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engineering
introductory chemical engineering thermodynamics

Engineering And Chemical Thermodynamics 2nd Edition Milo D. Koretsky - Solutions

Sets of data for two different binary mixtures are plotted in the following figure. On the top are two plots of the liquid phase fugacity coefficient of species a versus mole fraction of a, and on the bottom are plots of activity coefficient of a and b versus mole fraction of a. Take Lewis/Randall
Data for two different binary mixtures are plotted in the following fi gure. For each plot determine if the a-b interaction is stronger than or weaker than the (a-a, b-b) interactions. Explain. [bar] 200 150 100 50 0.5 Xa (a) 2 1.6 1.2 0.8 0.4 In Yb 0.5 Xa (b) In Ya
Consider the fugacity of water in the liquid. Rank the following from lowest value ofto highest value ofTry to do this without doing any calculations. fi psat i
Consider the Berthelot equation of state:(a) Develop an expression for the fugacity and fugacity coeffi cient of a pure species.(b) Use the results of Problem 4.29 to write the result of part(a) in terms of reduced pressure, reduced temperature, and reduced volume.Problem 4.29Consider the
Calculate the fugacity and the fugacity coeffi cient of steam at(a) 2 MPa and 500°C;(b) 50 MPa and 500°C.
A piston–cylinder assembly contains a mixture of water and nitrogen, which is in vaporliquid equilibrium. A third liquid species with negligible saturation pressure is added to the container while the pressure is kept constant. How will the number of moles of water in the vapor phase change? You
A tub of pure water sits in a room open to the atmosphere at 20°C. When the water has reached equilibrium with the air in the room, what is the fugacity of water in the vapor? You may assume the vapor behaves as an ideal gas.
Develop an expression for the fugacity and fugacity coeffi cient of a pure species based on the Redlich–Kwong equation of state.
Develop an expression for the fugacity and fugacity coeffi cient of a pure species based on thePeng–Robinson equation of state.
Calculate the fugacity of water at 647 K and 114 atm using(a) the steam tables;(b) the van der Waals equation;(c) generalized correlations. Which value do you believe the most?
Calculate the fugacity and fugacity coeffi cient of the following pure substances at 500°C and 150 bar:(a) CH4;(b) C2H6;(c) NH3;(d) (CH3) 2CO;(e) C6H12;(f) CO. Provide an explanation of the relative magnitude of these numbers based on molecular concepts.
You have a pure gas at 30 bar and 300 K. The compressibility factor (z) under these conditions is 0.9. As best you can, calculate the fugacity and the fugacity coeffi cient.
Experimental data taken from 0 to 50 bar give the fugacity of a pure gas to be:where P is the pressure in bar and C is a constant that depends only on temperature. For the region of 0°C to 100°C, C is given by:where T is in Kelvin.(a) Find an equation of state for this gas that is valid from
Consider a system containing pure hydrogen sulfi de at 300 K and 20 bar. The following equation of state characterizes the PvT behavior of H2S well under these conditions:Using this equation of state, find the fugacity and fugacity coefficient. [ 1 + 7/7 ( PT Pu RT 1+ = 0.083- 0.42271.6 T'1.6
In 1920, Schrieber proposed the following equation of state:where k, b, and c are constants. Develop an expression for the pure species fugacity coeffi cient of species i, ln φvi , based on the Schrieber equation of state. V RT P + kP - c T + b
The following expression describes the relation between pressure and molar volume of pureSF6 vapor at 30°C, where P is in bar and v is inConsider a container that is 10 L (10,000 cm3) that contains 10.79 mol of SF6 vapor at 30°C.Answer the following. cm mol 3 C
You have an unknown pure gas. Its volume has been measured to be 1.86 * 10-3 [m3/mol] at 15 bar and 100°C and 6.12 * 10–4 [m3/mol] at 40 bar and 100°C. As best you can, calculate the fugacity and fugacity coeffi cient of this gas at 50 bar and 100°C.
As accurately as you can, determine the fugacity of pure methane at 220 K and 69 bar.
