Last Part of the Course

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Filtration, Membrane Separations, Chromatography & Electrophoresis

2nd Part of the Course

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1st Part of the Course

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HW 9 - SP1 - Gel Permeation Chromatography of Urease - 3 pts

We plan a large scale purification of urease using a packed column of polyacrylamide beads. We obtain the following data.
Volume Eluted (L) , Concentration (arbitrary units)
174 L , 0.0063
190 L , 0.0152 (peak)

The bed volume is 20 L. Determine V0, sigma and the yield at 190 L and at 200 L

HW 9 - SP2 - Affinity Chromatography to Purify an Antibody - 5 pts

We need to purify an antibody which is to used as an affinity adsorbent in the production of a synthetic vaccine. The feed contains 1.63 g antibody and 0.45 g of a protein of similar molecular weight. We use gel permeation chromatography to obtain the following results.
Time(h), Antibody Concentration y1, Impurity Concentration y2
6.42 , 82 , ~ 0
7.00 , 63 , 0.14
7.60 , 28 , 43 (peak)

a.) Use these reults to plot the antibody and impurity yields as functions of time on the same graph.
b.) Plot the purity as a fuction of time.

HW 9 - SP3 - Discrete Stage Analysis of a Chromatographic Column - 5 pts

Ten grams of bovine serum albumin (BSA) is eluted from an 80 L Sephadex column which has a void fraction of 0.40. The concentration in the column peaks after 470 L have been eluted. The maximum concentration, y0, is 1.8% of the concentration in the sample that was injected.

a.) Estimate the equilibrium constant for binding the albumin to Sephadex
b.) Estimate the number of stages in the column
c.) Plot the elution chromatograph for this process. (y/y0 as a function of time)

HW 9 - SP4 - Kinetic Analysis of a Chromatographic Column - 6 pts

Racemic amino acids can be separated using l-proline attached with silanes to the surface of silica gel. In one set of experiments, aspartame isomers gave the following results.

d-aspartame: t0 = 62 min , σt0 = 3 min
l-aspartame: t0 = 71 min , σt0 = 6 min

These results were obtained with a 25 cm column, 0.41 cm in diameter, filled with 45 μm silica gel spheres. The void fraction of the bed was 0.62. The flow in the column was 2.0 mL/min. Find the apparent rate constants for this separation. Compare these rate constants with those predicted from the following mass transfer correlation.

mass transfer correlation



where: d = packing particle diameter, v = superficial solvent velocity, ν = solution kinematic viscosity, D = diffusion coefficient of the solute (7.0 x 10^-6 cm2/s).

HW 9 - SP5 - Scaling Up a Chromatographic Separation of Fumarase - 5 pts

Ten grams of the enzyme fumerase are being purified in an ion exchange chromatography column. At a superficial velocity of 30 cm/h, the peak exits the column in 93 min and the standard deviation of the peak is σt0 = 12 min.

a.) How long must we purify to obtain a 90% yield ?
b.) If we increase the flow to 60 cm/h, how long must we run to obtain the same 90% yield if the process is controlled by diffusion within the packing particles ?
c.) How long must we wait if the process is controlled by external mass transfer ?
d.) How long must we wait if Taylor Dispersion controls the rate of the process ?
e.) How long must we wait if the column actually contains equilibrium stages ?

HW 9 - SP6 - Approximate Analysis of an Elution Chromatograph - 6 pts

Three proteins, A, B and C, are eluted through a pilot plant chromatographic column. The outlet concentration as a function of time was determined using an ultraviolet spectrophotometer. The results appear in the graph shown below.



a.) Estimate y0, t0 and σt0 for each species.
b.) Determine the yield and purity of species B in a fraction collected between t = 30 min and t = 40 min.
c.) What is the concentration of species B in this fraction ?
Elution Chromatograph

