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chemical engineering
Questions and Answers of
Chemical Engineering
A small distillation column with a partial reboiler, a total condenser, and a liquid-liquid separator is separating \(100.0 \mathrm{kmol} / \mathrm{h}\) of saturated liquid feed that is \(19.0
Compare Colburn Eq. (16-81d) to the equivalent Kremser Eq. (13-9c), and compare Eq. (16-81e) to \((13-9 b)\). If we relate \(\mathrm{n}_{\mathrm{O}-\mathrm{Ey}}\) to \(\mathrm{N}\) and set
Mass transfer models include transfer in only the packed region. Mass transfer also occurs in the column ends where liquid and vapor are separated. Discuss how these end effects affect a design. How
Are stages with well-mixed liquids less or more efficient than stages with plug flow of liquid (assume \(\mathrm{K}_{\mathrm{G}} \mathrm{a}\) are the same)? Explain your result with a physical
a. The Bolles and Fair (1982) correlation indicates that \(\mathrm{H}_{\mathrm{G}}\) is more dependent on liquid flux than on gas flux. Explain this on the basis of a simple physical model.b. Why do
The following statement occurs after Eq. (16-50):"The variation in \(\mathrm{H}_{\mathrm{G}}\) over the column section is usually less than \(10 \%\). ." Explain why this statement is true. h=-
Construct your key relations chart for this chapter.
While designing a mixer-settler extraction system, you obtain a mass transfer correlation from a book. Unfortunately, the book does not explain which model was used. Which model would you use to
Explain why mass transfer correlations for co-flow cannot be used for countercurrent flow.
Why are mass transfer coefficients from clean drops higher than mass transfer coefficients in dirty systems? What is the practical significance of this?
The rate design method for distillation columns is less likely to converge, takes more time to set up, and requires more data than the equilibrium model. When would you decide you should use the rate
How do we determine the height of packing required for a concentrated absorber or stripper if \(\mathrm{H}_{\mathrm{G}}\) is not constant?
Why do \(\mathrm{H}_{\mathrm{OG}}\) and \(\mathrm{H}_{\mathrm{OL}}\) vary more than \(\mathrm{H}_{\mathrm{L}}\) and \(\mathrm{H}_{\mathrm{G}}\), which often vary by about \(10 \%\) ?
Develop contactor designs that combine advantages of cocurrent, crossflow, and countercurrent cascades.
Derive the relationships among the different NTU terms for binary distillation.
Derive the following expression for determining \(\mathrm{K}_{\mathrm{y}} \mathrm{a}\) from the measurement of \(\mathrm{E}_{\mathrm{MV}}\) in a distillation column if the flow pattern is plug
Derive the following equation to determine \(\mathrm{n}_{\mathrm{OG}}\) for distillation at total reflux for systems with constant relative volatility:\[ \begin{equation*}
Extraction is almost invariably a ternary mass transfer problem instead of binary because of partial miscibility of diluent and solvent. Typically, as solute is removed from diluent, solvent is less
Both the Kremser and Colburn equations have special forms when \(\mathrm{mV} / \mathrm{L}=1.0\). The results of comparing these equations are Eqs. (16-33) and (16-36a), which relate HETP to
A short connecting pipe between two tanks is clogged with a plug of \(\mathrm{NaCl}\) crystals. The plug formed as a cylinder of circular cross-sectional area with a constant diameter \(D=2.0
Repeat Example \(15-7\) except with a forced flow with a velocity of \(1.05 \mathrm{~cm} / \mathrm{s}\) past the sphere. Use Eq. (15-60b) to determine \(\mathrm{k}_{\mathrm{c}}\). The viscosity of
Two identical large glass bulbs are filled with gases and connected by a capillary tube that is \(\delta=0.0100 \mathrm{~m}\) long. Bulb 1 at \(\mathrm{z}=0\) contains the following mole fractions:
Repeat Example \(15-10\) but for a bulk gas that is \(40 \mathrm{~mol} \%\) air, \(15 \mathrm{~mol} \% \mathrm{NH}_{3}\), and 45 \(\mathrm{mol} \%\) water. Report \(\mathrm{x}_{\mathrm{NH} 3},
a. Repeat Problem 15.H1 (use the Maxwell-Stefan equations), but bulb 1 at \(\mathrm{z}=0\) contains the following mole fractions: \(\mathrm{y}_{\text {air }}=0.500, \mathrm{y}_{\mathrm{H} 2}=0.500\),
Repeat Problem 15.H1, but bulb 1 at \(\mathrm{z}=0\) contains the following mole fractions: \(\mathrm{y}_{\text {air }}\) \(=0.520, \mathrm{y}_{\mathrm{H} 2}=0.480\), and \(\mathrm{y}_{\mathrm{NH}
Repeat Example \(15-8\) but for a pressure of \(1.1 \mathrm{~atm}\). Note that the diffusivities depend on pressure. Also answer Problem 15.A6.Example 15-8Problem 15.A6In Problem \(15 . \mathrm{H}
A pipeline containing \(99.0 \mathrm{~mol} \%\) ammonia and \(1.0 \mathrm{~mol} \%\) hydrogen gas is vented to ambient air via a \(15 \mathrm{~m}\) long, \(3.5 \mathrm{~mm}\) diameter tube.
