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engineering
chemical engineering

Separation Process Engineering Includes Mass Transfer Analysis 5th Edition Phillip Wankat - Solutions

Oxygen reacts irreversibly in aqueous sodium sulfate solutions according to the following reaction kinetics:where k2 is a second-order rate constant. The reaction is catalyzed by cobalt ions in
A bubble of pure carbon monoxide (CO) gas at 1 atm, initially 0.2 cm in diameter, is held stationary in liquid water 25°C flowing at a constant velocity of 10 cm/s. (a) Estimate the diffusion
A double-pipe heat exchanger consists of 20 ft of 2-in. “Schedule 40”steel pipe (see Table 10-22 in Perry’s Chemical Engineers’ Handbook, 9th edition), jacketed with 3-in. “Schedule 40”
We are separating \(1.0 \mathrm{kmol} / \mathrm{min}\) of a mixture that is \(25 \mathrm{~mol} \% \mathrm{CO}_{2}\) and \(75 \mathrm{~mol} \% \mathrm{~N}_{2}\) at \(25^{\circ} \mathrm{C}\) on a
Your current project is purifying \(99.1 \mathrm{wt} \%\) pure 2-naphthol that contains a naphthalene impurity. At lunch, your boss overheard you talking about an equilibrium solution for zone
The following statement is made in the introduction to Section 18.7: "Removal of impurities with distribution coefficients less than 1.0 is easier than removal of impurities with distribution
Would you recommend EFC (Section 17.2.4) for separation of the naphthalene-phenol system? Explain your answer.
Using approximate average values for liquids, show that \(\delta_{\text {mass }}=D / \mathrm{k}\) is normally smaller than the thermal boundary layer, \(\delta_{\text {thermal }}=\mathrm{k}_{\text
E1. An alternate method for doing anti-solvent crystallization to crystallize relatively large molecules is to use constant volume diafiltration (Section 19.5.3).Repeat Example 17-15 except use
We have \(100 \mathrm{~L}\) of a \(70 \mathrm{vol} \%\) solution of acetone at \(25^{\circ} \mathrm{C}\) that is saturated with lovastatin. We plan to add more acetone to increase acetone
The solubility of an albumin is approximately \(12 \mathrm{~g} / \mathrm{L}\) at \(\left[\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\right]=2.5 \mathrm{M}\) and \(0.006 \mathrm{~g} /
Since sodium sulfate has reverse solubility, an evaporative crystallizer operating at \(100^{\circ} \mathrm{C}\) is used to concentrate and crystallize \(1500 \mathrm{~kg} / \mathrm{h}\) of an
Use a spreadsheet program with a sixth-order polynomial fit for the ethanol-water VLE to determine \(\mathrm{n}_{\mathrm{OG}}, \mathrm{H}_{\mathrm{OG}}\), and the height of the stripping section for
(This problem is extensive.) We want to design a separation to recover five product streams that are all \(99.9^{+} \mathrm{mol} \%\) of the respective light hydrocarbons. The feed is propane
We wish to generate additional arrangements for quaternary mixtures (see Problem 11.B1). Sketch possible arrangements that use one or two columns that have sidestreams for one or both of the
Repeat Example 10-2 except calculate the diameter at the bottom of the column at a pressure of \(400.0 \mathrm{kPa}\). The surface tension of pure \(\mathrm{n}-\) heptane at \(20^{\circ} \mathrm{C}\)
Valve trays are often constructed with two different weight valves. What would this do to Figure 12-21? What are the probable advantages of this design?
Develop a key relations chart for this chapter.
\(355 \mathrm{kmol} / \mathrm{h}\) of a liquid feed at a high pressure (see part a) and \(25^{\circ} \mathrm{C}\) that is 2.6 \(\mathrm{mol} \mathrm{\%} \mathrm{ethane,} 10.6 \mathrm{~mol} \%\)
Show that the spreadsheet in Figure 2.B-2 has convergence difficulties if Goal Seek is used to make cell B29 \(\left(\Sigma \mathrm{x}_{\mathrm{i}}=1\right)\) equal 1 by changing cell B12 (V/F).
