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All Textbook Solutions for Fundamentals of Chemical Engineering Thermodynamics (MindTap Course List)
Derive Equation 12.31. which is the expression for the mixture fugacity coefficient of component 1 in a binary mixture described by the virial equation.For an equimolar acetone (1) + methyl ethyl ketone (2) mixture, calculate the van der Waals and Peng-Robinson equation of state parameters at 35C.For an equimolar mixture of n-hexane (1) + benzene (2) at 150C and 5 bar, estimate the molar volume of the mixture three ways: A. Ideal gas law B. van der Waals equation of state C. Peng-Robinson equation of stateFor an equimolar mixture of water (1) + chloroform (2) mixture at 200C and 5 bar, estimate the molar volume of the mixture three ways: A. Ideal gas law B. van der Waals equation of state C. Peng-Robinson equation of stateFor a binary mixture you desire to produce a Txy diagram from an equation of state. List the equations needed and the unknown variables8EThe binary interaction parameters for the Peng-Robinson equation of state are reported (Moshfeghian et al., 1992) for the following systems: Ethane + isobutane: k12 = 20.0102 Trifluorochloromethane + n-butane: k12 = 0.0735 Ammonia + water: k12 = 0.2694 Does the magnitude of the k12 values make sense to you? Please explain.You need to determine the binary interaction parameter (k12) for the Peng-Robinson equation of state for the tetra-fluoromethane + trifluorochlo- romethane system at 250 K and 225 K. The literature lists the following values (Abu-Eishan, 1991): Tetrafluoromethane What values will you report? Which values will you have the most confidence in and why?An equimolar mixture of methane and propane is discharged from a compressor at 5500 kPa and 90C at a rate of 1.4 kg/s. If the velocity in the discharge line is not to exceed 30 m/s, what is the minimum diameter of the discharge line?Consider the propane (1) + n-butane (2) system at 508C. Using a gamma-phi modeling approach, predict the Pxy diagram for the system using the van Laar equation and the virial equation. Compare the predicted values with the experimental data provided (on the same plot) in Table P12-14. Also add the Raoults Law predictions and comment on the utility of the gamma-phi modeling approach for this system at this state. Table P12-14 Vapor-liquid equilibrium of propane (1) 1 n-butane (2) at 508C.Consider the 1,1,1- trifluoroethane [R-143a] (1) + n-butane (2) system at 508C. Using a gamma-phi modeling approach, calculate the Pxy diagram for the system using the 2-parameter Margules equation and the virial equation. Compare the predicted values with the experimental data provided in Table P12-15 (on the same plot). Also, please provide two additional modeling approaches to the plot. 1. Model the system using modified Raoults Law (ideal gas for the vapor). This includes calculating the activity coefficients assuming an ideal gas for the vapor (as in Chapter 11). 2. Model the system using Raoults Law. Table P12-15 Vapor-liquid equilibrium for R-143a (1) + n-butane (2) at 50C.Predict the Pxy behavior for a mixture of propane (1) + isobutane (2) at 30C using the Peng-Robinson equation of state. Compare the predicted values with experimental data as given in Table P12-16. Table P12-16 Vapor-liquid equilibrium of propane (1) + isobutane (2) at 30C.Predict the Pxy behavior for a mixture of pentafluoroethane [R-125] (1) + isobutane (2) at 308C using the Peng-Robinson equation of state. Compare the predicted values with experimental data given in Table P12-17. How would you suggest improving the modeling results from the Peng-Robinson equation relative to the experimental data? Table P12-17 Vapor-liquid equilibrium of R-125 (1) + isobutane (2) at 30C.Consider the pentafluorethane [R-125] (1) + isobutene (2) system at 308C. Using a gamma-phi modeling approach, calculate the Pxy diagram for the system using the 2-parameter Margules equation and the virial equation. Compare the predicted values with the experimental data provided in Table P12-18 (on the same plot). Also please provide two additional modeling approaches to the plot. 1. Model the system using modified Raoults Law (ideal gas for the vapor). This includes calculating the activity coefficients assuming an ideal gas for the vapor (as in Chapter 11). 2. Model the system using Raoults Law. Table P12-18 Vapor-liquid equilibrium of R-125 (1) 1 isobutane (2) at 30C.You work in a developing nation for a large chemical company. Your division works on refrigerants and foam-blowing agents. You have need to correlate a set of data for the trifluoromethane (1) + trifluorochloromethane (2) system at 31.9 F. You know the following about your system: Using a gamma-phi modeling approach, calculate the Pxy diagram for the system using the Wilson equation and the virial equation. Compare the predicted values with the experimental data provided (on the same plot) in Table P12-19. Also, please provide two additional modeling approaches to the plot. 1. Model the system using modified Raoults Law (ideal gas for the vapor). This includes calculating the activity coefficients assuming an ideal gas for the vapor (as in Chapter 11). 