In Example 15-2, operation is at a pseudo-steady state. Brainstorm alternative designs for this diffusion measurement.Example 15-2 Pure ethanol is contained at the bottom of a long, vertical tube
Although the additive approach traditionally used for coupling Fickian diffusion with convection appears logical and works for calculating total fluxes of \(A\) and \(B\), this is not the only way
Think of an experiment to measure diffusion coefficients that you could set up at home or in your apartment. Detail the equipment list. Estimate the amount of change you will observe. Will you be
You have been invited to give a talk on mass transfer at the local high school. You want to show a live demonstration. Brainstorm at least five different demonstrations that you can develop with very
Develop roleplays to illustrate:a. The difference between ordinary and Knudsen diffusion.b. The difference between Fickian and Maxwell-Stefan diffusion.
For binary diffusion with convection, use Eqs. (15-15e), (15-15f), (15-17a), (15-17b), and sum of mole fractions equals 1.0 to show that \(D_{\mathrm{AB}}=D_{\mathrm{BA}}\). Fick's law diffusive flux
For binary distillation with \(\mathrm{CMO}, \mathrm{v}_{\text {ref,mol }}=0\). If \(\mathrm{CMO}\) is valid, show that \(\mathrm{v}_{\text {ref,mass }} eq 0\) if \(\mathrm{MW}_{\mathrm{A}} eq
Derive the equation that is equivalent to Eqs. (15-32b) and (15-32c) in terms of a partial pressure driving force and a \(\log\) mean partial pressure difference:\[ \begin{equation*}
Derive Eq. (15-40a).Equation (15-40a) KPL.mol 1-C3XA.I.mol PL.mol NA,mol In C3=1+ C3 1-C3XA.bulk,mol. PS,mol
Use the general solution in Perry's Chemical Engineers' Handbook (Wankat and Knaebel, 2019, p. 5-47) to solve the problem of a dissolving solid in a concentrated fluid using the known ratio of
Starting with Eqs. (15-74a) and (15-74b), derive Eq. (15-74c). Note: Because \(\mathrm{x}_{\mathrm{W}}=1\) \(-\mathrm{x}_{\mathrm{E}}, \mathrm{x}_{\mathrm{W}}\) is not a constant. B A and In Yw
For the dissolution of platelets in dilute solution with independent dissolution mass transfer coefficients for the flat and growth sides,a. Show that\[ \begin{aligned} & h=-2 k_{\text {flat }}
Derive Eq. (15-63c) from Eq. (15-63a). kc (Sc) 2/3 hheat transfer pcpv (Pr)2/3 = hheat transfer JD = (k/v)(Sc)2/3=j = Sh(Sc) 1/3=Nu(Pr)-1/3 = Re f/2 = f/2 pcpv (15-63a) (15-63b) (15-63c)
Repeat the numerical integration in Example 15-5, except use the quadrature formula, Eq. \((9-12)\)Example 5-5Equation (9-12) A steady-state system of ethanol and water has equimolar counterdiffusion
For the same system as in Problem 15.D1, the high concentration \(\mathrm{C}_{\mathrm{A}, 0}=1.2 \mathrm{~kg} / \mathrm{m}^{3}\) and \(\mathrm{C}_{\mathrm{A}, \mathrm{L}}=0.9701 \mathrm{~kg} /
A column arrangement similar to Figure \(15-2\) is used for organic liquids. A large reservoir of water is under the column. The water is stirred and solute concentration in the water is constant.