We have 1200 kg/h of a feed that is 30.0 wt.% ethanol and 70.0 wt.% water. What is the mole fraction of ethanol, and what is the total flow rate in kmol/h? Data: The locations in this textbook of
Repeat Example 20-4 but using repressurization with pure product. A 0.50 m long column is used to remove methane (M) from hydrogen using Calgon Carbon PCB activated carbon. Feed gas contains 0.002
Find \(\mathrm{K}_{\mathrm{A}}\) and \(\mathrm{q}_{\max }\) for methane adsorption on PCB activated carbon at 296 and \(480 \mathrm{~K}\) (Table 20-3). TABLE 20-3. Equilibrium data for methane on
Adsorption of anthracene from cyclohexane on activated alumina follows a Langmuir isotherm, \(\mathrm{q}=22 \mathrm{c} /(1+375 \mathrm{c})\), where \(\mathrm{c}\) is in \(\mathrm{mol} / \mathrm{L}\)
For the chromatographic separation of fructose and glucose on ion-exchange resin in the calcium form, the equilibrium is linear for concentrations below \(0.05 \mathrm{~g} / \mathrm{ml}\). At
A thermal swing adsorption process is removing traces of toluene from n-heptane using silica gel adsorbent. Operation is at \(1.0 \mathrm{~atm}\). Feed is \(0.11 \mathrm{wt} \%\) toluene and \(99.89
A \(50.0 \mathrm{~cm}\) long column is packed with a resin that immobilizes a liquid stationary phase. The column is initially clean, \(\mathrm{c}_{\mathrm{A}}=0\). At \(\mathrm{t}=0\), we input a
We are adsorbing \(\mathrm{p}\)-xylene from \(\mathrm{n}\)-heptane on silica gel. Column is initially clean \((\mathrm{c}=\mathrm{q}=\) 0 ) and is at \(30^{\circ} \mathrm{C}\). At \(t=0\), we start
An initially clean \(60.0 \mathrm{~cm}\) long column contains activated carbon. At \(t=0\), we feed a dilute aqueous solution of acetic acid \(\left(\mathrm{c}=0.010 \mathrm{kmol} /
Redo Example 20-3 but with co-current thermal regeneration. Input the hot thermal wave (co-current purge step at superficial velocity of \(11.0 \mathrm{~cm} / \mathrm{min}\) ) so that it exits at
A very simple PSA cycle consists of three steps: (1) Pressurize column with feed. (2) Simultaneous feed step and product withdrawal at \(\mathrm{p}_{\mathrm{H}}\). (3) Counterflow blowdown to
Intermediate concentrations in the outlet concentration profile for trace PSA systems can be estimated using Eqs. (20-28a) to (20-28c). For Example 20-4,Example 20-4a. Show that point 10 in Figure
A column packed with activated carbon is used for adsorbing acetone from water at \(25^{\circ} \mathrm{C}\). The isotherm can be approximated as a Langmuir isotherm (Seader and Henley, 1998),
Use the local equilibrium model to estimate reasonable flow rates for separation of dextran and fructose using an SMB. Isotherms are linear, and both \(\mathrm{q}\) and \(\mathrm{c}\) are in
A \(50.0 \mathrm{~cm}\) long column is packed with a strong acid cation-exchange resin \(\left(\mathrm{c}_{\mathrm{RT}}=2.2 \mathrm{eq} / \mathrm{L}\right.\), \(\varepsilon_{\mathrm{e}}=0.42\) ).
