Design a stripping column to remove carbon dioxide from water by heating the water and passing it countercurrently to a nitrogen stream in a staged stripper. Operation is isothermal and isobaric at \(60.0^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm}\) pressure. Feed water contains \(9.2 \times 10^{-6}\) mole fraction \(\mathrm{CO}_{2}\) and flows at \(100,000 \mathrm{lb} / \mathrm{h}\). Entering nitrogen is pure and flows at \(2500.0 \mathrm{ft}^{3} / \mathrm{h}\). Nitrogen is at \(1.0 \mathrm{~atm}\) and \(60.0^{\circ} \mathrm{C}\). Outlet water concentration is \(2.0 \times 10^{-7} \mathrm{~mole}\) fraction \(\mathrm{CO}_{2}\). Ignore nitrogen solubility in water, and ignore water volatility. Equilibrium data are in Table 12-1. Use a Murphree vapor efficiency of \(40.0 \%\). Find the outlet vapor composition and the number of real stages needed.

Table 12-1

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TABLE 12-1. Henry's law constants H for Eq. (12-3) for CO2, CO, and H2S in water. H is in atm/mole fraction. TC CO2 CO HS 0 728 35,200 268 LO 5 876 39,600 315 10 1040 44,200 367 15 1220 48,900 423 20 1420 53,600 483 25 1640 58,000 545 30 1860 62,000 609 35 2090 65,900 676 40 2330 69,600 745 45 2570 72,900 814 50 2830 76,100 884 60 3410 82,100 1030 70 84,500 1190 80 84,500 1350 90 84,600 1440 100 84,600 1480