The following data are available for ethylene at 24.95°C. From these data, estimate the fugacity and the fugacity coeffi cient of ethylene at 50.5 bar and 24.95°C. P [bar] 1.0 5.1 10.1 15.2 20.2 25.3 30.3 35.4 40.4 45.5 50.5 v[m/mol] 2.45 10-2 4.78 X 10-3 2.32 X 10-3 1.50 X 10-3 1.08 x 10-3 8.34
Below is a plot of the natural log of the fugacity coeffi cient, ln (φi) , of pure NH3 as a function of pressure at a temperature of 100°C. From this plot, as best you can, determine the molar volume of this species at 500 bar and 100°C. (b)ul -0.25 -0.5 -0.75 -1 -1.25 -1.5 -1.75 -2 -2.25 0 100
A gas mixture containing an equal number of moles of species 1 and 2 at 300 K and 30 bar perfectly obeys the Lewis fugacity rule. Calculate the Gibbs energy of mixing.
Calculate the fugacity of n-butane, f^ v n2butane, in a vapor mixture of 1 mole n-butane, 2.5 moles isobutane, 4 moles n-pentene and 1 mole n-pentane at 318.9 K and 3.79 bar. You may use the Lewis fugacity rule.
(a) Calculate the fugacity of pure methane vapor at T = 190.6 K and P = 32.2 bar.(b) Using the Lewis fugacity rule, calculate the fugacity of methane in a mixture of 80 mol% methane and 20 mol% ethane at T = 190.6 K and P = 32.2 bar.
Consider a mixture of species 1, 2, and 3. The following equation of state is available for the vapor phase:where, P = RT + P [A(y - y) + B]
A mixture of 2 moles propane (1), 3 moles butane (2), and 5 moles pentane (3) is contained at 30 bar and 200°C. The van der Waals constants for these species are:Determine the fugacity and fugacity coeffi cient of propane using the following approximations:(a) the Lewis fugacity rule(b) the virial
Consider a ternary system of methane (a), ethane (b), and propane (c) at 25°C and 15 bar. Assume this system can be represented by the virial equation truncated at the second term:At 25°C, the second virial coeffi cients [cm3/mol] are given by:(a) Develop an expression for the fugacity coeffi
Consider a binary mixture of species 1 and 2 that obeys the Redlich–Kwong equation of state with van der Waals mixing rules. Show that the fugacity coeffi cient for species 1 is given by the “Species 1 in a binary mixture” row in Table 7.1. TABLE 7.1 Fugacity Coefficients for Three Cubic
Consider a binary mixture of species 1 and 2 that obeys the Peng–Robinson equation of state with van der Waals mixing rules. Show that the fugacity coeffi cient for species 1 is given by the “Species 1 in a binary mixture” row in Table 7.1. TABLE 7.1 Fugacity Coefficients for Three Cubic
Calculate the fugacity and the fugacity coeffi cient of phenol in a mixture of 20 mole % phenol (1) and 80 mole % oxygen (2) at 694.2 K and 24.52 bar using the following:(a) The ideal gas law(b) The Lewis fugacity rule (choose the method that gives you as accurate an answer as possible)(c) The
You wish to calculate in a mixture of 25.0 mole % propylene (1) and 75.0 mole % methane (2) at 219.0 K and 27.72 bar. For all your answers, use the following equation of state:where the reduced pressure and temperature are used:(a) i. Develop expressions for the fugacity and the fugacity coeffi
Consider a vapor phase mixture of 2 moles propane (1) and 3 moles nitrogen (2) at 15°C and 12 bar. You wish to come up with the fugacity and fugacity coeffi cient for propane. Answer the following questions using the truncated virial equation of state, as follows:and with parameter
Your supervisor has just stopped by your desk and is frantic. She has a meeting with the senior vice president in 25 minutes and has misplaced some data. She needs to report the fugacity of n-pentane at 192°C and 1.8 MPa in a mixture of 13.7 mol % n-pentane, 32.1 mol % n-butane, 21.5 mol %
Determine the expression for the fugacity coeffi cient of species 1 in a binary vapor mixture of 1 and 2 using the modifi ed form of the cubic equation of state that has been recommended by Martin, as follows: P = RT V a (v + c)