A \(50.0 \mathrm{~cm}\) long column is packed with a strong acid cation-exchange resin \(\left(c_{R T}=2.2 \mathrm{eq} / \mathrm{L}\right.\), \(\left.\varepsilon_{\mathrm{e}}=0.42\right)\). Fluid
A column packed with gas-phase activated carbon is initially filled with clean air. At \(t=0\), a feed gas containing \(y=0.05 \mathrm{wt} \%\) toluene in air is started. This feed continues until
A \(25.0 \mathrm{~cm}\) long column packed with gas-phase activated carbon is initially filled with air containing \(\mathrm{y}=0.10 \mathrm{wt} \%\) toluene. At \(\mathrm{t}=0\), a feed gas
A \(50.0 \mathrm{~cm}\) long column is packed with activated alumina adsorbent to adsorb anthracene (A) from cyclohexane. The adsorbent is initially in equilibrium with a fluid with
We are exchanging \(\mathrm{Ag}^{+}\)and \(\mathrm{K}^{+}\)on a strong acid resin with \(8 \%\) divinylbenzene (DVB). Total resin capacity is \(\mathrm{c}_{\mathrm{RT}}=2.0 \mathrm{eq} /
A column packed with a strong cation exchanger is initially in the \(\mathrm{K}^{+}\)form, \(\mathrm{c}_{\mathrm{T}}=0.020\) eq/L. The column is \(75.0 \mathrm{~cm}\) long, superficial velocity is
Isotherms for dilute amounts of toluene and xylene adsorbed on silica gel from n-heptane are linear at low concentrations (Matz and Knaebel, 1991). For toluene,
A \(25.0 \mathrm{~cm}\) long column packed with silica gel is in equilibrium with a liquid that is 0.0008 wt. frac. toluene and \(0.9992 \mathrm{wt}\). frac \(\mathrm{n}\)-heptane at \(0^{\circ}
A size exclusion chromatograph has \(\varepsilon_{\mathrm{e}}=0.42, \varepsilon_{\mathrm{p}}=0.7, \mathrm{~K}_{\mathrm{d}}=1.0\) for sugars, and \(\mathrm{K}_{\mathrm{d}}=0\) for proteins. There is
A \(50.0 \mathrm{~cm}\) long column contains activated carbon and is initially saturated with acetic acid at \(\mathrm{c}=0.007 \mathrm{kmol} / \mathrm{m}^{3}\) at \(4^{\circ} \mathrm{C}\). At
TSA regeneration can be combined with an SMB to reduce desorbent usage (Kim et al., 2005; Wankat, 1986). For the separation of toluene and xylene, repeat Problem 20.D21: interstitial feed velocity
The adsorption of acetic acid from aqueous solution onto activated carbon has been extensively studied. The adsorption follows a Freundlich isotherm, \(\mathrm{q}=\mathrm{A}(\mathrm{T}) \mathrm{c}^{1
A column packed with alumina initially contains pure cyclohexane liquid. At time zero a stream containing \(0.010 \mathrm{gmol} / \mathrm{L}\) of anthracene in cyclohexane is fed to an initially
A four-zone SMB with one column per zone is separating pyrene (P) and anthracene (A). The columns are \(100.0 \mathrm{~cm}\) long, and the switch time \(\mathrm{t}_{\mathrm{sw}}=312.5 \mathrm{~s}\).
A \(90.0 \mathrm{~cm}\) long laboratory column is packed with a strong acid cation-exchange resin ( \(\mathrm{c}_{\mathrm{RT}}\) \(\left.=2.5 \mathrm{eq} / \mathrm{L},
A \(500.0 \mathrm{~cm}\) long column is packed with a strong acid resin \(\left(c_{R T}=2.2 \mathrm{eq} / \mathrm{L}, \varepsilon_{\mathrm{e}}=0.42\right)\). Superficial velocity is \(25.0
A strong base resin is exchanging \(\mathrm{NO}_{3}{ }^{-}\)with \(\mathrm{Cl}^{-}\). The resin capacity is \(\mathrm{c}_{\mathrm{RT}}=1.25 \mathrm{eq} / \mathrm{L}, \varepsilon_{\mathrm{e}}\)
Complete the mole balance check in step E of Example \(20-7\) and show that mole balance agrees with results of solute movement analysis.Example 20-7 A 100.0 cm long column is packed with activated
A strong acid resin is exchanging \(\mathrm{Ni}^{+2}\) and \(\mathrm{H}^{+}\). The column is \(100.0 \mathrm{~cm}\) long and is initially at \(\mathrm{c}_{\mathrm{T}}=0.10\) eq/L with
Adsorption of anthracene from cyclohexane on activated alumina follows a Langmuir isotherm, \(\mathrm{q}=22 \mathrm{c} /(1+375 \mathrm{c})\), where \(\mathrm{c}\) is in mol anthracene/L and
