Equilibrium and Henry's Law Constant. The partial pressure of CO₂ in air is 1.333 × 10⁴ Pa and the total pressure is 1.133 × 10⁵ Pa. The gas phase is in equilibrium with a water solution at 303 K. What is the value of x_A for CO₂ in equilibrium in the solution? See Appendix A.3 for the Henry's law constant.

Gas Solubility in Aqueous Solution. At 303 K the concentration of CO₂ in water is 0.90 × 10⁻⁴ kg CO₂/kg water. Using the Henry's law constant from Appendix A.3, what partial pressure of CO₂ must be kept in the gas to prevent the CO₂ from vaporizing from the aqueous solution?

Phase Rule for a Gas–Liquid System. For the system SO₂–air–water, the total pressure is set at 1 atm abs and the partial pressure of SO₂ in the vapor is set at 0.20 atm. Calculate the number of degrees of freedom, F. What variables are unspecified and hence can be arbitrarily set?

Equilibirum Stage Contact for Gas–Liquid System. A gas mixture at 2.026 × 10⁵ Pa total pressure containing air and SO₂ is brought into contact in a single-stage equilibrium mixer with pure water at 293 K. The partial pressure of SO₂ in the original gas is 1.52 × 10⁴ Pa. The inlet gas contains 5.70 total kg mol and the inlet water 2.20 total kg mol. The exit gas and liquid leaving are in equilibrium. Calculate the amounts and compositions of the outlet phases. Use equilibrium data from Fig. 10.2-1.

Absorption in a Countercurrent Stage Tower. Repeat Example 10.3-2 using the same conditions but with the following change. Use a pure water flow to the tower of 108 kg mol H₂O/h, that is, 20% above the 90 used in Example 10.3-2. Determine the number of stages required graphically. Repeat, using the analytical Kremser equation.

Stripping Taint from Cream by Steam. Countercurrent stage stripping is to be used to remove a taint from cream. The taint is present in the original cream to the stripper at a concentration of 20 parts per million (ppm). For every 100 kg of cream entering per unit time, 50 kg of steam will be used for stripping. It is desired to reduce the concentration of the taint in the cream to 1 ppm. The equilibrium relation between the taint in the steam vapor and the liquid cream is y_A = 10x_A, where y_A is ppm of taint in the steam and x_A ppm in the cream (E1). Determine the number of theoretical stages needed. [Hint: In this case, for stripping from the liquid (L) stream to the vapor (V) stream, the operating line will be below the equilibrium line on the y_A − x_A diagram. It is assumed that none of the steam condenses in the stripping. Use ppm in the material balances.]

Overall Mass-Transfer Coefficient from Film Coefficients. Using the same data as in Example 10.4-1, calculate the overall mass-transfer coefficients and K_x, the flux, and the percent resistance in the gas film.

Interface Concentrations and Overall Mass-Transfer Coefficients. Use the same equilibrium data and film coefficients and as in Example 10.4-1. However, use bulk concentrations of y_AG = 0.25 and x_AL = 0.05. Calculate the following:

Countercurrent Water-Cooling Tower. A forced-draft countercurrent water-cooling tower is to cool water from 43.3 to 26.7°C. The air enters the bottom of the tower at 23.9°C with a wet bulb temperature of 21.1°C. The value of H_G for the flow conditions is H_G = 0.533 m. The heat-transfer resistance in the liquid phase will be neglected; that is, h_L is very large. Hence, values of should be used. Calculate the tower height needed if 1.5 times the minimum air rate is used.

Minimum Gas Rate and Height of Water-Cooling Tower. It is planned to cool water from 110°F to 85°F in a packed countercurrent water-cooling tower using entering air at 85°F with a wet bulb temperature of 75°F. The water flow is 2000 lb_m/h · ft² and the air flow is 1400 lb_m air/h · ft². The overall mass-transfer coefficient is K_Ga = 6.90 lb mol/h · ft³atm.

Design of Water-Cooling Tower. Recalculate Example 10.5-1, but calculate the minimum air rate and use 1.75 times the minimum air rate.

Effect of Changing Air Conditions on Cooling Tower. For the cooling tower in Example 10.5-1, to what temperature will the water be cooled if the entering air enters at 29.4°C but the wet bulb temperature is 26.7°C? The same gas and liquid flow rates are used. The water enters at 43.3°C, as before. (Hint: In this case T_L1 is the unknown. The tower height is the same as in Example 10.5-1. The slope of the operating line is as before. The solution is trial and error. Assume a value of T_L1 that is greater than 29.4°C. Do numerical or graphical integration to see if the same height is obtained.)