Use the following mixing rules:Simplify the expression as much as possible. Only include T, v, z, y1, y2, R, a1, a12, a, c1, and c in the fi nal form. a = ya + 2yy2a12 + ya C = = yc + yc
The following form of a cubic equation of state has been recommended by Martin: P = RT v-b a (v + c)
Consider a mixture of CH4 and H2S at 444 K and 70 bar. Use the results of Example 7.4 to plot the fugacity coeffi cient of methane as a function of methane mole fraction using the van der Waals equation of state and mixing rules. Compare the result with that obtained from the text software,
Consider a mixture of CH4 and H2S at 444 K and 70 bar. Calculate the fugacity coeffi cient of methane in an equimolar mixture using each of the following:(a) the van der Waals equation of state(b) the Redlich–Kwong equation of state(c) the Peng–Robinson equation of state(d) ThermoSolver
You wish to represent a binary mixture of species a and b at 127°C and 80 bar by the virial equation. At 127°C, the second virial coeffi cients are given by:You have also found that at infi nite dilution—that is, as ya → 0—the value of the fugacity coeffi cient is reported asAs best as you
A binary mixture of species 1 and 2 can be described by the following equation of state:with the mixing rule:The pure species coeffi cients are given by: P = RT V a VvT
Verify that : ag JP / T = vi = RT (Infi) aP T
You wish to determine the fugacity of water at 300°C and 300 bar. Using only data for saturated steam and superheated vapor from the steam tables, determine, as accurately as you can, the fugacity of water at 300°C and 300 bar. State any assumptions that you make.
What is the fugacity of pure liquid n-butane at 260 K at the following pressures:(a) 1 bar;(b) 200 bar. You may assume the density of liquid butane, 0.579 g/cm3, is independent of pressure.
Determine the fugacity of pure liquid acetone at 100 bar and 382 K. The molar volume of the liquid is 73.4 cm3/mol. You may assume vi does not change with pressure.
Calculate the fugacity of pure liquid propane at 333 K and 22 bar.
Determine the fugacity of pure water at 25°C and 500 bar. State any assumptions that you make.
Consider a binary mixture of a and b at T = 300 K and P = 40 kPa. A graph of the fugacity of species a as a function of mole fraction is shown below. Use Henry’s law as the reference state for species a and the Lewis/Randall rule for species b. Show all your work.(a) What is the Henry’s law
Below is a plot of the natural log of the activity coeffi cients ( ln γi) a binary liquid mixture of species a and b vs. mole fraction of species a (xa) at 300 K.(a) What is the reference state for each species (Lewis-Randall or Henry’s)?(b) Show that the Gibbs–Duhem equation is satisfi ed
Consider a binary mixture of species a and species b at 300 K and 1 bar. The vapor pressure of pure a at 300 K is 80 kPa. A plot of the activity coeffi cient of species a vs. mole fraction of species a is shown below. Based on this plot, answer the following questions:(a) Specify the reference
The following plot shows values of excess Gibbs energy over the ideal gas constant, gE/R in [K], for mixtures of benzene–cyclohexane at 343 K. Answer the following questions:(a) Estimate the activity coeffi cient of cyclohexane in benzene (1)–cyclohexane (2) at 343 K for(i) a mole fraction of
Derive the expressions for the activity coeffi cients for a binary mixture from the following models for gE:(a) the three-suffi x Margules equation(b) the van Laar equation(c) the Wilson equation(d) NRTL
Consider an equimolar binary mixture of species a and b. The activity coeffi cients at infi nite dilution are given by: γa ∞ = 2.0 and γb ∞ = 1.5. Calculate the activity coeffi cient of species a and b using the three-suffi x Margules equation, the van Laar equation, and the Wilson equation.