HW 9 - SP7 - Electrophoresis of BSA and Human Hemoglobin - 5 pts

A sample of bovine serum albumin (BSA) in solution was placed in a small electrophoretic cell. A laser anemometer measured its velocity as -1.4 x 10-3 cm/sec under the influence of an electric field of 10 V/cm. This experiment was repeated with a sample of human hemoglobin in solution and a velocity of -7.7 x 10-4 cm/sec was observed. Both samples were at 20oC.

a.) How much time is required to separate a mixture of BSA and human hemoglobin by gel electrophoresis ? An electric field of 4 V/cm is used and the initial band width of the mixture is 3 mm. Neglect diffusion. Assume the electrophoretic mobility of the proteins is unaffected by the presence of the gel.

b.) A Rayleigh light scattering experiment yields the diffusion coefficients of macromolecules. This experiment at 20oC yields the following results.

Do20,w (cm2/sec)
Bovine Serum Albumin
6.15 x 10-7
Human Hemoglobin
6.90 x 10-7

What is the charge number, z, of a molecule of BSA ? Human hemoglobin ?

Data: R = 8.314 g-cm2 / sec2-mole-K and F = 96487 coul/equiv

HW 8 - SP1 - Filtration of a Beer Containing Protease - 4 pts

A suspension of Bacillus subtilis has been fermented to produce the enzyme protease. In order to separate the biomass, we added 1.3 times the biomass of a Celatom filter aid, yielding a beer containing 3.6 wt% solids with a viscosity of 6.6 cP. With a Buchner funnel 5 cm in diameter attached to an aspirator, we have found that we can filter 100 mL of this beer in 24 minutes with a pressure drop of 14.7 psi. However, previous studies with this type of beer have had a compressible cake with s = 2/3.

We now need to filter 3000 L of this beer in a plate-and-frame filter press. The press has 15 frames, each with an area of 3520 cm2 on each side. The resistance of the filter medium is much smaller than the resistance of the filter cake.

a.) How long will take to filter the beer at 50 psig ?
b.) How long will it take at 25 psig ?

HW 8 - 14.3 - Separation of N2 from CH4 Using an Assymetric Polyimide Membrane - 6 pts

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HW 8 - 14.15- Desalinization of an Aqueous Solution by Electrodialysis - 5 pts

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HW 8 - 14.20 - Separation of Air by Gas Permeation - 10 pts

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HW 8 - 14.23 - Calculating Permeance from Pervaporation Data - 5 pts

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HW 8 - 14.24 - Separation of Benzene from Cyclohexane by Pervaporation - 2 pts

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HW 8 - SP2 - Estimating the Time Required for Vaccine Ultrafiltration - 5 pts

We want to filter 840 L of a solution containing 0.061 wt% of a protein used as a vaccine for herpes. This protein has a MW of 16,900 and a diffusivity of 1.1 x 10-6 cm2/sec. We want to raise the concentration to 2.0 wt%. The ultrafilter we hope to use has eight hollow fiber cartridges., each of which has a surface area of 1.2 m2. The solution is chilled to 4oC. When a pressure drop of 31 atm is used, the membrane in the cartridges gives an initial volume flux of 5.7 x 10-5 cm/s (that is just over 1 gal/ft2/day). Assume the density of the solution is essentially the same as that of water (1000 g/L). Also, assume that the boundary layer is 0.01 cm thick.

a.) Assuming that concentration polarization is negligible, estimate the timerquired to filter the entire solution using all eight cartridges in paralel.
b.) Test whether concentration polarization is significant.

MT Test #2, 11/22 @ 10:30 in Johnson 075.

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Best of luck on the test !