2. Model the system using Raoults Law. Table P12-19 Vapor-liquid equilibrium of trifluoromethane (1) + trifluorochloromethane (2) at 31.9F.20PPredict the Txy behavior for a mixture of ethanol (1) + 1-butanol (2) at 101.33 kPa using the Peng- Robinson equation of state Compare the predictions to the experimental data given in Table P12-21. Is the Peng-Robinson equation of state a reasonable model for this system at this state? Please explain. Table P12-21 Vapor-liquid equilibrium of ethanol (1) 1 1-butanol (2) at 101.33 kPa.Predict the Txy behavior for a mixture of acetone (1) + 1-hexene (2) at 101.33 kPa using the Peng-Robinson equation of state. Compare the predictions to the experimental data given in Table P12-22. Determine an optimal binary interaction value by defining an objective function in terms of the temperature (it can be called OBJ_T). Is the Peng-Robinson equation of state a reasonable model for this system at this state? Please explain. Table P12-22 Vapor-liquid equilibrium of acetone(1) + 1-hexene (2) at 101.33 kPa.Predict the Pxy behavior for a mixture of diethyl ether (1) + methanol (2) at 303.15 K using the Peng-Robinson equation of state. Compare the predictions to the experimental data given in Table P12-24. Using the OBJ_P objective function, calculate an optimal binary interaction parameter. Is the Peng-Robinson equation of state a reasonable model for this system at this state? Please explain. Table P12-24 Vapor-liquid equilibrium of diethyl ether (1) + methanol (2) at 303.15K.Predict the Pxy behavior for a mixture of cyclohexane (1) + 1-butanol (2) at 383.15 K using the Peng-Robinson equation of state. Compare the predictions to the experimental data given in Table P12-25. Determine a best fit binary interaction parameter (k12) that best matches the equation of state pressures to the experimental pressures. Plot those new predictions on the same curve. Comment on your results. Table P12-25 Vapor-liquid equilibrium of cyclohexane (1) + 1-butanol (2) at 383.15K.Predict the Pxy behavior for a mixture of acetone (1) + 2-propanol (2) at 328.15 K using the Peng-Robinson equation of state. Compare the predictions to the experimental data given in Table P12-26. Determine a best fit binary interaction parameter that best matches the equation of state pressures to the experimental pressures. Plot those new predictions on the same curve. Comment on your results. Table P12-26 Vapor-liquid equilibrium of acetone (1) 1 2-propanol (2) at 328.15K.You are interested in the location of the azeotrope for the acetonitrile (1) + benzene (2) system at 346.85 K. However, you only have that information for this system at 318.15 K. At that state (318.15 K) the azeotropic pressure is 37.197 kPa, while the azeotrope is located at x1 = y1 = 0.53 (Palmer and Smith, 1972). Use this information to predict the azeotropic pressure and composition at the temperature of interest (346.85 K). [Note: P at the azeotrope (346.85 K) = 101.325 kPa; x1 = y1 = 0.44 (Lecat, 1946)] Solve the problem using the Peng-Robinson equation of state.28PIn Problem 12-18 in this section, you used a gamma-phi modeling approach for the pentafluoroethane [R-125] (1) 1 isobutane (2) system at 30C. There (if you solved that problem), you realized the benefit of incorporating a gamma-phi approach (i.e., treating the vapor phase as a real gas rather than an ideal gas) as compared to using modified Raoults law. In this problem repeat the gamma-phi modeling, but treat the vapor-phase as an ideal solution. Here, you are not including the composition effects on the fugacity coefficient, but modeling it as a pure component at the mixture temperature and pressure. Plot both results (the full gamma-phi approach from Problem 12-18 and the current approach) as well as the experimental data (as symbols). Additionally, report the following information in tabular form: The experimental activity coefficients for both approaches The ratio of the mixture fugacity coefficient of component i to the saturation fugacity coefficient of component i What can you conclude about the ideal solution approach to the vapor phase in the context of this problem? Table P12-29 Vapor-liquid equilibrium of R-125 (1) 1 isobutane (2) at 30C.Use - approach to model the vapor-liquid equilibrium of an ethyne [acetylene] (1) + 1, 1 difluoro ethane [R-152a] (2) system at 303.2 K. Treat the liquid using the 2-parameter Margules equation and the vapor as an ideal solution (described by the virial equation). Report the following: Raoults Law predictions Modified Raoults Law predictions (ideal gas for the vapor phase) - modeling results Experimental data as symbols given in Table P12-30 Table