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engineering
chemical engineering
Questions and Answers of
Chemical Engineering
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
A mixture of carbon dioxide, methane, and nitrogen is fed to a perfectly mixed GP system with a natural rubber membrane. Membrane properties are given in Geankoplis data in Table 19-2. Membrane
The feed to a pair of gas permeators connected with retentate in series is \(40 \mathrm{~mol} \%\) carbon dioxide and 60 \(\mathrm{mol} \%\) nitrogen. The perfectly mixed membrane separators are
UF membranes operated in the diafiltration operating mode are commonly used for changing solvent or buffer systems when solute is a large molecule such as a protein. Usually, the process is operated
Because of the great variation in seawater, a standard seawater has been defined as total dissolved salts (TDS) of \(35,000 \mathrm{ppm}\) by weight. The simplest treatment is to assume the salts are
Show that for identical conditions, mass transfer correlation Eq. (19-35d) predicts a higher mass transfer coefficient at low Reynolds numbers and Eq. (19-35a) predicts a higher mass transfer
Your company's well water, which contains \(190.0 \mathrm{ppm}\) (weight) of salt, is fine for most purposes but not for a particular manufacturing process that needs purer water. A vendor is trying
We are doing \(\mathrm{RO}\) of dilute aqueous sucrose solution at \(25.0^{\circ} \mathrm{C}\). A feed that is \(2.20 \mathrm{wt} \%\) sucrose is separated in a very-well-stirred system \((M=1.0)\)
A perfectly mixed pervaporation unit is separating a benzene-isopropyl alcohol mixture. Wankat (1990) shows the separation factor of benzene with respect to isopropyl alcohol versus the weight
A crossflow membrane module is separating oxygen and nitrogen at \(25^{\circ} \mathrm{C}\). Feed rate \(\mathrm{F}_{\text {in }}=0.8270 \mathrm{~mol} / \mathrm{s}\). The membrane is \(1.1 \mu
A mixture of helium, oxygen, carbon dioxide, and nitrogen is fed to a perfectly mixed GP system with a poly (dimethylsiloxane) membrane at \(25^{\circ} \mathrm{C}\). Membrane properties are given in
Pervaporation problems are guess and check but can be conveniently solved on a spreadsheet if selectivity is constant. Solve Problem 19.D14a with a spreadsheet, and check your answer with graphical
Repeat spreadsheet solution of Problem 19.D14a but with the feed at \(80.0^{\circ} \mathrm{C}\).Problem 19.D14aa. Calculate concentration polarization modulus \(\mathrm{M}\).
RO experiments are done in a laboratory stirred-tank membrane system at \(45.0^{\circ} \mathrm{C}\). With pure water, we measure the pure water flux \(=17.89 \mathrm{~g} /\left(\mathrm{m}^{2}
Repeat Problem 19.H5 except in experiment \(B x_{i n}=0.0006\) and find the value of \(k\) that gives \(M_{B}=1.1\). Report \(\mathrm{k}, \mathrm{R},{ }^{\prime}\) solv, \(\mathrm{x}_{\mathrm{p}}\),
Repeat Problem 19.H5 except in experiment \(B x_{i n}=0.003, p_{r}=21.4 \mathrm{~atm}\) and \(p_{p}=1.1 \mathrm{~atm}, \theta^{\prime}=0.45\), and a mass transfer coefficient of \(k=4.63 \times
Permeabilities of carbon dioxide and methane in a cellulose acetate membrane were measured as \(\mathrm{P}_{\mathrm{CO} 2}=15.0\) \(\times 10^{-10}\) and \(\mathrm{P}_{\mathrm{CH} 4}=0.48 \times
We wish to purify \(99.78 \mathrm{wt} \%\) anthracene to \(\mathrm{x}_{\text {anthracene,avg }}=99.99^{+} \mathrm{wt} \%\) by zone melting. The only impurity is fluorene. Determine the smallest
Do the heat transfer calculation for a clean heat exchanger \(\left(t_{C}=0\right.\) and no crystal formation) in a natural convection progressive freezing device (see Figure 18-7) with the same
The size of the shell on the feed side of the flat plate static heat exchanger in Figure 18-7 controls the volume of feed, which sets the amount of feed. For the same recovery of product, the
Challenging! When feed concentration of naphthalene in the naphthalene-phenol separation is closer to the eutectic concentration than in Example 18-5 and recovery is high, the run can become
Membrane systems are rate processes, and flash distillation is an equilibrium process. Explain why solution methods are so similar for well-mixed membrane separators and flash distillation.
How would you use the crossflow spreadsheet program in this chapter's appendix as a simulator instead of as a design program?
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