HW 7 - p 8.1 - LLE vs. Distillation for Recovery of Dilute Benzoic Acid - 2 pts

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HW 7 - p 8.7 - Solvent Selection for LLE - 3 pts

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HW 7 - p 8.11 - LLE of Acetone from Water Using TCE - 9 pts

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HW 7 - p 8.18 - TMW Extraction with Multiple Solvent Streams - 9 pts

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HW 7 - p 9.6 - Distillation of an Acetone-Water Mixture: Fenske vs. McCabe Thiele - 10 pts

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HW 7 - p 9.18 - Distillation of Chlorination Reactor Effluent : Fenske-Underwood (class 2)-Gilliland - 10 pts

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HW 7 - p 13.1 - Rayleigh Distillation of nC7 in Toluene - 8 pts

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HW 7 - p 13.11 - Batch Rectification of an Equimolar Mixture of Benzene and Toluene at Constant Reflux - 6 pts

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Mass Transfer Test #1

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HW 6 - p 7.11 - McCabe - Thiele Analysis of Benzene-Toluene Distillation - 12 pts

A saturated-liquid mixture containing 70 mol% benzene and 30 mol% toluene is to be distilled at atmospheric pressure to produce a distillate of 80 mol% benzene. Calculate and tabulate:
(a) Moles of distillate per 100 moles of feed,
(b) Moles of total vapor generated per mole of distillate,
(c) Mole percent benzene in residue, and
(d) For each part, construct a x-y diagram. On this indicate the compositions of the overhead product, the reflux, and the composition of the residue.
(e) If the objective is to maximize total benzene recovery, which, if any, of these procedures is preferred?
Note: relative volatility equals 2.5.

HW 6 - p 7.27 - Distillation of CS2 and CCl4 in a Tray Column with EMV = 80% - 10 pts

A mixture of 40 mol% carbon disulfide (CS2) in carbon tetrachloride (CCl4) is continuously distilled. The feed is 50% vaporized (q = 0.5). The top product from a total condenser is 95 mol% CS2, and the bottoms product from a partial reboiler is a liquid of 5 mol% CS2.

The column operated with a reflux ratio, L/D, of 4 to 1. The Murphree vapor efficiency is 80%.
(a) Calculate graphically the minimum reflux, the minimum boilup ratio from the reboiler, V/B, and the minimum number of stages (including reboiler).
(b) How many trays are required for the actual column at 80% efficiency by the McCabe-Thiele method?

HW 6 - p 7.42 - Calculation of Column Efficiency and EMV from EOV- 4 pts

For the conditions of exercise 7.41, a laboratory Oldershaw column measures an average Murphree vapor-point efficiency of 65%. Estimate EMV and Eo.

HW 6 - p 7.50 - Determination of HETP from Experimental Data - 7 pts

A mixture of benzene and dichloroethane is used to test the efficiency of a packed column that contains 10 ft of packing and operates adiabatically at atmospheric pressure. The liquid is charged to the reboiler, and the column is operated at total reflux until equilibrium is established. At equilibrium, liquid samples from the distillate and reboiler, as analyzed by refractive index, give the following compositions for benzene: xD = 0.653, xB = 0.298.
Give the value of HETP in inches for this packing. What are the limitations on using this calculated value for design?

HW 6 - p 7.51 - Design of a Packed Distillation Column to Separate an Ethanol-Water Mixture- 8 pts

Consider a distillation column for separating ethanol from water at 1atm. The following specifications are set:
Feed: 10 mol% ethanol (bubble-point liquid)
Bottoms: 1 mol% ethanol
Distillate: 80 mol% ethanol (saturated liquid)
Reflux Ratio: 1.5 times the minimum
Constant molar overflow may be assumed and vapor-liquid equilibrium data are given in Exercise 7.29.
(a) How many theoretical plates are required above and below the feed if a plate column is used?
(b) How many transfer units are required above and below the feed if a packed column is used?
(c) Assuming that the plate efficiency is approximately 80% and the plate spacing is 18 in., how high is the plate column.
(d) Using an HOG value of 1.2 ft., how high is the packed column?
(e) Assuming that you had HTU data available only on the benzene-toluene system, how would you go about applying the data to obtain HTU for the ethanol-water system?