P12-30 Vapor-liquid equilibrium of ethyne (1) + R-152a (2) at 303.2K.N-formylmorpholine can be used as a solvent in an extraction process for producing high-purity aromatic compounds. To that end, liquid-liquid equilibrium data has been prepared for this compound with a variety of aromatics, including methylcyclopentane. Using the LLE diagram in Figure E13-1 for the methylcyclopentane (1) + N-formylmorpholine (2) system, answer the following questions: A. For an equimolar mixture at 320 K, what is the composition of the stable phase(s)? B. For an equimolar mixture at 420 K, what is the composition of the stable phase(s)? C. Estimate the UCST for this system and the composition of the UCST. D. Provide the structure for both compounds. By examining the structure, explain why this system would produce a miscibility gap. FIGURE E 13-1 Liquid-liquid equilibrium for the methylcyclopentane + N-formylmorpholine system.For an ethylene glycol n-butyl ether (1) + water (2) system at 360 K with 70% by mass water, determine if the system is one stable liquid phase or two stable liquid phases at equilibrium. If the latter, provide the mass fraction of the co-existing phases.3EFor an ethylene glycol n-butyl ether (1) + water (2) system at 340 K with 80% by mass water, determine if the system is one stable liquid phase or two stable liquid phases at equilibrium. If the latter, provide the mass fraction of the co-existing phases and the amount of each phase.For a propylene glycol n-propyl ether (1) + water (2) system at 335 K with 80% by mole water, determine if the system is one stable liquid phase or two stable liquid phases at equilibrium. If the latter, provide the mole fraction of the co-existing phases.6E8EWill the 2-parameter Margules equation show a miscibility gap for a system described by the following parameters: (A12 = 2.1 and A21 = 3.2)?10E11E12EFor the copper (1) + silver (2) system, identify the type and number of stable phases at equilibrium and their composition. a. 30 wt% copper and 1000C b. 70 wt% copper and 600C c. 70 wt% copper and 825C Figure 13-15 The solidliquid equilibrium for the copper + silver system. The eutectic composition is 28.1% by weight copper.For the copper (1) + silver (2) system, identify the number of stable phases and their composition at the eutectic. Figure 13-15 The solidliquid equilibrium for the copper + silver system. The eutectic composition is 28.1% by weight copper.Liquidliquid equilibrium is realized for the system carbon tetrachloride and water at 258C. The aqueous-rich phase contains 0.083 wt% organic and the organic-rich phase contains 0.011 wt% water. Estimate the activity coefficient of the carbon tetrachloride in the aqueous phase and the water in the organic phase.17PGiven the 1-parameter Margules equation, plot the molar Gibbs free energy of mixing as a function of x1 for three temperatures: 325 K, 300.7 K, and 250 K on the same plot. Determine if there is a miscibility gap at each of the three temperatures. For this study, let the product of the Margules parameter (A) and RT be equal to 5000 J/mol.19PUsing the double-tangency method, determine if the following systems (defined by their Margules equation parameter values) exhibit a miscibility gap. If so, identify the composition of the coexisting phases. A. A12 = 2.5; A21 = 3.0 B. A12 = 1.2; A21 = 3.0 C. A12 = 3.3; A21 = 0.3 D. A12 = 2.0; A21 = 1.4Does a mixture of water (1) and 1-butanol (2) form a miscibility gap at 92C? If it does, what is the range of compositions over which this miscibility gap exists? Note: You know that the van Laar parameters for this system are as follows: L12 = 1.2739 and L21 = 3.9771 (Gmehling and Onken, 1977).The infinite-dilution activity coefficients for the 1-butanol (1) + p-xylene (2) mixture at 333.15 K are 1=7.2360 and 1=4.9720 (Prasad, 1998). Will the 2-parameter Margules equation predict a miscibility gap for this system at this temperature? If so, what is the composition of the equilibrium phases?The infinite dilution activity coefficients for the methanol (1) + n-heptane (2) mixture at 30C are 1=84.20 (Wobst et al., 1992) and 2=35.10 (Gmehling et al., 1986). You know that this system shows a miscibility gap at this temperature (x1=.167; x1=.884) (Sorensen and Arlt, 1979). Will the 2-parameter Margules equation predict a miscibility gap for this system? If so, what is the composition of the equilibrium phases and how do they compare with the experimental data?24PAt 10C, n-pentane (1) + water (2) shows a miscibility gap. The composition of the phases in equilibrium is as follows: x1=0.00107 and x1=0.0184, where is for the water-rich phase and is for the organic-rich phase (Sorensen and Arlt, 1979). Estimate the pressure and composition where this mixture would show vapor-liquid-liquid equilibrium at this temprature.Estimate the pressure and composition for VLLE for the diethyl ether (1) + water (2) system at 35C. Assume the liquid can be modeled by