Carbon dioxide dissolved in water makes the water slightly acidic. We desire to remove most of the \(\mathrm{CO}_{2}\) from \(10.00 \mathrm{kmol} / \mathrm{h}\) of water containing \(\mathrm{x}_{0}=\) \(0.00001 \mathrm{~mol}\) fraction \(\mathrm{CO}_{2}\). The water enters at \(15^{\circ} \mathrm{C}\), the operation is isothermal, pressure is \(2.0 \mathrm{~atm}\), and the exiting water is at \(\mathrm{x}_{\mathrm{N}}=2.2 \times 10^{-7} \mathrm{~mol}\) fraction \(\mathrm{CO}_{2}\). The gas used for stripping out the \(\mathrm{CO}_{2}\) is pure air \(\left(\mathrm{y}_{\mathrm{N}+1, \mathrm{CO} 2}=\right.\) \(0)\). Henry's law constants are in Table 12-1.

Table 12-1

a. If gas flow rate \(\mathrm{V}=0.10 \mathrm{kmol} / \mathrm{h}\), what is \(\mathrm{y}_{1, \mathrm{CO} 2}\), the outlet gas mole fraction \(\mathrm{CO}_{2}\) ?

b. If \(\mathrm{V}=0.10 \mathrm{kmol} / \mathrm{h}\), how many equilibrium stages are required (include the fractional number)?

c. What is the minimum gas flow rate required?

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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