A boating accident causes a spill of a 20 L bucket of fiberglass gel coat polish into a lake that has an area of 3000 m^2 and an average depth of 5 m. This polish is 30% by volume petroleum distillates that, on average, behave like dodecane (C12H26).
The lake receives water from a stream with a flow rate of 0.2 m^3/s, carrying 80 mg/L suspended solids. These suspended solids are 10% organic carbon (fOC = 0.10).
(a) At what rate ([M/T]) is organic carbon being delivered to the sediments?
(b) At what rate ([M/T]) is dodecane being delivered to the sediments immediately after the spill? Assume there are no degradation processes, the KOC of dodecane is 103.77, the density of dodecane is 0.8 g/mL, and the polish is quickly mixed into the entire lake volume.
(c) There is a single outlet from the lake, also with a flow rate of 0.2 m^3/s. Treating the lake as a perfectly mixed reactor, write a mass balance equation for dodecane in the lake. What is the concentration of dodecane in the lake after 1 day?
(d) What fraction of the petroleum distillates will be transferred to the sediments after 1 day?