Question

4) Imagine you have a fish tank with a volume of 0.25 cubic meters. Initially the water in it has an ammonia concentration of 0 parts per million or ppm (1 ppm means there is 1 g of ammonia out of every million g of water in the tank). a. What is the mass of water in the tank (assume that the water has a mass of 1 kg per liter)? b. If the water in the tank had a concentration of 2 ppm, what mass (in g) of ammonia would that be. c. If the tank contains 20 fish, and each one produces 1 mg of ammonia per day, how much ammonia is produced per day? d. How many days would it take the tank to reach a dangerous ammonia concentration of 2 ppm if you don't change the water?

Answer 1

a) The volume capacity of the tank 0.25 m³. This corresponds to 250l (1m³=1000l). Since density of water is 1kg/l, this corresponds to a mass of 250kg.

b) For ammonia to reach a concentration of 2ppm, there wiould have to be 2 parts of ammonia per 10⁶. Total ammonia in the tank would have to be (2/10⁶)x250 = 5x10^-4kg = 0.5g or 500mg.

c)The tank contains 20 fish, each giving out 1mg of ammonia per day. The total ammonia produced would simple be the sum total of ammonia produced by each fish. Thus, the total ammonia produced by the fish in the tank is 20mg per day.

d) Since the daily addition of ammonia is 20mg. There is no volume flux since we aren't changing the water. We have also calculated previously that a concentration corresponding to 2ppm is 500mg. Thus, it will take 500/20 = 25 days to reach a concentration of 2ppm.