A body of water is polluted with mercury. The lake has a volume of 200 million c

Question

A body of water is polluted with mercury. The lake has a volume of 200 million cubic meters and mercury is present in a concentration of 5 grams per million cubic meters. Health officials state that any level above 1 g per million cubic meters is considered unsafe. Is water unpolluted by mercury flows into the lake at a rate of 0.5 million cubic meters per day, and uniformly mixed lake water flows out of the lake at the same rate, how long will it take for the lake to reach a mercury concentration that is considered safe?

Explanation / Answer

The overall volume of the lake is 200 MM m3 (MM stands for million)

The mercury volume is 5 grams per MM m3 which means overall lake has 200 X 5 = 1000 grams of mercury uniformily distributed across the lake.

Acceptable limit of mercury is 1 gram per MM m3 which means overall lake can have a maximum of 200 grams in the entire lake to be considered safe.

The objective is therefore to remove 800 grams of mercury from the lake. Since 1 MM m3 has 5 grams & is uniformly distributed, 160 MM m3 will have 800 grams of mercury.

So the objective is to remove 160 MM m3 of water from the 200 MM m3 lake.

As the rate of inflow of non polluted water is 0.5 MM m3 per day which mixes uniformily and outflow is the same rate, it will take 160/0.5 i.e. 320 days for the 160MM m3 to be replaced with non polluted water.

Hence 320 days will be required for the lake to be in acceptable limits of mercury.

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