a. Estimate the Fickian diffusivity of a binary mixture of benzene and air at \(298.2 \mathrm{~K}\) and \(1.0 \mathrm{~atm}\) pressure using Chapman-Enskog theory and Table 15-2.b. Compare your
What is the Fickian diffusivity of chlorobenzene in liquid bromobenzene at \(300 \mathrm{~K}\) when the mole fraction of chlorobenzene is 0.0332 ? Assume that the diffusivity follows an Arrhenius
Water at \(60^{\circ} \mathrm{C}\) and 0.95 bar is evaporating into a \(12.0 \mathrm{~cm}-1\) ong tube (also at \(60^{\circ} \mathrm{C}\) ) and diffusing through a stagnant layer of air. The device
Assuming that the mixture is ideal, estimate infinite dilution Fickian diffusivities at 283.3 \(\mathrm{K}\) for chlorobenzene in liquid bromobenzene and for bromobenzene in liquid chlorobenzene from
Use the Wilke-Chang theory to estimate infinite dilution Fickian diffusivity of ethanol in liquid water at \(293.16 \mathrm{~K}\) and of water in liquid ethanol. Data are available at
Determine the modified Sherwood number \(\mathrm{Sh}_{\text {gas,partial_pressure }}=\frac{\mathrm{k}_{\mathrm{p}} \mathrm{d}_{\text {tube
A pipeline containing ammonia gas is vented to ambient air via a \(20-\mathrm{m}\) long, \(3-\mathrm{mm}\) diameter tube. What is the mass flow ( \(\mathrm{g} /\) day) of ammonia into the atmosphere?
We have steady-state diffusion of ammonia in air across a \(0.033 \mathrm{~mm}\) thick film. On one side of the film ammonia concentration is \(0.000180 \mathrm{kmol} / \mathrm{m}^{3}\), and on the
Water at \(20^{\circ} \mathrm{C}\) is flowing down a \(3.0 \mathrm{~m}\) long vertical plate at a volumetric flow rate per meter of plate width of \(q=0.000005 \mathrm{~m}^{2} / \mathrm{s}\).
Repeat all parts of Problem 15.D12 but with a water rate of \(q=0.000015 \mathrm{~m}^{2} / \mathrm{s}\).Problem 15.D12Water at \(20^{\circ} \mathrm{C}\) is flowing down a \(3.0 \mathrm{~m}\) long
Repeat Problem 15.D12 but for \(\mathrm{q}=0.0015 \mathrm{~m}^{2} / \mathrm{s}\).a. Determine film thickness \(\delta\), average vertical velocity of film, and Reynolds number.b. Determine average
We are measuring the diffusivity of water in air at \(42^{\circ} \mathrm{C}\). A tube is placed with one end in the water and the other end in a stream of dry air. The air column in the tube is
Repeat Example 15-10 but with a mass transfer coefficient that is 10 times larger (use \(\delta=0.001 \mathrm{~m})\). Report \(\mathrm{x}_{\mathrm{NH} 3}, \mathrm{y}_{\mathrm{NH} 3, \text { surface
A particle of pure \(\mathrm{NaCl}\) is dissolving in an aqueous liquid solution at \(18^{\circ} \mathrm{C}\). The dissolution of the particle is controlled by mass transfer. The system is vigorously
Calculate the value of Maxwell-Stefan diffusivity for ethanol water at \(40^{\circ} \mathrm{C}\) for ethanol mole fractions of \(0.0,0.2,0.3,0.4,0.7\), and 1.0 . The Fickian diffusivities are
\(\mathrm{NaCl}\) is crystallizing from an aqueous (water) liquid solution onto a crystal particle of pure \(\mathrm{NaCl}\) at \(18^{\circ} \mathrm{C}\). Assume particle growth is controlled by mass
A \(2 \mathrm{~cm}\)-diameter, \(19 \mathrm{~cm}\)-long tube is placed touching a pool of liquid. The end away from the liquid pool \((\mathrm{z}=0.19 \mathrm{~m})\) is in an air stream (component C)
A crystal particle of pure \(\mathrm{NaCl}\) is dissolving in an aqueous liquid (water) solution at \(18^{\circ} \mathrm{C}\). The dissolution of the particle is controlled by mass transfer. The
Solve Example 15-7 using the difference equation form of the Maxwell-Stefan equations.Example 15-7 Because naphthalene C10Hg melts at 80.2C, it is solid at room temperature. Naphthalene also has a
Repeat Example 15-11 for the following conditions:a. \(0.03 \mathrm{~g} \mathrm{CO}_{2} / 1000 \mathrm{~g}\) water in the drop. \(\mathrm{y}_{\text {water, bulk }}=0, \mathrm{y}_{\mathrm{CO} 2, \text
Estimate \(\mathrm{Sc}_{\mathrm{V}}\) for a saturated vapor mixture that is \(80 \mathrm{~mol} \%\) ethanol and \(20 \mathrm{~mol} \%\) water at \(1.0 \mathrm{~atm}\).