HW 5 - p 6.8 - Graphical Analysis of the Absorption of Acetone in a Tray Tower - 7 pts

95% of the acetone in an 85 vol% air stream is to be absorbed by countercurrent contact with pure water in a valve-tray column with an expected overall tray efficiency of 50%. The column will operate essentially at 20oC and 101 kPa pressure.

Calculate:
a) The minimum value of L’/V’, the ratio of moles of water per mole of air.
b) The number of equilibrium stages required using a value of L’/V’ of 1.25 times the minimum.
c) The concentration of acetone in the exit water.

Feed flow rate can be taken to be 100kmol/h.

HW 5 - p 6.10 - Graphical Analysis of Steam Stripping Benzene from Straw Oil in a Tray Tower - 7 pts

A straw oil used to absorb benzene from coke-oven gas is to be steam stripped in a sieve-plate column at atmospheric pressure to recover the dissolved benzene. Equilibrium conditions at the operating temperature are approximated by Henry’s law such that, when the oil phase contains 10 mol% C6H6, the C6H6 partial pressure above the oil is 5.07 kPa. The oil may be considered non-volatile. The oil enters containing 8 mol% benzene, 75% of which is to be recovered. The steam leaving contains 3 mol% C6H6. (a) How many theoretical stages are required? (b) How many moles of steam are required per 100 mol of oil-benzene mixture? (c) If 85% of the benzene is to be recovered with the same oil and steam rates, how many theoretical stages are required?

HW 5 - p 6.14 - Absorption of a Hydrocarbon Mixture in n-Decane - 6 pts

1,000 kilomoles per hour of rich gas at 70oF with 25% C1, 15% C2, 25% C3, 20% nC4 and 15% nC5 by moles is to be absorbed by 500 kmol/h of nC10 at 90oF in an absorber operating at 4 atm. Calculate by the Kremser method the percent absorption of each component for 4, 10 and 30 theoretical stages. What do you conclude from the results?

HW 5 - p 6.16 - Absorption of C1 and C2 from H2 Fuel Gas Using Oil- 9 pts

Several hydrogenation processes are being considered that will require hydrogen of 95% purity. A refinery stream of 800,000 scfm(at 32oC and 1 atm), currently being used for fuel and containing 72.5 mol% H2, 25 mol% CH4 and 2.5 mol% C2H6 is available. To convert this gas to the required purity, oil absorption, activated charcoal adsorption and membrane separation are being considered. For oil absorption, an available n-octane stream can be used as the absorbent. Because the 95% H2 must be delivered to a hydrogenation process at not less than 375 psia, it is proposed to operate the absorber at 400 psia and 100 oF. If at least 80% of the H2 fed to the absorber is the leave in the exit gas, determine:
(a) The minimum absorbent rate in gallons per minute.
(b) The actual absorbent rate if 1.5 times the minimum amount is used.
(c) The number of theoretical stages.
(d) The stage efficiency for each of the three species in the feed gas, using O’Connell correlation.
(e) The number of trays actually required.
(f) The composition of the exit gas, taking into account the stripping of octane.
(g) If the octane lost to the exit gas is not recovered, estimate the annual cost of this lost oil if the process operates 7,900 h/year and the octane is valued at $1.00/gal.

HW 5 - p 6.25 - Scrubbing an SO2-Air Mixture with Water in a Packed Tower- 8 pts

An SO2-air mixture is being scrubbed with water in a countercurrent flow packed tower operating at 20oC and 1 atm. Solute-free water enters the top of the tower at a constant rate of 1,000 lb/h and is well-distributed over the packing. The liquor leaving contains 0.6 lb SO2/100 lbs of solute-free water. The partial pressure of SO2 in the spent gas leaving the top of the tower is 23 torr. The mole ratio of water to air is 25. The necessary equilibrium data are given.
(a) What percent of the SO2 in the entering gases is absorbed in the tower?
(b) In operating the tower it was found that the rate coefficients kp and kL remained substantially constant throughout the tower at the following values:
kL = 1.3 ft/h
kp = 0.195 lbmol/h-ft2-atm
At a point in the tower where the liquid concentration is 0.001 lbmol SO2 per lbmol of water, what is the liquid concentration at the gas-liquid interface in lbmol/ft3?

