Chapter 10, Problem 10.18P

10.18. A 40.0-ft³oxygen tent initially contains air at 68°F and 14.7 psia. At a time t = 0 an enriched air mixture containing 35.0% v/v O₂and the balance N₂is fed to the tent at 68°F and 1.3 psig at a rate of 60.0 ft³/min, and gas is withdrawn from the tent at 68°F and 14.7 psia at a molar flow rate equal to that of the feed gas.

1. Calculate the total lb-moles of gas (O₂+ N₂) in the tent at any time.

Let x(t) equal the mole fraction of oxygen in the outlet stream. Write a differential mole balance on oxygen, assuming that the tent contents are perfectly mixed (so that the temperature, pressure, and composition of the contents are the same as those properties of the exit stream). Convert the balance into an equation for dx/dt and provide an initial condition.

Integrate the equation to obtain an expression for x(t). How long will it take for the mole fraction of oxygen in the tent to reach 0.33? Sketch a plot of x versus f, labeling the value of x at t = 0 and the asymptotic value at t ? 8.