A \(28.0 \mathrm{~cm}\) long column packed with gas-phase activated carbon is initially filled with clean air. At \(\mathrm{t}=0\), a feed gas containing \(\mathrm{y}=0.10 \mathrm{wt} \%\) toluene in
At very low concentrations, isotherms for separation of enantiomers of 1,1'-bi-2-naphtol using a 3,5-dinitrobenzoyl phenylglycine bonded silica gel adsorbent with heptaneisopropanol (72:28) solvent
Use a thermal swing adsorption process to remove traces of toluene from liquid n-heptane using silica gel as adsorbent. Adsorber operates at \(1.0 \mathrm{~atm}\). Feed is \(0.11 \mathrm{wt} \%\)
An adsorption with thermal regeneration experiment was done in laboratory with a \(17 \mathrm{~cm}\) long adiabatic column that was initially clean (filled with pure n-heptane) and at \(30^{\circ}
Column is initially clean \(\left(\mathrm{c}_{\mathrm{init}}=0\right)\). Feed is \(\mathrm{c}_{\mathrm{F}}>0\).1. If solute follows a linear isotherm, the resulting solute wave will be(a) diffuse
Column initially is saturated with solute at concentration \(\mathrm{c}_{\text {init }}>0\). Feed is \(\mathrm{c}_{\mathrm{F}}=0\).1. If solute follows a linear isotherm, the resulting solute wave
Sorption separations are not always used in industry in cases where they would be most economical. What are some noneconomic barriers to more use of sorption separations?
Explain why an adsorption isotherm that is too steep may not work well in a PSA process.
Briefly explain why the SMB system is much more efficient (i.e., uses less solvent and less adsorbent) than an elution chromatograph doing the same binary separation. Assume that both systems are
Although a number of important industrial separations can be operated as either gas or liquid, all of these adsorption applications, which could be done as gas, are operated as liquids. What are the
In an SMB, suppose A (weakly adsorbed component) product purity is okay, but B product purity is too low. We can increase \(\mathrm{B}\) product purity while maintaining A product purity bya.
Many variations of the basic Skarstrom cycle shown in Figure 20-11 have been developed. One variation is to include a partial co-flow blowdown step before the counterflow blowdown shown in Figure
A dilute ternary mixture consisting of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) dissolved in \(\mathrm{D}\) (A is least strongly adsorbed and \(\mathrm{C}\) is most strongly adsorbed) is
Brainstorm some possible alternative adsorbents made from common agricultural and/or forest products or wastes.
The PSA cycle used in Example 20-4 does not produce pure hydrogen throughout the entire feed step. Brainstorm what can be done to change the cycle so that it will produce pure hydrogen during the
What can be done to develop more economical sorption separations?
A molecular sieve zeolite adsorbent consists of pellets that are agglomerates of zeolite crystals with density \(ho_{\text {crystal }}\) scattered in a continuous phase of clay binder with a density
Developments of Eqs. (20-14, a-d) are efficient but tend to hide the reasons the solute velocity equations are different. Start with Eq. (20-9) and derive solute velocity equations when
Use mass action expression to prove Eqs. (20-40a) and (20-41). KAB CRACB YAXB YA (1-XA) = CACRB (1-) (20-40a)
Derive Eq. (20-44) by modifying development used for adsorption in Eqs. (20-10) to (2014). Fraction solute in = (moles in )/[moles in: ( + (1 - ) + adsorbed)]
Derive the equation for solute velocity for linear isotherms \(\mathrm{q}_{\mathrm{i}}=\mathrm{K}_{{ }_{i}} \mathrm{c}_{\mathrm{i}}\) using a singleporosity model (equivalent to setting
Derive appropriate mass balance equation and solutions equivalent to Eqs. (20-22) to (2024) but for the case where \(u_{S}\left(T_{\text {hot }}\right)>u_{S}\left(T_{\text {cold
Derive the thermal wave velocity when steam is used for regeneration of an activated carbon solvent recovery system.