HW 5 - p 6.30 - Scrubbing an NH3-Air Mixture with Water in a Packed Tower- 8 pts

A 2 mol% NH3-in-air mixture at 68oF and 1 atm is to be scrubbed with water in a tower packed with 1.5 in. ceramic Berl saddles. The inlet water mass velocity will be 2400 lb/h-ft2, and the inlet gas mass velocity 240 lb/h-ft2. Assume that the tower temperature remains constant at 68oF, at which the gas solubility relationship follows Henry’s law, p = Hx. HNH3 is 2.7 atm/mol fraction.
(a) Calculate the required packed height for absorption of 90% of the NH3.
(b) Calculate the minimum water mass velocity in lb/h-ft2 for absorbing 98% of the NH3.
(c) What changes are caused by using Hiflow rings in KGa, pressure drop, maximum liquid rate, KLa, column height, column diameter, HOG and NOG?

HW 5 - p 6.35 - Scrubbing a Concentrated Cl2-Air Mixture with Water in a Packed Tower- 8 pts

Exit gas from a chlorinator consists of a mixture of 20 mol% chlorine in air. This concentration is to be reduced to 1% chlorine by water absorption in a packed column to operate isothermally at 20oC and atmospheric pressure. Calculate for 100 kmol/h feed gas.
(a) The minimum flow rate in kilograms per hour.
(b) NOG for twice the minimum flowrate.

HW 4 - p 5.6 - Countercurrent Washing of Al2(SO4)3 from Processed Bauxite Ore - 6 pts

Aluminum sulfate, commonly called alum, is produced as a concentrated aqueous solution from bauxite ore by reaction with aqueous sulfuric acid, followed by a three-stage, countercurrent washing operation to separate soluble aluminum sulfate from the insoluble content of the bauxite ore, followed by evaporation. In a typical process, 40,000 kg/day of solid bauxite ore containing 50 wt% Al2O3 and 50% inert is crushed and fed together with the stoichiometric amount of 50 wt% aqueous sulfuric acid to a reactor, where the Al2O3 is reacted completely to alum by the reaction

Al2O3 + 3H2SO4  Al2(SO4)3 + 3H2O

The slurry effluent from the reactor, consisting of solid inert material from the ore and an aqueous solution of aluminum sulfate is then fed to a three-stage, countercurrent washing unit to separate the aqueous aluminum sulfate from the inert material. If the solvent is 240,000 kg/day of water and the underflow from each washing stage is 50 wt% water on a solute-free basis, compute the flow rates in kilograms per day of aluminum sulfate, water, and inert solid in each of the two product streams leaving the cascade. What is the percent recovery of the aluminum sulfate? Would the addition of one more stage be worthwhile?

HW 4 - p 5.10 - Multistage Extraction of Uranyl Nitrate - 5 pts

The uranyl nitrate (UN) in 2 kg of a 20 wt% aqueous solution is to be extracted with 500 g of tributyl phosphate. Using the equilibrium data in Exercise 5.9, calculate and compare the percentage recoveries for the following alternative procedures:
(a) A single stage batch extraction
(b) Three batch extractions with one-third of the total solvent used in each batch
(c) A two-stage cocurrent extraction
(d) A three-stage countercurrent extraction
(e) An infinite-stage countercurrent extraction
(f) An infinite-stage crosscurrent extraction

HW 4 - p 5.18 - Absorption of Light Hydrocarbons in n-Hexane - 6 pts

One million pound-moles per day of a gas of the following composition is to be absorbed by n-heptane at -30oF and 550 psia in an absorber having ten theoretical stages so as to absorb 50% of the ethane. Calculate the required flow rate of absorbent and the distribution, in lbmol/h, of all the components between the exiting gas and liquid streams.

