Fish toxicity test

You want to carry out a fish toxicity test in a tank with a volume of 100 L. To work reproducibly and under well defined conditions, you want to keep the aqueous concentration of the analyzed substance (i.e., acenaphtylene) constant throughout the experiment (the decrease should be less than 10% of the initial starting concentration). Therefore, you want to use few fish to minimize the total amount of acenaphthylene taken up by the fish and hence to avoid a pronounced decrease in the aqueous concentration.

a) Please estimate how many grams of fish (living, not dry mass) you may introduce to the tank to fulfill the above requirements. Assume that the compound only partitions into the fat (i.e., lipid fraction) of the fish. Further assume that there is no chemical transformation of the chemical (i.e., no metabolism in the fish). Make your estimate for a temperature of 25°C.
From the literature you know that the fat content of the fish is 3% of the living total mass of the fish. The distribution coefficient of acenaphtylene between water and fat is log K_lip/w= 4.15 (units of K_lip/w are L_water/kg_lipid).

b) Your client asks you to place more fish into the tank than what you have calculated under a). Can you think of a way to modify your experiment to still comply to the requirement that the aqueous concentration does not drop to less than 90% of the initial aqueous concentration by introducing the fish.

Help: In this case the approach is not directly obvious. The question can be translated into the following expression:

And further:

	Proceed