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King Saud University ChE 314 College of Engineering Tutorial # 1 Chemical Engineering Dept. 14/9/1428

Mass Transfer Operations Dr Anis Fakeeha, Eng. M Gaily

1. Methane and helium gas mixture is contained in a tube at 101.32 k Pa pressure and

298 K. At one point the partial pressure methane is pA1 = 61 k Pa and at a point 0.02 m distance away, pA2 = 21 k Pa. If the total pressure is constant through the tube, calculate the flux of methane at steady-state for equimolar counter diffusion.

2. Helium and nitrogen gas are contained in a conduit 6 mm in diameter and 0.1 m long

at 298 K and a uniform constant pressure of 1.0 atm abs. The partial pressure of He at point one of the tube is 0.06 atm. and 0.02 atm at the other end (point two). Calculate the following for steady-state equimolar counter diffusion.

a. Flux of He in kg mol/s. m2. b. Flux of N2. c. Rate of He in kg mol/s. d. Partial pressure of He at a point 0.03 m from point one.


Mass Transfer Operations

Dr Anis Fakeeha, Eng. M Gaily

1. Ammonia gas is diffusing through N2 under steady-state conditions with N2

nondiffusing. The total pressure is 1.0132 x 105 Pa and the temperature is 298 K. The partial pressure of NH3 at one point is 1.333 x 104 Pa and at the other point 25 mm away it is 6.666 x 103 Pa. The DAB for the mixture at 1.013 x 105 Pa and 298 K is 2.3 x 10-5 m2/s.

a. Calculate the flux of NH3 in kg mol/s.m2. b. Do the same as (a) but assume that N2 also diffuses; i.e. the flux is eqimolar

counter diffusion. In which case the flux greater?

2. Methane gas is diffusing in a straight tube 0.15 m long containing helium at 298 K and a total pressure of 1.01325 x 105 Pa. The concentration of CH4 at one end is 15.816 mole % and 1.516 mole % at the other end. Helium is insoluble in one boundary, and hence is nondiffusing or stagnant. Calculate the flux of methane in kg mole/s. m2 at steady-state.

3. Oxygen (A) is diffusing through carbon monoxide (B) under steady-state conditions,

with CO nondiffusing. The total pressure is 1 x 105 N/m2, and the temperature 0 ºC. The partial pressure of oxygen at two planes 2.0 mm apart is, respectively 13000 and 6500 N/m2. The diffusivity for the mixture is 1.87 x 10-5 m2/s. Calculate the rate of diffusion of oxygen in kgmol/s through each square meter of the two planes.




1. The gas CO2 is diffusing at steady-state through a tube 0.2 m long having a diameter

of 0.01 m and containing N2 at 298 K. The total pressure is constant at 101.32 kPa . The partial pressure of CO2 at one end is 456 mm Hg and 76 mm Hg at the other end. The diffusivity DAB is 1.67 x 10-5 m2/s at 298 K. Calculate the flux of CO2 for equimolar counterdiffusion.

2. For a mixture of ethanol vapor and methane, predict the diffusivity using the method

of Fuller et al.

a. At 1.0132 x 105 Pa and 298 and 373 K. b. At 2.0265 x 105 Pa and 298 K.

3. Determine the mass transfer for the conical section shown in Fig. (1) below. The concentration of CO2 in air is 30 mole % at the 10 cm opening, and 3 mole % at the 5 cm opening. For this mixture, the diffusion coefficient is 0.164 cm2/s. The gas is at 1 atm and 25 ºC (298.15 K) everywhere. The section is 30 cm thick.

x 10 cm 5 cm

30 % CO2 3 % CO2

Fig. (1): A conical section for mass transfer




1. For a mixture of ethanol vapor and methane, predict the diffusivity using the method

of Fuller et al.

a. At 1.0132 x 105 Pa and 298 and 373 K. b. At 2.0265 x 105 Pa and 298 K.