Show that if the entire column is heated (or cooled) simultaneously (known as direct heating), Eq. (20-24) simplifies to\[ \mathrm{c}\left(\mathrm{T}_{2}\right) /
For divalent-monovalent exchange, show that when a total ion wave passes through a segment of the column, \(\mathrm{y}_{\mathrm{i}, \mathrm{after}}=\mathrm{y}_{\mathrm{i}, \text { before }}\). Hint:
Derive the mass action equilibrium expression for trivalent-trivalent ion exchange and derive derivative of \(\mathrm{y}_{\text {tri }}\) with respect to \(\mathrm{x}_{\text {tri. }}\)
The feed to a gas permeator is \(35 \mathrm{~mol} \%\) carbon dioxide and \(65 \mathrm{~mol} \%\) nitrogen. The perfectly mixed membrane separator is equipped with a silicone rubber membrane with an
You are working for a company that is trying to use membrane GP to remove carbon dioxide from natural gas (methane). Carbon dioxide has a higher permeability than methane in polymer membranes.
We are doing RO experiments with a completely mixed laboratory unit.Experiment \(A\). With a very high stirrer speed so that there is no concentration polarization, we do an experiment with a feed
You are working on a low-temperature and energy-efficient method of concentrating syrup for a sugar company. Initial experiments are done with aqueous sucrose solutions and an RO system with a
We are continuing our efforts to concentrate syrup for a food company by using a cellulose acetate RO membrane to concentrate a dilute sucrose mixture. Operation is at \(25.0^{\circ} \mathrm{C}\).a.
Your employer supplies dextran to a pharmaceutical company. Unfortunately, there are difficulties with gel formation on the membrane during UF operation. You are asked to analyze the problem.UF of a
A UF membrane is first tested in a stirred cell in which there is no concentration polarization. Experimental values obtained are listed in the following table. Then the same membrane is used in a
A perfectly mixed membrane module is used to concentrate helium in retentate. Feed is 5.0 vol \(\%\) helium and \(95.0 \mathrm{vol} \%\) hydrogen at \(5.0 \mathrm{~atm}\). Membrane is natural rubber
The following data were obtained for UF of skim milk in a spiral-wound system (Conlee et al., 1998).a. Estimate gelling weight fraction, \(\mathrm{x}_{\mathrm{g}}\), and mass transfer coefficient,
The natural gas company you work for wants to see the effect of a modern experimental membrane as compared to an older membrane for the removal of \(\mathrm{CO}_{2}\) from \(\mathrm{CH}_{4}\). Repeat
Obtaining high purity for medical applications with GP membranes requires a lack of pores and holes. With thin membranes, ensuring there are no holes is difficult. The PRISM membrane separator uses
A perfectly mixed membrane module with \(10,000 \mathrm{ft}^{2}\) of membrane area is separating oxygen and nitrogen at \(25^{\circ} \mathrm{C}\). The membrane is \(1.1 \mu \mathrm{m}\) thick poly (
A mixture of helium, methane, carbon dioxide, and nitrogen is fed to a perfectly mixed GP system with a silicone rubber membrane. Membrane properties are given in Table 19-2. Membrane active layer
The biofuel startup that you consult for wants to use a pervaporation system to remove water from n-butanol using a cellulose 2.5 -acetate membrane in a perfectly mixed module. You have been asked to
A paint company is concentrating latex particles in an aqueous suspension with a UF module. The module is perfectly mixed on the retentate side and operates with \(p_{p}=1.0\) bar and \(p_{r}=2.2\)
We are doing RO experiments with a completely mixed laboratory unit. Data: \(\mathrm{K}_{\text {solv }}^{\prime} / \mathrm{t}_{\mathrm{ms}}=1.387 \mathrm{~g} /\left(\mathrm{atm} \mathrm{m}^{2}
On a Robeson (1991) plot (a log-log plot of selectivity versus oxygen permeability in Barrer), the upper bound for separation of oxygen from nitrogen plots as a straight line. Approximate values of
Your plant has a catalytic system for burning methane in the stoichiometric quantity of air. All of the methane is converted to carbon dioxide and water vapor. The flue gas is cooled, and the water

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