Glycerol(a) and benzyl ethyl amine(b) form two partially miscible liquid phases. At 220°C and 1 atm, the compositions of the two phases are given by From these data, estimate the parameters in the three-suffi x Margules equation. At equilibrium, the fugacities in each liquid phase must be
Calculate the fugacity of liquid water in a binary liquid mixture with 40 mole % water and 60 mole % ethanol at 70°C. The following activity coeffi cient data, at infi nite dilution, are available: HO = 2.62 and yethanol = 7.24.
Cline Black proposed the following model for excess Gibbs energy:Develop the corresponding expressions for ln γa and ln γb. 1 1 --[2] + Axa Bxb = -1 + xaxb(xa - xb)
For isobaric data, you want to account for the temperature change of the activity coeffi cientsin the test for thermodynamic consistency. Develop the following equation to use in place ofEquation (7.50): (1/T),-1 Ah mix Ah mix |- ( ) - = I = = - T+ ( ) d In dT RT R 0 T-0 (1/7) -0
The activity coeffi cients at infi nite dilution of a mixture of hexane(a) and toluene(b) at 30°C are Estimate the fugacity of hexane in mixtures with the following compositions at 1 bar:(a) 20% liquid hexane;(b) 50% liquid hexane;(c) 90% liquid hexane. Ya 1.27 and yo = = 1.34.
Consider a binary liquid mixture of 40 mole % 1-propanol (1) in water (2) at 25°C and 100 bar. For this system, the Henry’s law constant for 1-propanol has been estimated to be:The density of pure liquid 1-propanol is 0.80 g/cm3.(a) As best as you can, determine the fugacity of 1-propanol in
Your supervisor has assigned you to obtain parameters A and B for the three-suffi x Margules equation to input in the company’s phase equilibrium computer database. The binary mixture of interest is benzene(a) in 1-propanol(b) at 75°C. You cannot fi nd any values in the literature for the
You wish to determine the fugacity of a in a liquid mixture with 1 mole of a and 4 moles of b at 30 kPa and 20°C. At this temperature, the saturation pressure of pure a is 50 kPa. The excess Gibbs energy for a mixture of a and b has been fi t to the following relation: gE = (0.25x + 0.5x)x a Xb
Calculate the activity coeffi cients of a binary mixture of 30 mol% acetone (1) in water (2) at 61.1°C using the UNIQUAC activity coeffi cient model. Compare the values to the experimentally measured values, The UNIQUAC parameters are reported as follows: exp = = 2.30 and 1 YExp exp = 1.32.
Calculate the activity coeffi cients of a binary mixture of 41.5 mol% ethanol (1) in benzene (2) at 45°C using the UNIQUAC activity coeffi cient model. The UNIQUAC parameters are reported as follows:The system pressure under these conditions has been reported to be 309.59 torr and a mole fraction
Calculate the activity coeffi cients of a binary mixture of 20.0 mol% acetone (1) in chloroform (2) at 35.17°C using the UNIQUAC activity coeffi cient model. The UNIQUAC parameters are reported as follows:The system pressure under these conditions has been reported to be 261.9 torr and a mole
Wilson parameters for mixtures of ethanol (1), 1-propanol (2), and water (3) at 60°C are reported as follows:Calculate the fugacity of ethanol in a liquid mixture containing 30% ethanol, 20% 1-propanol, and 50% water at 60°C and 1 bar. y = 1.216 Ag1 = 0.617 3 = 0.203 131 = 0.838 23 = 0.048 132 =
Estimate the fugacity of ethanol in a liquid mixture containing 30% ethanol, 20% 1-propanol, and 50% water at 8°C and 1 bar using the Wilson equation. Wilson parameters at 60°C are given in Problem 7.38.Problem 7.38You wish to calculate in a mixture of 25.0 mole % propylene (1) and 75.0 mole %
Enthalpy of mixing data for binary mixtures of water (1) and acetone (2) have been fi t to the following equation:where Δhmix has units of J/mol. At 60°C, the activity coeffi cient of water in an equimolar mixture of water and acetone is 1.65. Estimate the activity coeffi cient of water in an
In Problem 6.48 heats of mixing for binary mixtures of solid-phase cadmium (Cd) and tin (Sn) were reported as:where, XCd and XSn are the cadmium and tin mole fractions, respectively. If we assume cadmium and tin form a regular solution, calculate the activity coeffi cient of cadmium in a mixture of