2. The diffusivity of dilute methanol in water has been determined experimentally to be

1.26 x 10-9 m2/s at 288 K.

a. Estimate the diffusivity at 293 K using the Wilke-Chang equation. b. Estimate the diffusivity at 293 K by correcting the experimental value at 288 K

to 293 K. (Hint: Do this by using the relationship DAB ∞T/µ. 3. Equimolarcounter diffusion is occurring at steady-state in a tube 0.11 m long

containing N2 and CO gases at a total pressure of 1 atm abs. The partial pressure of N2 is 80 mm Hg at one end and 10 mm at the other end. Predict the DAB by the method of Fuller et al.

a. Calculate the flux in kg mol/s m2 at 298 K for N2. b. Repeat at 473 K. does the flux increase? c. Repeat at 298 K but for a total pressure of 3.0 atm abs. The partial pressure of

N2 remains at 80 and 10 mm Hg, as in part (a). Does the flux change? 4. It is desired to predict the diffusion coefficient of dilute acetic acid (CH3COOH) in

water at 282.9 K and at 298 K using the Wilke-Change method. Compare the predicted values with the experimental values in Table 6.3-1.




1. Mass transfer is occurring from a sphere of naphthalene having a radius of 10 mm.

The sphere is in a large volume of still of air at 52.6 ºC and 1 atm. Abs . The vapor pressure of the naphthalene at 52.6 ºC is 1.0 mm Hg. The diffusivity of the naphthalene in air at 0º is 5.16 x 10-6 m2/s. Calculate the rate of evaporation of naphthalene from the surface in kg mol/s. m2. [D is proportional to T1.75]

2. The solute HCl (A) is diffusing through a film of water (B) 1.5 mm thick at 283 K.

The concentration of HCl at point 1 at one boundary of the film is 14.0 wt % HCl (desity, ρ1 = 11060.7 kg/m3), and at the other boundary at point 2 it is 7.0 wt % HCl (ρ2 = 1030.3 kg/m3). The diffusion coefficient of HCl in water is 2.5 x 10–9 m2/s. Assuming steady-state at one boundary impermeable to water, calculate the flux of HCl in kg mol/s.m2.

3. A flat plug 30 mm thick having an area of 4 x 10-4 m2 and made of vulcanized rubber

is used for closing an opening in a container. The gas CO2 at 25 ºC and 2 atm pressure is inside the container. Calculate the total leakage or diffusion of CO2 through the plug to the outside in kg mol CO2/s at steady-state. Assume that the partial pressure of CO2 outside is zero. The solubility of the CO2 gas is 0.9 m3 gas (at STP of 0 ºC and 1 atm.) per m3 rubber per atm pressure of CO2. The diffusivity is 0.11 x 10-9 m/s.




1. The gas hydrogen is diffusing through a sheet of vulcanized rubber 20 mm thick at 25

ºC. The partial pressure of H2 inside is 1.5 atm and 0 outside. Using the data from table 6.5-1, calculate the following.

a. the diffusivity DAB from the permeability PM and solubility S and compare

with the value in Table 6.5-1. b. The flux NA of H at steady-state.

2. Nitrogen gas at 2 atm and 30 ºC is diffusing through a membrane of nylon 2.0 mm

thick and polyethylene 7.0 mm thick in series. The partial pressure at the other side of the two films is 0 atm. Assuming no other resistances, calculate the flux NA at steady-state.

3. It is desired to calculate the rate of diffusion of CO2 gas in air at steady-state through a

loosely packed-bed of sand at 276 K and a total pressure of 1.013x105 Pa. The bed depth is 1.3 m and the void fraction ε is 0.35. the partial pressure of CO2 at the top of the bed is 2.026 x 103 Pa and 0 Pa at the bottom. Use τ of 1.87.

4. A mixture of He (A) and Ar (B) is diffusing at 1.013 x 105 Pa total pressure and 298 K

through a capillary having a radius of 100Ǻ. a. Calculate the Knudsen diffusivity of He (A). b. Calculate the Knudsen diffusivity of Ar (B).

5. A mixture of He (A) and Ar (B) at 298 K is diffusing through an open capillary 15

mm with a radius 1000 Å. The total pressure is 1.013 x 105 Pa. The molecular diffusivity DAB at 1.013 x 105 Pa is 7.29 x 10-5 m2/s.

c. Calculate the Knudsen diffusivity of He (A). d. Predict the flux NA using equation (7.6-18) and Equation (7.6-12) if xA1 =0.8

and xA2 = 0.2. Assume steady state. e. Predict the flux NA using the approximate equations (7.6-14) and (7.6-16).




1. A value of kG was experimentally determined to be 1.08 lbmol/h.ft2.atm for A

diffusing through stagnant B. For the same flow and concentrations it is desired to predict k`G and the flux of A for equimolar counter diffusion. The partial pressures are pA1 = 0.2 atm, pA2 = 0.05 atm, and P = 1.0 atm abs total. Use English and SI units.

