a. Using a spreadsheet to perform the calculations, prepare a graph of the equilibrium distribution data for each solute as partial pressure in the gas vs. molar concentration dissolved in the liquid (pA − cAL), and also in mole fraction coordinates (yA − xA) at 1.0 atm total system pressure. Which solute is the most soluble in water? Which solute dissolved in water can be stripped into air the easiest?
b. For each solute at the appropriate concentration range, estimate the Henry’s law constant (H) based on the definition ..., and the distribution coefficient m based on the definition ... at 1.0 atm total system pressure.
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27.2 Hydrogen sulfide (H2S) is a common contaminant in natural gas. The dissolution of H2S gas in water is a linear function of partial pressure, as is described by Henry’s law of the form .... Values of H vs. temperature are provided below:...Given the relatively low solubility of H2S in water, an aminebased chelating agent is added to the water to improve the solubility of H2S. Equilibrium distribution data for H2S in a 15.9 wt% solution of monoethanolamine (MEA) in water at 40 °C is provided below:4...
a. Describe the effect of temperature on the solubility of H2S gas in water.
b. Prepare equilibrium distribution plots, in mole-fraction coordinates (yA − xA), for the solubility of H2S in water vs. H2S in 15.9 wt% MEA solution at 40 °C and 1.0 atm total system pressure. Comment on the relative solubility of H2S in water vs. MEA solution.
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27.3 Consider an interphase mass-transfer process for the chlorine dioxide (ClO2)-air-water system at 20 °C, where ClO2 gas (solute A) is sparingly soluble in water. At the current conditions of operation, the mole fraction of ClO2 in the bulk gas phase is yA = 0.040 and the mole fraction of ClO2 in the bulk liquid phase is xA = 0.00040. The mass density of the liquid phase is 992.3 kg/m3 and is not dependent on the very small amount of ClO2 dissolved in it. The molecular weight of water is 18 g/gmole, and the molecular weight of ClO2 is 67.5 g/gmole. The total system pressure is 1.5 atm. The liquid film mass-transfer coefficient for ClO2 in water is kx = 1.0 gmole/m2 · s, and the gas film mass-transfer coefficient ClO2 in air is kG = 0.010 gmole/m2 · s · atm. The equilibrium distribution data for the ClO2-water-air system at 20 °C are provided below:...
a. Plot out the equilibrium line in pA − cAL coordinates, and the operating point (pA, cAL). Is the process gas absorption or liquid stripping?
b. What is the equilibrium relationship as m equal to?
c. What is kL for the liquid film?
d. If the ClO2 mole fraction in the bulk gas phase is maintained at 0.040 under 1.5 atm total system pressure, what is the maximum possible dissolved ClO2 concentration (gmole A/m3) in the liquid phase that could possibly exit the process—i.e., ...?
e. What are the compositions at the gas–liquid interface, pA, i and cAL, i?
f. What is Ky, the overall mass-transfer coefficient based upon the overall gas phase mole fraction driving force? There are several valid approaches for calculating Ky based on the information provided. Show at least two approaches that lead to the same result.
g. What is the mass-transfer flux NA for ClO2 in units of gmole/m2 · s?
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27.4 It is desired to recover hexane vapor (solute A) from air using an absorption process. The absorption solvent is a nonvolatile mineral oil, which has a mass density of 0.80 g/cm3 and a molecular weight of 180 g/gmole. In the dilute concentration range, the equilibrium relationship for the dissolution of hexane vapor in the mineral oil at 20 °C is described by pA,i = HxA,i, where H = 0.15 atm. At the present conditions of operation, the hexane partial pressure in the bulk gas stream is 0.015 atm, and the dissolved hexane in the bulk absorption solvent is 5.0 mole%. The total system pressure is 1.50 atm, and the temperature is 20 °C. The liquid film mass-transfer coefficient kx is 0.01 kgmole/m2 · s, and the gas film mass-transfer coefficient ky is 0.02 kgmole/m2 · s.
a. What is the overall mass-transfer coefficient based on the liquid phase, KL, and molar flux NA?
b. What is the composition of hexane at the gas–liquid interface, in terms of pA,i and xA,i?
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27.5 A packed-bed tower is used for absorption of sulfur dioxide (SO2) from an air stream using water as the solvent. At one point in the tower, the composition of SO2 is 10% (by volume) in the gas phase, and 0.30 wt% in the liquid phase, which has a mass density 61.8 lbm/ft3.The tower is isothermal at 30 °C, and the total system pressure is 1.0 atm. The convective mass-transfer coefficients are kL = 2.5 lbmole/ft2 · h · (lbmole/ft3) for the liquid film, and kG = 0.125 lbmole/ft2 · h · atm for the gas film. Equilibrium distribution data for the SO2-water-air system are provided in Problem 29.1.
a. Plot out the equilibrium line in units of pA (atm) vs. cAL (lbmole/ft3). Plot out the operating point (pA, cAL) on the same graph. Determine ... and ... and plot on the same graph.Problem 29.1The table below presents equilibrium distribution data for four gaseous solutes dissolved in water, using air as the carrier gas:......
