Question

Redo the fish tank problem seen in class, but now include the nitrogen gas as well into the system, along with the previously existing components. Use all the data from before. Assume that the Henry’s Law constant for nitrogen in water (Hn,w) at 25°C is 87008.55 atm and for oxygen in water (Ho,w) at the same temperature = 42538.46 atm. Does your pet fish still have enough dissolved oxygen in the tank to survive? (Minimum mole fraction of dissolved oxygen required by a typical fish is around 4 x 10-6 ). Hints: a. Assume that there are 2 moles of O2 for every 8 moles of N2 in air (this will serve as your 4th equation) to solve for the 4 unknowns (xo, xn, yo, yn). b. Use steam tables to find Psat for water, instead of using Antoine equation. P=1atm P_w^sat=0.0313

Answer 1

P = 1 atm

Pwsat = 0.0313 atm

Net total pressure of air = 1 - 0.0313 = 0.9687 atm

According to Daltons Law:

PO2 + PN2 = P

P. yo + P. yn = P

yo + yn = 1

Also given that : yn = 4 yo

Therefore, we have

yo = 0.2

yn = 0.8

PO2 = 0.2 X P = 0.2 X 0.9687 = 0.19374 atm

PN2 = 0.8 X P = 0.8 X 0.9687 = 0.77496 atm

Using henry's law;

xo = PO2 / Ho = 0.19374/42538.46 = 4.55 X 10-6

xn = Pn2 / Hn = 0.77496/87008.55 = 8.91 X 10-6

For fish to survive, xo > 4 X 10-6

Here xo = 4.55 X 10-6

Hence the fish will survive.