In the ThermoSolver software that comes with the text, go to the Models for gE—Parameter Fitting menu. Find best-fi t model parameters for the ethanol (a) and water (b) system at 74.79°C for the following activity coeffi cient models:(a) two-suffi x Margules(b) three-suffi x
Repeat Problem 7.75 for pentane (a) and acetone (b) at 25°C.Problem 7.75In the ThermoSolver software that comes with the text, go to the Models for gE—Parameter Fitting menu. Find best-fi t model parameters for the ethanol (a) and water (b) system at 74.79°C for the following activity coeffi
Repeat Problem 7.75 for chloroform (a) and heptane (b) at 25°C.Problem 7.75In the ThermoSolver software that comes with the text, go to the Models for gE—Parameter Fitting menu. Find best-fi t model parameters for the ethanol (a) and water (b) system at 74.79°C for the following activity
An aqueous emulsion of perfl ubron (perfl uorooctyl bromide) and water is being considered for an artifi cial blood. The perfl ubron emulsion contains 24 g perfl ubron per 100 cm3 solution. A plot of the amount of O2 dissolved in the artifi cial blood (mL/100 cm3 ) versus O2 partial pressure at
Determine the fugacity and the fugacity coeffi cient for saturated steam at 1 atm.
Determine an expression for the fugacity of a pure gas from the van der Waals equation of state.
Determine the fugacity and the fugacity coeffi cient of ethane at a pressure of 50 bar and a temperature of 25°C using generalized correlations.
Consider a binary gas mixture composed of species a and b. Determine an expression for the fugacity of species a from the van der Waals equation of state. Use mixing rules given by Equations (7.15), (7.16), and (7.18). dimitr = auty = Vaway (7.15) (7.16)
Show that the two-suffi x Margules equation satisfi es the Gibbs–Duhem equation.
Provide a molecular explanation for the form of the two-suffi x Margules equation:Show how the relative magnitude of the unlike interactions to the like interactions determines the value of two-suffi x Margules parameter, A. gE = Axaxb
Consider a binary mixture of cyclohexane(a) and dodecane(b) at 39.33°C. Activity coeffi cients at infi nite dilution have been reported to be:Use these data to estimate the value of the two-suffi x Margules parameter A. and, Ya = 0.88 Y = 0.86
Consider a binary system of dissolved gas a in solventb. Henry’s law is used for the reference state for a and the Lewis/Randall reference state forb. If the activity coeffi cient for b is given by the two-suffi x Margules expression:determine the expression for the activity coeffi cient of
Prepare a plot of the activity coeffi cients of a binary mixture of ethanol (1) and n-heptane (2) versus ethanol mole fraction in a binary mixture at 50°C using the UNIQUAC activity coeffi cient model. The UNIQUAC parameters are reported as follows:Compare the results to the following set of
Enthalpy of mixing data6 for benzene (1)–cyclohexane (2) at 18°C has been fi t to the following expression:The two-suffi x Margules parameter A at 10°C is 1401 [J/mol]. Estimate A at 60°C. Compare to data from the literature. Ahmix = 3250x1x2[J/mol] (E7.13A)
You need to separate toluene from a vapor-phase mixture of toluene and cyclohexane. Your colleague suggests that because the boiling point of toluene is higher, all you need to do is lower the temperature to a value between the boiling points of toluene and cyclohexane. In that way, you can
A piston–cylinder assembly contains components 1 and 2 in vapor–liquid equilibrium. Assume ideal solution and ideal gas behavior. The composition of species 1 in the liquid is x1 = 0.50 and in the vapor is y1 = 0.25. Your technician performs an experiment where she adds a weight to the piston
A piston–cylinder assembly contains a pure mixture of liquid water and steam in equilibrium.A second species that has negligible vapor pressure is mixed into the liquid at a constant temperature and constant pressure. Describe how the system will respond to maintain equilibrium.