2. In a wetted-wall tower an air- H2S mixture is flowing by a film of water which is

flowing as a thin film down a vertical tube. The H2S is being absorbed from the air to the water at a total pressure of 1.5 atm abs and 30 ºC. The value of k`c of 9.567 x 10-4 m/s has been predicted for the-gas phase-mass transfer coefficient. At a given point the mole fraction of H2S in the liquid at the liquid gas interface is 2 x 10-5 and pA (atm) = 609 xA (mole fraction liquid). Calculate the rate of absorption of H2S. [Hint: Call point 1 the interface and point 2 the gas phase. Then calculate pA1 from Henry’s law and the given xA. The value of pA2 is 0.05 atm].

3. It is desired to estimate the mass transfer coefficient kG in kg mol/s. m2.Pa for water

vapor in air at 338.6 K and 101.32 kPa flowing in a large duct past different geometry solids. The velocity in the duct is 3.66 m/s. The water vapor concentration in the air is small, so the physical properties of air can be used. Water vapor is being transferred to the solids. Do this for the following geometries:

a. A single 25.4 mm diameter sphere. b. A packed bed of 25.4 mm spheres with ε = 0.35




2. Pure water at 26.1 ºC is flowing at a velocity of 0.0305 m/s in a tube having an inside

diameter of 6.35 mm. The tube is 1.829 m long with the last 1.22 m having walls coated with benzoic acid. Assuming that the velocity profile is fully developed, calculate the average concentration of benzoic acid at the solute. [Hint: first calculate the Reynolds number. Then calculate NRe NSc (D/L)(π/4), which is the same as W/DAB.ρL] Useful data:

CAi = 0.02948 kgmole/m3 (Solubility)

3. A tube is coated on the inside with naphthalene and has an inside diameter of 20 mm

and a length of 1.1 m. Air at 318 K and an average pressure of 101.3 kPa flows through this pipe at a velocity of 13 m/s. Assuming that the absolute pressure remains constant, calculate the mass transfer coefficient of the naphthalene (KC). Calculate the exit concentration CA2 of naphthalene in leaving air.

Data:

a. DAB = 6.92 X 10-6 m/s b. Vapor pressure of naphthalene @ 318 K = 70 Pa c. Hint: Flux = KC (∆CM). ∆CM = log mean concentration difference.

4. Mercury at 26.5 ºC is flowing through a packed bed of lead spheres having a diameter

of 2.096 mm with a void fraction of 0.499.The superficial velocity is 0.02198 m/s. The solubility of lead in mercury is 1.721 wt %, the Schmidt number is 124.1, the viscosity of the solution is 1.577 x 10-3 Pa.s, and the density is 13530 kg/m3.

a. Predict the value of JD. Use Eq. (7.3-38) if applicable. Compare with the experimental of JD = 0.076.

b. Predict the value of kc for the case A diffusing through non diffusing B.




1. A thin plate of solid salt, NaCl, measuring 6 in. by 6 in., is to be dragged through

seawater (edgewise) at a velocity of 2 ft/s. The 64 ºF seawater has a salt concentration of 0.039 g/cm3; if saturated, the seawater would have a concentration of 35 g/cm3. The kinematic viscosity of seawater is approximately 1.1 x10-5 ft2/s. Estimate the rate at which the salt goes into solution if the edge effects can be ignored.

2. Air at 100 ºF and 1 atm flows over a naphthalene ball. Since naphthalene exerts a

vapor pressure of 5 mm Hg at 100 ºF, it will sublime into the passing air stream, which has a negligibily small concentration of naphthalene in the bulk airstream. If a ¾ -in. naphthalene ball is suspended into a 5 ft/s airstrem, where the physical properties at the film temperature are:

mass diffusivity = 0.37 ft2/hr kinematic viscosity of air = 0.651 ft2/hr

Determine: a. The mass transfer coefficient. b. The molar flux of naphthalene into the airstream.

3. Air passes through a naphthalene tube that has an inside diameter of 2.5 cm, flowing

at a bulk velocity of 15 m/s. The air is at 283 K and an average pressure of 1.013 x 105 Pa. Assuming that the change in pressure along the tube is negligible and that the naphthalene surface is at 283 K, determine the length of tube that is necessary to produce a naphthalene concentrationin the exiting gas stream of 4.75 x 10 –4 mol/m3. At 283 K, naphthalene has a vapor pressure of 3 Pa and a diffusivity in air of 5.4x 10-6 m2/s.




