Question

Imagine that a polluter starts dumping sodium chloride into Lake Charles at a rate of 1413.7 kg per day, that the background concentration of NaCl in the lake was 8.3 ppm, and that the residence time of NaCl in the lake is 3.5 years. After 5 years, the Environmental Protection Agency catches on and turns off this source of NaCl. What would be the maximum concentration of NaCl in the lake? Please give your answer in ppm. Lake Charles has a volume of 1.8*107 m3.

Answer 1

The residence time of NaCl is 3.5 year. So anything added before 1.5 year will not be there in the lake at the end of 5 th year. So we need to calculate amount of NaCl added after 1.5 year, which means we need to calculate amount of NaCl added in 3.5 year.

1) Present amount of NaCl in lake

a)Volume of the lake = 1.8*10^7 m3 = 1.8*10^10L

b) Present amount of NaCl in lake is 8.3 ppm, which means the lake has

1000000 has 8.3

So 1.8*10^10 L has 149400 kg NaCl

So the lake has originally 149400 kg of NaCl present in it

2) Amount of NaCl added into lake in 3.5 years

a) In one day amount of NaCl added = 1413.7 kg

so in 3.5 years amount of NaCl added into the lake = 1413.7*365*3.5 = 1806001.75 kg

So in 3.5 years amount of NaCl added into the lake in 1806001.75 kg

3) So total amount of NaCl present in lake at the end of 5th year is = 149400+1806001.75 = 1955401.75

Which means at the end of 5th year 1.8*10^10 L water have 1955401.75 kg Nacl

which is equal to 108.63 ppm

So the final answer is - At the end of 5th year the Lake Charles would have 108.63 ppm of NaCl in it

(In the problem density of water is considered 1g/cm3)