A rigid container contains a pure mixture of liquid water and steam in equilibrium. A second species that has negligible vapor pressure is mixed into the liquid at a constant temperature.Describe how the system will respond to maintain equilibrium.
A closed container contains a two-phase (liquid–vapor) mixture of water and air. The system temperature is 100°C. The mole fraction of water in the vapor is 0.333. Estimate the system pressure.State any assumptions that you make.
For each of the following binary mixtures, describe if the like interactions are stronger, weaker, or the same as the unlike interactions. Explain your reasoning.(a) Activity coeffi cients (Lewis/Randall) versus xa(b) Pxy phase diagram(c) Txy phase diagram In (Y;) 0.0 -0.2 -0.4 -0.6 -0.8 0.0 0.2
From the list of the following species, choose the appropriate binary mixture (group of two species) for each of the following questions.Explain your answers.(a) Consider liquid–vapor equilibrium at 1 bar.(i) What binary mixture will have the largest positive deviations from ideality?(ii) What
The Gibbs energies for the liquid phase and the vapor phase vs. mole fraction a for two systems (system I and system II) follow. These plots are at constant temperature and pressure. What type of behavior does each of these plots correspond to? g T= T P= P System I gvapor gliquid Xa g|| T = T P= P1
Determine whether the following statements are true or false. Explain your choice.(a) A binary liquid mixture contains species a and b. The two species are completely miscible at all temperatures that they exist in the liquid phase (i.e., they just form one liquid phase). This result means that
In the winter, salt is used as a deicer to improve traction on the roads. Use the phase diagram below to explain how this process works. Note that only part of the phase diagram is illustrated.How much salt would you add? To what temperature is this method effective? T[C] 10 O -10 -20 -30 Ice and
A binary mixture of solids a and b is known to form three distinct solid phases: a, b and g.Gibbs energy is plotted vs. mole fraction a for the two systems shown on the next page. Each of these plots is made at constant temperature and pressure. For each system, describe the phases that are present
Rank the following from highest boiling point to lowest boiling point: pure water, 0.05 M NaCl, 0.05 M MgCl2, 0.05 M glucose (C6H12O6). Explain.
Rank the following from highest freezing point to lowest freezing point: pure water, 0.05 M NaCl, 0.05 M MgCl2, 0.05 M glucose (C6H12O6). Explain.
Consider a fl exible container with two compartments, A and B, separated by a semipermeable membrane. The membrane allows movement of water but not solute molecules. For each of the following initial concentrations determine if compartment A will (increase in size/stay the same size/decrease in
Para-xylene (p-xylene) is an important chemical intermediate in the manufacture of polyester fi bers. It is produced in high volume (around 109 kg/year). Consider a mixed stream of 60% m-xylene, 14% p-xylene, 9% o-xylene, and 17% ethylbenzene, as shown in the following fi gure. To manufacture
Construct a Txy phase diagram for a binary mixture of cyclohexane and n-hexane at 1 bar.Assume that the liquid forms an ideal solution.
What is the lowest temperature to which a vapor mixture of 1 mole n-pentane and 2 moles n-hexane at 1 bar can be brought without forming liquid? Assume the liquid forms an ideal solution.
What is the composition of vapor that is in equilibrium with a liquid mixture with the following composition at 250 K? What is the pressure? Assume ideal behavior. Species Propylene Propane n-Butane Isobutane n-Pentane Mole fraction 0.1 0.25 0.2 0.35 0.1
A liquid mixture containing 40% cyclohexane, 20% benzene, 25% toluene, and 15% n-heptane is in equilibrium with its vapor at 1 bar. Determine the temperature and the vapor composition.
A compressed liquid feed stream containing an equimolar mixture of n-butane and isobutane fl ows into a fl ash unit at fl ow rate F. At steady state, 40% of the feed stream is vaporized and leaves the drum as a vapor stream with fl ow rate V. The rest leaves as liquid with fl ow rate L. If the fl

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