Amount of Absorption in a Tray Tower. An existing tower contains the equivalent of 3.0 theoretical trays and is being used to absorb SO₂ from air by pure water at 293 K and 1.013 × 10⁵ Pa. The entering gas contains 20 mol % SO₂ and the inlet air flow rate is 150 kg inert air/h · m². The entering water rate is 6000 kg/h · m². Calculate the outlet composition of the gas. (Hint: This is a trial-and-error solution. Assume an outlet gas composition of, say, y₁ = 0.01. Plot the operating line and determine the number of theoretical trays needed. If this number is not 3.0 trays, assume another value of y₁, and so on.)

Analytical Method for Number of Trays in Absorption. Use the analytical equations in Section 10.6 for countercurrent tray contact to calculate the number of theoretical trays needed for Example 10.6-3 using 1.3.

Absorption of Ammonia in a Tray Tower. A tray tower is to be used to remove 99% of the ammonia from an entering air stream containing 6 mol % ammonia at 293 K and 1.013 × 10⁵ Pa. The entering pure water flow rate is 188 kg H₂O/h · m²and the inert air flow is 128 kg air/h · m². Calculate the number of theoretical trays needed. Use equilibrium data from Appendix A.3. For the dilute end of the tower, plot an expanded diagram to step off the number of trays more accurately.

Minimum Liquid Flow in a Packed Tower. The gas stream from a chemical reactor contains 25 mol % ammonia and the rest inert gases. The total flow is 181.4 kg mol/h to an absorption tower at 303 K and 1.013 × 10⁵ Pa pressure, where water containing 0.005 mol frac ammonia is the scrubbing liquid. The outlet gas concentration is to be 2.0 mol % ammonia. What is the minimum flow ? Using 1.5 times the minimum, plot the equilibrium and operating lines.

Steam Stripping and Number of Trays. A relatively nonvolatile hydrocarbon oil contains 4.0 mol % propane and is being stripped by direct superheated steam in a stripping tray tower to reduce the propane content to 0.2%. The temperature is held constant at 422 K by internal heating in the tower at 2.026 × 10⁵ Pa pressure. A total of 11.42 kg mol of direct steam is used for 300 kg mol of total entering liquid. The vapor–liquid equilibria can be represented by y = 25x, where y is mole fraction propane in the steam and x is mole fraction propane in the oil. Steam can be considered as an inert gas and will not condense. Plot the operating and equilibrium lines and determine the number of theoretical trays needed.

Absorption of Ammonia in Packed Tower. A gas stream contains 4.0 mol % NH₃ and its ammonia content is reduced to 0.5 mol % in a packed absorption tower at 293 K and 1.013 × 10⁵ Pa. The inlet pure water flow is 68.0 kg mol/h and the total inlet gas flow is 57.8 kg mol/h. The tower diameter is 0.747 m. The film mass-transfer coefficients are = 0.0739 kg mol/s · m³mol frac and = 0.169 kg mol/s · m³mol frac. Using the design methods for dilute gas mixtures, do as follows:

Tower Height Using Overall Mass-Transfer Coefficient. Repeat Example 10.6-4, using the overall liquid mass-transfer coefficient to calculate the tower height.

Experimental Overall Mass-Transfer Coefficient. In a tower 0.254 m in diameter absorbing acetone from air at 293 K and 101.32 kPa using pure water, the following experimental data were obtained. Height of 25.4-mm Raschig rings = 4.88 m, V' = 3.30 kg mol air/h, y₁ = 0.01053 mol frac acetone, y₂ = 0.00072, L' = 9.03 kg mol water/h, x₁ = 0.00363 mol frac acetone. Calculate the experimental value of K_ya.

Conversion to Transfer-Unit Coefficients from Mass-Transfer Coefficients. Experimental data on absorption of dilute acetone in air by water at 80°F and 1 atm abs pressure in a packed tower with 25.4-mm Raschig rings were obtained. The inert gas flow was 95 lb_m air/h · ft² and the pure water flow was 987 lb_m/h · ft². The experimental coefficients are k_Ga = 4.03 lb mol/h · ft³atm and k_La = 16.6 lb mol/h · ft³ · lb mol/h · ft³. The equilibrium data can be expressed by c_A = 1.37p_A, where c_A = lb mol/ft³ and p_A = atm partial pressure of acetone.