b. Determine the gas–liquid interface compositions pA,i and cAL,i;
c. Estimate KG and KL, Ky and Kx at the operating point, and the molar flux NA.
d. Determine the % resistance in the gas phase at the operating point.
a. Using a spreadsheet to perform the calculations, prepare a graph of the equilibrium distribution data for each solute as partial pressure in the gas vs. molar concentration dissolved in the liquid (pA − cAL), and also in mole fraction coordinates (yA − xA) at 1.0 atm total system pressure. Which solute is the most soluble in water? Which solute dissolved in water can be stripped into air the easiest?
b. For each solute at the appropriate concentration range, estimate the Henry’s law constant (H) based on the definition ..., and the distribution coefficient m based on the definition ... at 1.0 atm total system pressure.
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27.6 An engineer at a pulp mill is considering the feasibility of removing chlorine gas (Cl2, solute A) from an air steam using water, which will be reused for a pulp bleaching operation. The process will be carried out in a countercurrent flow gas absorption tower filled with inert packing, where liquid water containing no dissolved Cl2 is pumped into the top of the tower (... = 0), and air containing 20% by volume Cl2 (... = 0.20) at 1.0 atm is fed into the bottom of the tower. Gas–liquid contact is promoted by the inert packing surface as the gas and liquid flow around the packing. As the gas moves to the top of the tower, the Cl2 composition decreases, and as liquid moves down the tower, the dissolved Cl2 concentration increases. At the gas and liquid flow rates of operation, the liquid leaving the bottom of the tower has a composition of 0.05 mole% (... = 0.00050), and the gas exiting the top of the tower has been lower to 5% by volume (... = 0.050). At the flow rates of operation, the gas film mass-transfer coefficient based on a mole fraction driving force (ky) is 5.0 lbmole/ft2 · hr, and the liquid film mass-transfer coefficient based on a mole fraction driving force (kx) is 20 lbmole/ft2 · hr. Equilibrium data for the Cl2-water-air system at 20 °C and 1.0 atm are provided in the table below....
a. Draw a diagram of what the packed tower might look like, labeling liquid flow with L, gas flow with G, and terminal steam mole fraction compositions ... and ... at the bottom and top of the tower.
b. Plot out the equilibrium line in mole fraction coordinates. Then plot out the operating points ... and ... for the bottom and the top of the tower respectively.
c. Determine the local overall mass-transfer coefficients Ky at the top and bottom of the tower? Why are the values for Ky different?
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27.7 Ammonia (NH3) and hydrogen sulfide (H2S) must both be stripped from wastewater in a packed tower before the wastewater can be treated for reuse. Individual mass-transfer coefficients for ammonia transfer within a packed tower are kG = 3.20 × 10–9 kgmole/m2 · s · Pa for the gas film, and kL = 1.73 × 10–9 m/s for the liquid film. At the temperature and concentration ranges of the solutes within the process, the equilibrium distribution data for the solutes NH3 and H2S are in the linear range. The Henry’s law constants are 1.36 × 103 m3 · Pa/kgmole for NH3, and 8.81 × 105 m3 · Pa/kgmole for H2S. Under the assumption that both kG and kL for H2S transfer is the same as those for NH3 transfer, estimate and compare the overall mass-transfer coefficients KG and KL for H2S and NH3, respectively.
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27.8 Wastewater containing dissolved hydrogen sulfide (H2S) at concentration of 2.50 gmole/m3 (85 mg/L) enters an open tank at a volumetric flow rate of 20 m3/h, and exits at the same volumetric flow rate, as shown in the figure on the next page. The open tank is within a large enclosed building. The ventilation for the air surrounding the open tank is such that the composition of H2S in the bulk, well-mixed air over the tank is 0.5 mole% H2S (gas-phase mole fraction of 0.005), which has a pungent odor. The total system pressure is 1.0 atm, and the temperature is 20 °C. The diameter of the cylindrical tank is 5.0 m, and the depth of the liquid in the tank is 1.0 m. At the conditions of operation, the film mass-transfer coefficients for H2S transfer are kL = 2.0 · 10–4 m/s in the liquid film, and kG = 5.0 · 10–4 kgmole/m2 · s · atm in the gas film. The solute H2S (solute A) is sparingly soluble in water, with the linear equilibrium distribution data at 20 °C described by Henry’s law with H = 9.34 m3 · atm/kgmole. At 20 °C, the mass density of the wastewater is 1000 kg/m3.The molecular weight of H2S is 34 g/gmole, and H2O is 18 g/gmole....
a. Estimate m, the equilibrium distribution constant based upon the mole fraction equilibrium relationship—e.g., yA,i = mxA,i. Plot out the operating point (xA, yA) and the equilibrium line in mole fraction coordinates. Is the process gas absorption or liquid stripping?
b. What is the overall mass-transfer coefficient Ky based upon the overall gas-phase mole fraction driving force?
c. Perform a material balance on the process. At the conditions of operation, what is the concentration of dissolved H2S exiting the tank, cAL, in units of gmole/m3?