HW 4 - p 5.24 - Distillation Calculations Using the Edmister Group Method - 9 pts

A bubble-point liquid feed is to be distilled as shown in Figure 5.25. Use the Edmister group method to estimate the mole-fraction compositions of the distillate and bottoms. Assume initial overhead and bottoms temperatures are 150 and 250oF, respectively.

HW 4 - p 5.29 - Degree of Freedom Analysis on an Equilibrium Stage - 4 pts

Verify ND for unit operations (e) and (f) in Table 5.4. How would ND change if a vapor side stream was pulled off some stage located between the feed stage and the bottom stage?

HW 4 - p 5.38 - Degree of Freedom Analysis on a Distillation Process with Volatile Impurities - 3 pts

When the feed to a distillation column contains a small amount of impurities that are much more volatile then the desired distillate, it is possible to separate the volatile impurities from the distillate by removing the distillate as a liquid substream from a stage located several stages below the top stage. As shown in Figure 5.30, this additional top section of stages is referred to as a pasteurizing section.
(a) Determine the number of degrees of freedom for the unit.
(b) Determine a reasonable set of design variables.

HW 3 - p 4.3 - Degree of Freedom Analysis of an Adiabatic Flash - 3 pts

Consider an adiabatic equilibrium flash. The variables are all indicated in Figure 4.36.
(a) Determine the number of variables.
(b) Write all the independent equations that relate the variables.
(c) Determine the number of equations.
(d) Determine the degrees of freedom.
(e) What variables would you prefer to specify in order to solve a typical adiabatic flash problem?

HW 3 - p 4.15- VLE, K-values, a and the q-line from VLE Data - 4 pts

Vapor liquid equilibrium data for mixtures of water and isopropanol at 1 atm are given.
(a) Prepare T-x-y and x-y diagrams.
(b) When a solution containing 40 mol% isopropanol is slowly vaporized, what will be the composition of the initial vapor formed?
(c) If this same 40% mixture is heated under equilibrium conditions until 75 mol% has been vaporized, what will be the composition of the liquid and vapor produced?

HW 3 - p 4.23 - VLE for Hydrocarbons Using K-Values - 5 pts

An equimolar mixture of ethane, propane, n-butane, and n-pentane is subjected to a flash vaporization at 150 oF and 205 psia. What are the expected amounts and compositions of the liquid and vapor products? Is it possible to recover 70% of the ethane in the vapor by a single-stage flash at other conditions without losing more than 5% of nC4 to the vapor?

HW 3 - p 4.35 - Bubble Pt, Dew Pt and Azeotrope of Ethanol-Ethyl Acetate Mixtures - 7 pts

(a) For a liquid solution having a molar composition of ethyl acetate (A) of 80% and ethyl alcohol (E) of 20%, calculate the bubble-point temperature at 101.3 kPa and the composition of the corresponding vapor using (2-27) with vapor pressure data and the van Laar equation of Table 2.9 with AAE = 0.855, AEA = 0.753.
(b) Find the dew point of the mixture.
(c) Does the mixture from an azeotrope? If so, predict the temperature and composition.

HW 3 - p 4.46 - Analysis of Extraction Using a Ternary Phase Diagram- 6 pts

Forty-five kilograms of a solution containing 30wt% ethylene glycol in water is to be extracted with furfural. Using Figures 4,14a and 4,14e, calculate:
(a) The minimum quantity of solvent.
(b) The maximum quantity of solvent.
(c) The weights of solvent-free extract and raffinate for 45 kg solvent, and the percent glycol extracted.
(d) The maximum possible purity of glycol in the finished extract and the maximum purity of water in the raffinate for one equilibrium stage.

HW 3 - p 4.48 - Extraction of Acetic Acid from Water Using Chloroform as the Solvent- 5 pts

A mixture of chloroform and acetic acid at 18oC and 1 atm is to be extracted with water to recover the acid.
(a) Forty-five kilograms of a mixture containing 35 wt% CHCl3 and 65 wt% acid is treated with 22.75 kg of water at 18oC in a simple one stage batch extraction. What are the compositions and weights of the raffinate and extract layers produced?
(b) If the raffinate layer from the above treatment is extracted with one-half its weight of water, what will be the compositions and weights of the new layers?
(c) If all the water is removed from this final raffinate layer, what will its composition be?