1. The solute A is being absorbed from a gas mixture of A and B in a wetted-wall tower with the liquid flowing as a film downward along the wall. At a certain point in the tower the bulk gas concentration yAG = 0.38 mol fraction and the bulk liquid concentration is xAL = 0.10. The tower is operating at 298 K and 101.3 x 105 Pa and the equilibrium data are as follows:

xA 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 yA 0 0.022 0.052 0.087 0.131 0.187 0.265 0.385

The solute A diffuses through a stagnant B in the gas phase and then through a non-diffusing liquid. Using correlations for dilute solutions in wetted-wall towers, the film mass transfer coefficient for A in the gas phase is predicted as ky = 1.465 x 10-3 kg mol A/s.m2.mol frac. (1.08 lb mol/h. ft2. mol frac) and for the liquid phase as kx = 1.967 x 10-3 kg mol A/s. mol frac (1.45 lb mol/h. ft2. mol frac.). Calculate the interface concentrations yAi and xAi and the flux NA.

2. Using the same data as in (1), calculate the overall mass-transfer coefficient K`x and

Kx, the flux, and the percent resistance in the gas film.

3. Use the same equilibrium data and film coefficients k`y and k`x as in (1). However use bulk concentration of yAG = 0.25 and xAL = 0.05. Calculate the following:

a. Interface concentrations yAi and xAi and flux NA. b. Overall mass-transfer coefficients K`y and Ky and flux NA. c. Overall mass-transfer coefficients K`x and flux NA.

King Saud University ChE 314 College of Engineering Tutorial 11 Chemical Engineering Dept. 30/12/1428



1. In an experimental study of the absorption of NH3 by water in a wetted-wall column, the value of KG was found to be 0.205 lb mole NH3/h ft2 atm. At one point in the column, the gas contained 8 mole % NH3 and the liquid phase concentration was 0.004 mole of NH3 per ft3 of solution. The temperature was 68 ºF, and the total pressure was one atmosphere. 85% of the total resistance to the mass transfer was found to be in the gas phase. If Henry`s constant at 68 ºF is 0.215 atm/(lb mole NH3/ft3 of solution), calculate the individual film coefficients and the interfacial compositions.

2. In the absorption of component A from an air stream into an aqueous stream, the bulk

composition of the two adjacient streams were analyzed to be pA,G = 0.1 atm and cA,L = 0.25 lb mole/ft3. The Henry`s constant for this system is 0.265 atm/(lb mole A/ft3 of solution). The overall gas coefficient, KG = 0.055 lb mole A/(h ft2 atm). If 57 % of the total resistance of mass transfer is encountered in the gas film, determine

a. The mass flux of A. b. The concentration on the liquid side of the interface cA,i. c. The gas-film coefficient kG. d. The liquid-film coefficient, kL.

King Saud University ChE 314 College of Engineering Tutorial 12 Chemical Engineering Dept. 7/1/1429



1. Calculate the diameter of an absorption column that packed with ceramic Rashing

rings 25 mm in size to treat 1000 m3/h of a gas mixture by absorbing liquid. For special circumstances in this absorption operation the ratio of liquid to gas flow is not to exceed the double and the column operates at 75% of the flooding rate. Liquid density ρL = 1000kg/m3 and has a viscosity of 0.001 Pa.s. The average gas density ρG = 1.0 kg/m3 and the packing coefficient FP for the ceramic Rashing rings 25mm in size is 525/m.

2. Water is used to absorb SO2 from air flowing in a packed column. The following data

were recorded during the actual operation of the column. Water enters the column at the top free of SO2 at a rate of 4 kmoles/s. The gas mixture enters at the bottoms with a concentration of 2% mol SO2 and a rate of 0.08 kmoles/s and leaves the column at the top containing 0.5 %mol SO2. The column cross-sectional area is 1.0 m2 and the height of the packing material in the column is 5 m. The operation is at 1 atm and 25 ºC. Equilibrium relationship between the liquid phase and the gas phase at the column operating conditions is given by:

yi = 40 xi From the above data, calculate the overall mass transfer capacity coefficient for the gas phase, Ky a

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