DO NOT USE PV=CONSTANT APPROACH. IT IS WRONG SINCE MOLES ARE NOT CONSTANT. Befor

Question

DO NOT USE PV=CONSTANT APPROACH. IT IS WRONG SINCE MOLES ARE NOT CONSTANT.

Before another dive, Jacques needs to refill his air tank. When filled, the tank holds 15.0L of air at 200 atm. Below 30 atm, the tank is, for all practical purposes, empty at the depths it will be used. Jacques uses a pump that compresses air at atmospheric pressure into the tank at a rate of 170 L/min. Suppose that the temperature of the air remams unchanged during the compression process. How long does it take fill the tank?

Explanation / Answer

since below 30 atm,tank is supposed to be empty for all practical purposes. so number of moles in the practically empty tank is

ni=(30 atm).(15.0 L)/(R.T)

Where R is gas constant, and T is the temperature of the air.

For the fully filled tank

Pf = 200 atm, and V = 15.0 L

Then number of moles in a fully filled tank

nf = (200 atm).(15.0 L)/(R.T)

We are filling 170 L OF air at 1 atm in the tank per minut. So we are filling r moles(say) in the tank per minut.

r = (170 L).(1 atm)/(R.T)

And we need to fill (ni - nf) moles in the tank.

then time required in minutes is given by

t=(nf - ni)/r minutes

t = { (200 atm).(15.0 L) - (30 atm).(15.0 L)} / {(170 L).(1 atm)}

=> t = (15.0 L).(170 atm) / (170 L).(1 atm)

=> t= 15.0 minutes

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