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27.9 Ozone gas (O3, solute A) dissolved in high-purity water is commonly used in wet cleaning processes associated with semiconductor device fabrication. It is desired to produce a liquid water stream containing 3.0 gmole O3/m3 (238 mg/L) by a process that does not create any gas bubbles. One engineer’s idea is shown in the figure below. Liquid water containing 1.0 gmole O3/m3 enters a well-mixed tank at a volumetric flow rate 0.050 m3/h. A pressurized gas mixture of O3 diluted in inert N2 is continuously added the headspace of the tank at a total pressure of 1.5 atm. Both the liquid and gas inside the tank are assumed to be well mixed. The gas–liquid surface area inside the tank is 4.0 m2. The process is maintained at 20 °C. At 20 °C, the solution density is 992.3 kg/m3. For a well-mixed, non-bubbled ozonation tank, the appropriate film mass-transfer coefficients for the liquid and gas films are kL = 3.0 · 10–6 m/s andkc = 5.0 · 10–3 m/s, respectively. Equilibrium distribution data for O3 gas dissolved in water at 20 °C follows Henry’s law, with H = 68.2 m3 · atm/kgmole based on the definition pA,i = H · cAL,i....
a. What are m, and the Henry’s law constant H in units of atm? Is O3 very soluble in water?
b. What is the overall mass-transfer coefficient KG, based on the overall gas-phase driving force?
c. What is the overall mass-transfer coefficient KL based on the overall liquid-phase driving force?
d. For the process to operate as intended, what are the required partial pressure (pA) and mole fraction (yA) of ozone (O3) in the gas phase inside the tank? As part of your solution, develop a material balance model in algebraic form for solute A that contains the following terms: vo, volumetric flow rate of liquid (m3/hr); cAL,o, inlet concentration of solute A in liquid (gmole A/m3); cAL, outlet concentration of solute A in liquid (gmole O3/m3); KG, overall mass-transfer coefficient based on gas-phase driving force (gmole/m2 · s · atm), pA, partial pressure of O3 in bulk gas phase (atm); H, Henry’s law constant for O3 between gas and liquid (m3 · atm/gmole); S, surface area for interphase mass-transfer (m2).
e. What is the total transfer rate of O3, WA?
f. Is the mass-transfer process is gas film controlling, liquid film controlling, or neither? Comment on the relative contributions of the film mass-transfer coefficients and the equilibrium distribution relationship on the controlling mass-transfer resistance.
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27.10 Jasmone (molecular formula C11H16O) is a valuable specialty chemical that is obtained from the jasmine plant. A common method of manufacture is to extract the plant material in water, and then use benzene to concentrate the jasmone in a simple liquid-liquid extraction process. Jasmone (species A) is 170 times more soluble in benzene than in water, and so...where ... is the concentration of jasmone in benzene, and cA is the concentration of jasmone in water. In a proposed extraction unit, the benzene phase is well mixed with the film mass-transfer coefficient ... = 3.5 × 10–6 m/s. The aqueous phase is also well mixed with its film mass-transfer coefficient kL = 2.5 × 10–5 m/s. Determine
a. The overall liquid mass-transfer coefficient, ..., based on the benzene phase
b. The overall liquid transfer coefficient, KL, based on the aqueous phase
c. The percent resistance to mass-transfer encountered in the aqueous liquid film
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27.11 Ammonia (NH3) in air is being absorbed into water within the enclosed tank shown in the figure (next page). The liquid and gas phases are both well mixed, and mass-transfer occurs only at the exposed gas–liquid interface. The diameter of the cylindrical tank is 4.0 m, and the total liquid volume inside the tank is constant. The bulk gas partial pressure of NH3 is maintained at 0.020 atm, and the total gas pressure is constant at 1.0 atm. The system is isothermal at 20 °C. The inlet volumetric flow rate of water is 200 L/h (0.20 m3/hr), and there is no NH3 in the inlet liquid stream (i.e., cAL,o = 0). You may assume that Henry’s law adequately describes the equilibrium distribution of NH3 between the gas and liquid phases, given by PA,i = H · cAL,i, where H = 0.020 m3 · atm/kgmole. The mass-transfer coefficients for the gas and liquid films are kG = 1.25 kgmole/m2 · hr · atm and kL = 0.05 kgmole/(m2 · hr · (kgmole/m3)), respectively....
a. Develop a material balance equation for NH3 (solute A). Then determine cAL, the concentration of dissolved NH3 in the outlet liquid stream. In material balances involving interphase mass-transfer, base the material balance on one phase. For this process, consider a material balance on NH3 based on the liquid phase.
b. Determine pA,i the partial pressure of NH3 at the gas–liquid interface, and cAL,i, the dissolved NH3 concentration at the liquid side of the gas–liquid interface.
c. Determine WA, the total rate of ammonia transfer.
d. In the above system, the flux NA would increase by increasing which of the following: the liquid volume level in the tank at fixed surface area; the agitation intensity of the bulk liquid; the agitation intensity of the bulk gas; the inlet liquid volumetric flow rate; the system temperature.
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