Question

Assume that algae need C, N, and P in the atomic (or molar) ratios 106:16:1. What are the atomic (or molar) ratios in a lake that contains the following concentrations: C = 20 mg L-1, N = 0.80 mg L-1, and P = 0.16 mg L-1? what is the limiting nutrient? Assume that 1/2 of the phosphorus originates from the use of phosphate detergents. Will banning the use of those detergents slow down eutrophication? Why or why not?

Answer 1

We have :algae need C, N, and P in the atomic (or molar) ratios 106:16:1.

Atomic (or molar) ratios in a lake :

In lake, C = 20 mg L^-1 = 20*10^-3 g L^-1 = 0.02 g L^{-1​​​​​​​}

we have , 1 g = 1000 mg ; Molar mass of C = 12 g /mol

or C = 0.02 g L^{-1​​​​​​​} /  12 g /mol =  0.00167 mol / L

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N = 0.8 mg L^{-1​​​​​​​} = 0.8*10^-3 g L^{-1​​​​​​​} = 8*10^-4 g L^{-1​​​​​​​}

we have , 1 g = 1000 mg ; Molar mass of C = 14 g /mol

or C = 8*10^-4 g L^{-1​​​​​​​} /  14 g /mol = 0.000057​​​​​​​ mol / L

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N = 0.16 mg L^{-1​​​​​​​} = 0.16*10^-3 g L^{-1​​​​​​​} = 1.6*10^-4 g L^{-1​​​​​​​}

we have , 1 g = 1000 mg ; Molar mass of P = 31 g /mol

or C = 1.6*10^-4 g L^{-1​​​​​​​} /  31 g /mol = 0.00000516 mol / L

C, N, and P in the atomic (or molar) ratios in lake = 0.00166 :0.000057​​​​​​​ :0.0000052

C:N: P = 322 :11: 1

Requirement by Algae : C:N: P =  106:16:1

Using both data we can say that Nitrogen acts as limiting nutrient in this lake for algal growth. A lilting nutrient ,is one of nutrients/ elements required by plants/algae abundance which limits physiological process , as available amount of that less than optimal level.Though molar ratio is also lesser than biological requirement than carbon, but its availability is more than required when compared with N: thus Nitrogen is limiting nutrient.

If half of the 'P' originates  from the use of phosphate detergents​​​​​​​ , than molar ratios will be :

C:N: P = 644 :22: 1 (if we remove 'P' which originates  from the use of phosphate detergents)

Banning the use of those detergents will slow down eutrophication​​​​​​​ ,  since now 'P' will act as limiting nutrient and growth of algae will be slow down (reduction in algal bloom) : now growth will be regulated by availability of 'P' earlier it was ~10 % of 'N' (requirement 6.25 % ) , now it is ~5% , thus ~ 37% reduction in algal growth.