Height of Tower Using Transfer Units. Repeat Example 10.6-4 but use transfer units and calculate H_L, N_L, and tower height.

Experimental Value of H_OG. Using the experimental data given in Problem 10.6-8, calculate the number of transfer units N_OG and the experimental value of H_OG.

Pressure Drop and Tower Diameter. Use the same conditions as in Example 10.6-1 but with the following changes. The gas feed rate is 2000 lb_m/h and the design ratio of G_L/G_G is 2.2/1. Using 60% of flooding and 1 in Intalox packing, calculate the pressure drop, gas and liquid flows, and tower diameter.

Minimum Liquid Flow Rate in Absorption. Using the data from Example 10.6-3, calculate the number of trays graphically and analytically for an operating flow rate of 1.3 times the minimum liquid flow rate.

Experimental Height of Transfer Unit and Analytical Equations. A packed tower 4.0 m tall is used to absorb ethyl alcohol from an inert gas by 90 kg mol/h of pure water at 303 K and 101.3 kPa. The total gas stream flow rate of 100 kg mol/h contains 2.0 mol % alcohol and the exit concentration is 0.20 mol %. The equilibrium relation is y = mx = 0.68x for this dilute stream. Using the analytical equations, calculate the number of theoretical trays N, the number of transfer units N_OG, H_OG, and HETP.

Liquid Film Coefficients and Design of SO₂ Tower. Using the data for Example 10.7-1, calculate the height of the tower using Eq. (10.6-18), which is based on the liquid film mass-transfer coefficient . [Note: The interface values x_i have already been obtained.]

Design of SO₂ Tower Using Overall Coefficients. Using the data for Example 10.7-1, calculate the tower height using the overall mass-transfer coefficient . [Hint: Calculate at the top of the tower and at the bottom of the tower from the film coefficients. Then use a linear average of the two values for the design. Obtain the values of y^* from the operating- and equilibrium-line plot. Numerically or graphically integrate Eq. (10.6-19), keeping outside the integral.]

Height of Packed Tower Using Transfer Units. For Example 10.7-1, calculate the tower height using the H_G and the number of transfer units N_G. [Hint: Calculate H_G at the tower top using Eq. (10.6-39) and at the tower bottom. Use the linear average value for H_G. Calculate the number of transfer units N_G by numerical or graphical integration of the integral of Eq. (10.6-35). Then calculate the tower height.]

Design of Absorption Tower Using Transfer Units. The gas SO₂ is being scrubbed from a gas mixture by pure water at 303 K and 1.013 × 10⁵ Pa. The inlet gas contains 6.00 mol % SO₂ and the outlet 0.3 mol % SO₂. The tower cross-sectional area of packing is 0.426 m². The inlet gas flow is 13.65 kg mol inert air/h and the inlet water flow is 984 kg mol inert water/h. The mass-transfer coefficients are H_L = 0.436 m and k_Ga = 6.06 × 10⁻⁷ kg mol/s · m³ · Pa and are to be assumed constant in the tower for the given concentration range. Use equilibrium data from Appendix A.3. By numerical or graphical integration, determine N_G. Calculate the tower height. (Note: The equilibrium line is markedly curved, so numerical or graphical integration is necessary even for this dilute mixture.)

Correction of Film Coefficients for NH₃ Absorption. Use the same system and conditions given in Example 10.8-1, except that NH₃ is being absorbed instead of CO₂. The flow rates are the same. Predict H_G, H_L, H_OG, and percent resistance in the liquid phase.

Prediction of Film Coefficients for Acetone Absorption. Predict H_G, H_L, and H_OG for absorption of acetone from air by water in a dilute aqueous solution using 2-in. Intalox metal IMTP packing at 20°C and 1 atm abs pressure. The flow rates are G_x = 3.391 kg/s · m² (2500 lb_m/h · ft²) and G_y = 0.678 kg/s · m² (500 lb_m/h · ft²). Use equilibrium data from Appendix A.3-21 and the diffusivity for acetone in water from Table 6.3-1. The diffusivity of acetone in air at 1 atm abs is 0.109 × 10⁻⁴ m²/s at 0°C (P1).

Nonisothermal Absorption Tower. Use the same operating conditions as in Example 10.9-1 for absorption of NH₃ except for the following change. The inlet gas temperature is 15°C and it is saturated with water vapor. Calculate the outlet water temperature T₁ and the overall number of transfer units N_Oy by numerical or graphical integration.