HW 3 - p 4.52 - Leaching Oil from Soybeans Using Benzene as a Solvent - 4 pts

Repeat Example 4.9 for 200,000 kg/h of hexane.

HW 3 - p 4.55 - Crystallization from a Solution of Napthalene in Benzene- 3 pts

A total of 6,000 lb/h of a liquid solution of 40 wt% benzene in naphthalene at 50 oC is cooled to 15 oC. Assuming that equilibrium is achieved, use Figure 4.23 to determine the amount of crystals formed, and the flow rate and composition of the mother liquor. Are the crystals benzene or naphthalene?

HW 3 - p 4.64 - Absorption of Ammonia in Water- 8 pts

A vapor mixture having equal volumes of NH3 and N2 is to be contacted at 20 oC and 1 atm with water to absorb a portion of NH3. If 14 m3 of this mixture is brought into contact with 10 m3 of water and if equilibrium is attained, calculate the percent of the ammonia originally in the gas that will be absorbed. Both temperature and pressure will be maintained constant during absorption.

HW 3 - p 4.68 - Adsorption of Propane and Propylene on Silica Gel - 4 pts

A gas containing 50 mol% propylene in propane is to be separated with silica gel having the equilibrium properties shown in Figure 4.30. The final products are to be 90 mol% propylene and75 mol% propane. If 1,000 lb of silica gel/lbmol of feed gas or less is used, can the desired separation be made in one equilibrium stage? If not, what separation can be achieved?

HW 2 - p 3.28 - Evaporation of a Water Film on a Flat Plate - 5 pts

Air at 1 atm flows at 2 m/s across the surface of a 2-in.-long surface that is covered with a thin film of water. If the air and water are maintained at 25oC, and the diffusivity of water in air at these conditions is 0.25cm2/s, estimate the mass flux for the evaporation of water at the middle of the surface assuming laminar boundary-layer flow. Is this assumption reasonable?

HW 2 - p 3.30 - Dissolution of a Napthalene Tube in Laminar Flow- 7 pts

Air at 1 atm and 100oC flows through a straight, 5-cm-diameter circular tube, cast from naphthalene, at a Reynolds number of 1,500. Air entering the tube has an established laminar-flow velocity profile. Properties are given in Example 3.14. If pressure drop through the tube is negligible, calculate the length of a tube needed for the average mole fraction of naphthalene in the exiting air to be 0.005.

HW 2 - p 3.32 - Dissolution of a Benzoic Acid Tube in Turbulent Flow- 7 pts

Water at 25oC flows at 5ft/s through a straight, cylindrical tube cast from benzoic acid, of 2-in. inside diameter. If the tube is 10 ft long, and fully developed, turbulent flow is assumed, estimate the average concentration of benzoic acid in the water leaving the tube. Physical properties are given in Example 3.15.

HW 2 - p 3.36 - Absorption of CO2 into Water Using a Packed Column- 6 pts

Water is used to remove CO2 from air by absorption in a column packed with Pall rings. At a certain region of the column where the partial pressure of CO2 at the interface is 150 psia and the concentration in the bulk is negligible, the absorption rate is 0.017 lbmol/h-ft2. The diffusivity of CO2 in water is 2.0 x 10-5 cm2/s. Henry’s law for CO2 is p = Hx, where H = 9,000 psia. Calculate:
(a) The liquid-phase mass-transfer coefficient and the film thickness
(b) Contact time for penetration theory
(c) Average eddy residence time and the probability distribution for the surface-renewal theory.

