The shark tank at an aquarium houses 5 sharks that deplete the aquarium water of

Question

The shark tank at an aquarium houses 5 sharks that deplete the aquarium water of a total of 65.00 g of oxygen per hour. Water from the tank is diverted through a bubbler unit that oxygenates the water using a stream of oxygen-rich air, and then is returned to the tank. At steady state, water enters the bubbler containing 0.000700 wt% O2 and exits the bubbler containing 0.001000 wt% O2. For every kilogram of the inlet water stream that enters the bubbler, 0.00500 mol of oxygen-rich air with an initial composition of 35.00 mole% O2 and 65.00 mole% N2 is fed through the bubbler.

What is the flow rate of the inlet water stream?

What is the mol% of O2 in the oulet air stream?

Explanation / Answer

Let  flow rate of the inlet water stream be X kg/hr

O2 present in inlet water stream = 7 x 10-6 * x kg

For every kg of inlet water stream -

Moles of air = 5 x 10-3

Moles of O2 = 0.35 * 5 x 10-3 = 1.75 x 10-3

Moles of N2 = 3.25 x 10-3

For every kg of inlet stream, amount of oxygen rich air added = 5 x 10-3 * [9.6 + 19.6] g

= 1.46 x10-4kg

For X kg of inlet stream = X * 1.46 x10-4kg

Outlet stream = X + X * 1.46 x10-4kg

Weight of O2 in outlet stream = X*7 x 10-6 + X*48 x 10-6

= X*55 x10-6 kg

Weight of N2 in outlet stream = X*98 x 10-6 kg

Mole percent of O2 = (X*55 x 10-6 / 0.032 ) / [ (X*55 x 10-6 / 0.032) + (X*98 x 10-6 / 0.028) ] * 100

= 32.95 %

5 sharks deplete 65.00 g of oxygen per hour.

So,

Flow rate * 7 x 10-6 = 0.065

Flow rate = 9285.714 kg / hr

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