This problem can be solved analytically or with a spreadsheet. Two identical large glass bulbs are filled with gases and connected by a capillary tube that is \(\delta=0.0090\) \(\mathrm{m}\) long.
Repeat Problem 15.D27, but bulb 2 at \(\mathrm{z}=\delta\) contains \(\mathrm{y}_{\mathrm{air}}=0.610, \mathrm{y}_{\mathrm{H} 2}=0.010\), and \(\mathrm{y}_{\mathrm{NH} 3}=0.380\).Problem 15.D27This
Check the solution to Example 14-1 with a McCabe-Thiele calculation.Example 1 In production of sodium hydroxide by the lime soda process, a slurry of calcium carbonate particles in a dilute sodium
Alumina solids are being washed to remove \(\mathrm{NaOH}\) from liquid entrained with solids. The wet feed is a mixture of \(5.0 \mathrm{vol} \%\) solids (dry basis) and \(95.0 \mathrm{vol} \%\)
Repeat Problem 14.D2 except for countercurrent process witha. Three stages.b. Eight stages.Data From Problem 14.D2Alumina solids are being washed to remove \(\mathrm{NaOH}\) from liquid entrained
Wash alumina solids to remove \(\mathrm{NaOH}\) from the entrained liquid. Underflow from the settler tank is \(20.0 \mathrm{vol} \%\) solid and \(80.0 \mathrm{vol} \%\) liquid. Two feeds to the
Your boss thinks it will be just as good to combine the two feeds in Problem 14.D4 than to keep them separate. Calculate the number of equilibrium stages required to achieve the same outlet
Your company is interested in purchasing a small company that produces barium that they sell to superconductor and electroceramic manufacturers. They have asked you to do some lab scale batch-washing
You are designing a new glass factory near the ocean. Sand is to be mined wet from the beach. However, wet sand carries with it seawater entrained between sand grains. Salt must be removed by a
We plan to remove dilute sulphuric acid and dilute \(\mathrm{HCl}\) from crushed rock by washing it with water in a continuous countercurrent process with five equilibrium stages. The feed is
Experimental data for leaching sugar from sugarcane with water show that a reasonable value for effective equilibrium constant \(y / x=m_{E}\) is 1.18 where \(\mathrm{y}\) and \(\mathrm{x}\) are the
Use of slurry adsorbents has received some industrial attention because it allows for countercurrent movement of the solid and fluid phases. Your manager wants you to design a slurry adsorbent system
To provide a simplified calculation method for the variable flow rate leaching problem solved in Example 14-2, your boss asks you to force-fit the problem so that a Kremser equation solution can be
A countercurrent leaching system is recovering oil from soybeans with five stages. On a volumetric basis, liquid flow rate/solids flow rate \(=1.36\). Recovery of oil in the solvent is \(97.5 \%\).