HW 2 - p 3.40 - Overall Mass Transfer Coefficient for a Packed Tower- 6 pts

A new type of cooling-tower packing is being tested in a laboratory column. At two points in the column, 0.7 ft apart, the following data have been taken. Calculate the overall volumetric mass-transfer coefficient Kya that can be used to design a large, packed-bed cooling tower, where a is the mass-transfer area, A per unit volume, V, of tower.

Bottom Top
Water temperature, oF 120 126
Water vapor pressure, psia 1.69 1.995
Mole fraction H2O in air 0.001609 0.0882
Total pressure, psia 14.1 14.3
Air rate, lbmol/h 0.401 0.401
Column area, ft2 0.5 0.5
Water rate, lbmol/h 20 20

Welcome

Welcome to the Blog for ChemE 435 at the University of Washington.
This blog will help students solve mass transfer problems from the 2nd edition of Separation Process Principles by Seader & Henley.
I hope you find this helpful and convenient.
Dr. B

HW 1 - p 3.4 - Evaporation of Water into Air by Unimolecular Diffusion - 5 pts

Air at 25 oC with a dew point of 0 oC flows past the open end of a vertical tube filled with liquid water maintained at 25 oC. The tube has an inner diameter of 0.83 in., and the liquid level was originally 0.5 in. below the top of the tube. The diffusivity of water in air at 0oC is 0.256 cm^2/s.

HW 1 - p 3.5 - Mixing of Argon and Xenon by Equimolar Counter Diffusion - 5 pts

Two bulbs are connected by a tube, 0.002 m in diameter and 0.20 m in length. Initially bulb 1 contains argon, and bulb 2 contains xenon. The pressure and temperature are maintained at 1 atm and 105 oC, at which the diffusivity is 0.180 cm^2/s. At time t = 0, diffusion is allowed to occur between the two bulbs. At a later time, the argon mole fraction in the gas at end 1 of the tube is 0.75, and 0.20 at the other end. Determine at the later time:
(a) The rates and directions of mass transfer of argon and xenon
(b) The transport velocity of each species
(c) The molar average velocity of the mixture

HW 1 - p 3.14 - Effective Film Thickness Over Water Evaporating Into Air - 4 pts

Water in an open dish exposed to dry air at 25oC is found to vaporize at a constant rate of 0.04 g/h-cm^2. Assuming the water surface to be at the wet-bulb temperature of 11.0 oC, calculate the effective gas-film thickness (i.e., the thickness of a stagnant air film that would offer the same resistance to vapor diffusion as is actually encountered at the water surface).

HW 1 - p 3.15 - Diffusivity & Mass Transfer of Isopropanol in H2O(l) and N2(g) - 6 pts

Isopropyl alcohol is undergoing mass transfer at 35 oC and 2 atm under dilute conditions through water, across a phase boundary, then through nitrogen. Based on the data given below estimate for isopropyl alcohol:
(a) The diffusivity in water using the Wilke-Chang equation
(b) The diffusivity in nitrogen using the Fuller et al. equation
(c) The product, DAB ρ_M, in water
(d) The product, DAB ρ_M, in air
Where ρ_M is the molar density of the mixture
Using the above results, compare:
(e) The diffusivities in parts (a) and (b)
(f) The diffusivity-molar density products in Parts (c) and (d)
Lastly:
(g) What conclusions can you come to about molecular diffusion in the liquid phase versus the gaseous phase?
Data:
Component Tc,oR Pc, psia Zc V_L, cm^3/mol
Nitrogen 227.3 492.9 0.289 -
Isopropyl alcohol 915 691 0.249 76.5

HW 1 - p 3.24 - Drying a Clay Brick

A wet, clay brick measuring 2 x 4 x 6 in. has an initial uniform moisture content of 12 wt%. At time = 0, the brick is exposed on all sides to air such that the surface moisture content is maintained at 2 wt%. After 5 h, the average moisture content is 8 wt%. Estimate:
(a) The diffusivity of water in the clay in cm^2/s.
(b) The additional time for the average moisture content to reach 4 wt%. All moisture contents are on a dry basis.