sulfide concentrations that originate froma nearby leaking landfill. To combat the problem the citydecided to aerate the lake in an attempt to oxidize the odorousH2S to non-odourous sulfate ion according to thefollowing oxidation reaction:
H2S+2O2-->SO42-+2H
It has been determined experimentally that the reactionfollows frst order kinetics with respect to both oxygen andhydrogen sulfide concentrations: d[H2S]/dt =-k[H2S][O2]
The present rate of aeration maintains that the oxygenconcentration in the lake at 2 mg/L. The rate constant k forthe reaction was determined to be 1000L/mole-day. If the aeration completly inhibits the production of hydrogen sulfide, how long would it take to reduce H2S concentration fomm500μM to 1μM?