Batch leaching is similar to batch extraction, and the equations developed in Section 13.6 can be adapted when the solution is dilute or there is an insoluble solid matrix. We have \(12.5
Barium sulfide is produced by reacting barium sulfate ore with coal. The result is barium black ash, which is \(\mathrm{BaS}\) plus insoluble solids. Since \(\mathrm{BaS}\) is soluble in water, it
Repeat Problem 14.D14 except the feed has \(4.5 \mathrm{~kg}\) liquid \(/ \mathrm{kg}\) solids.Problem 14.D14Barium sulfide is produced by reacting barium sulfate ore with coal. The result is barium
A slurry of pure \(\mathrm{NaCl}\) crystals, \(\mathrm{NaCl}\) in solution, \(\mathrm{NaOH}\) in solution, and water is sent to a system of thickener(s) at a rate of \(100.0 \mathrm{~kg} /
This problem looks at the trade-offs between purity measured by \(\mathrm{y}_{\mathrm{I}, \text { out }} / \mathrm{y}_{\text {sugar, out }}\) and sugar recovery in the liquid,
Repeat Example 14-2 except for a single-stage system and unknown underflow product concentration.Example 14-2 We wish to treat 1000.0 kg/h (wet basis) of insoluble meal (D) that contains 20.0 wt% oil
Repeat Example 14-2 except for a three-stage countercurrent system and unknown underflow product concentration.Example 14-2 We wish to treat 1000.0 kg/h (wet basis) of insoluble meal (D) that
Repeat Example 14-2 except for a three-stage crossflow system, with pure solvent at a rate of \(421 \mathrm{~kg} / \mathrm{h}\) added to each stage and unknown underflow product concentration.Example
You are processing halibut livers that contain approximately \(25.2 \mathrm{wt} \%\) fish oil and \(74.8 \mathrm{wt} \%\) insoluble solids. The following data for leaching fish oil from halibut
Your company continues to have the stinky job of processing halibut livers detailed in Problem 14.E1. Halibut arrive in batches on the fishing boats, so you decide to evaluate a continuous solvent
Solve Problem 14.E2, part b, but do not assume \(R_{t}\) is constant. Derive an alternative for Eq. (13-29a) for nonconstant \(\mathrm{R}_{t}\) but with a constant amount of insoluble solids. Then
Suppose we have a volume of nitrogen plus a small amount of water vapor at \(1.0 \mathrm{~atm}\). The walls of the container are at \(25^{\circ} \mathrm{C}\), and there is a hot pipe at \(105^{\circ}
Dirty solutions typically have lower mass transfer rates than clean solutions. Where does the increased resistance come from?
Explain why infinite dilution Fickian diffusivities for binary liquid systems are not equal, \(D_{\mathrm{AB}}^{\circ} eq D_{\mathrm{BA}}^{\circ}\)
The constant in Eq. (15-22b) is \(1.173 \times 10^{-16}\), which agrees with Geankoplis et al. (2018). However, Cussler (2009) and Wankat and Knaebel (2019) use a constant of 7.4 \(\times 10^{-8}\).
What is a controlling resistance? How do you determine which resistance, if either, is controlling?
In Problem \(15 . \mathrm{H} 5\) changing the pressure changes the diffusivities but does not change the Henry's law constant of ammonia. However, changing the pressure does change the surface
You design a new type of absorber that has a number of slanted plates with falling films on each plate and gas flowing counter to the liquid. In the laboratory, the new system works well. Its high
When is \(\mathrm{J}_{\mathrm{A}}=\mathrm{N}_{\mathrm{A}}\), and when are they not equal?
For the extraction in Example 13-7, suppose we decide to have \(\mathrm{H}_{\text {tank }}=\) \(2 \mathrm{~d}_{\text {tank }}\) and want a 1.5 minute residence time. Find the tank dimensions.Example
Estimate value of \(\varphi_{\mathrm{d}}\) in the tank and power \(\mathrm{P}\) required for Example 13-7 with \(\mathrm{H}_{\text {tank }}=\mathrm{d}_{\text {tank }}=0.8279 \mathrm{~m}\) and a
Extract meta-, ortho-, and para-xylenes from \(n\)-hexane using \(\beta, \beta^{\prime}-\) thiodipropionitrile as solvent. Solvent and diluent ( \(n\)-hexane) are immiscible. Feed flow rate is
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