the 2-parameter Margules equation where A12 = 4.62 and A21 = 3.35 (Villamanan et al., 1984). If you treated the liquid as immiscible, how would your results change?27PProduce the SLE phase diagram for the m-chloronitrobenzene (1) + p-chloronitrobenzene (2) system at 1 atm. Treat the liquid phase as an ideal solution and the solid phase as immiscible. On each section of the phase diagram, denote which phases are in equilibrium. Please plot your phase diagram using component 1 as the independent variable. What is the eutectic temperature and composition for this system? If you have an equimolar liquid mixture and cool it until you meet the liquidus line, what is the composition of the solid precipitate and the temperature at which this occurs?29PProduce the SLE phase diagram for the p-dichlorobenzene (1) + p-dibromobenzene system at 1 atm. You will do the modeling in two ways and answer each part of the question. Some helpful data are provided in Table P13-30a: TABLE P13-30a Relevant pure component data for p-dichlorobenzene and p-dibromobenzene at 1 atm. 1 Heat of melting and molar volume data are from Yaws, 2003. 2 Heat of melting data is from the NIST Webbook (Linstrom and Mallard, 2012). Molar volume data are from Hildebrand, 1919. 3 Enthalpy of vaporization data are estimated using the Antoine equation from the NIST Webbook and the Clausius-Clapeyron equation. A. Treat the liquid phase as an ideal solution and the solid phase as immiscible. Please plot your phase diagram using the p-dichlorobenzene as the independent variable. What is the eutectic temperature and composition from the model? Compare your work with the experimental data provided in Table P13-30b. B. Treat the liquid phase as described by regular solution theory using the Scatchard-Hildebrand approach and the solid phase as immiscible. Please plot your phase diagram using the p-dichlorobenzene as the independent variable. What is the eutectic temperature and composition from this model? Compare your work with the experimental data provided in Table P13-30b. C. If you have a liquid mixture that is 76% p-dichlorobenzene and cool it until you meet the liquidus line, what is the composition of the solid precipitate and the temperature at which this occurs for both models? How does this compare to the experimental result? TABLE P13-30b Solid-liquid equilibrium for the p-dichlorobenzene + p-dibromobenzene system at 1 atm.Determine the equilibrium constant at T = 298.15 K for each of the following reactions: A. Formation of ethanol from ethylene and water: C2H4(g)+H2O(g)C2H5OH(g) B. Dehydrogenation of cyclohexane to form benzene: C6H12(g)C6H6(g)+3H2(g) C. Combustion of methane: CH4(g)+2O2(g)CO2(g)+2H2O(g)Determine the equilibrium constant at T = 298.15 K for each of the following reactions: A. Formation of ethanol from ethylene and water: C2H4(g) + H2O(g) C2H5OH(g) B. Dehydrogenation of cyclohexane to form benzene: C6H12(g) C6H6(g) + 3H2(g) C. Combustion of methane: CH4(g) + 2O2(g) CO2(g) + 2H2O(g) 14-2. For each of the three reactions listed in Exercise 14-1, use the shortcut van t Hoff equation to compute the equilibrium constant at T = 500 K.Determine the equilibrium constant at T = 298.15 K for each of the following reactions. A. 2NO(g)+O2(g)N2O4(g) B. 3O2(g)2O2(g) C. 2SO2(g)+O2(g)2SO3(g)4E5E6E8EFor the following gas phase reaction, CH4(g)+2H2O(g)CO2(g)+4H2(g) A. Find the equilibrium constant at T = 300C using the shortcut van t Hoff approach. B. Find the equilibrium constant at T = 300C using the rigorous approach.12EA closed system reactor initially contains two moles of SO2 and two moles of O2, and the following reaction is carried out until it reaches equilibrium: 2SO2(g) + O2(g) 2SO3(g) A. For a constant reaction pressure of 1 bar, plot the final number of moles of SO3 as a function of temperature over the range 300 to 1000 K using the shortcut van t Hoff equation. B. Repeat part A for pressures of 2, 5, 10, and 25 bar. Assume the system is an ideal mixture of real gases.15PReactants A and B combine to form product P in the vapor phase reaction: A +B P But a side reaction also occurs, forming by-product U: 2A U The Gibbs free energy and enthalpy of each compound at T = 300 K and P = 1 bar are given in Table P14-17. It is reasonable to assume that both reactions have CP = 0 and that A, B, P, and U form ideal solutions. These reactions are carried out in an isothermal batch reactor at a constant pressure of 1 bar. Find the contents of the reaction at equilibrium for each of the following. A. The reactor is at T 5 300 K and initially contains 10 moles each of A and B. B. The reactor is at T 5 500 K and initially contains 10 moles each of A and B. C. The reactor is at T 5 300 K and initially contains 15 moles of B and 5 moles of A. D. The reactor is at T 5 500 K and initially contains 15 moles of B and 5 moles of A. E. The reactor is at T 5 500 K and initially contains a total of 20 moles of reactants, A and B. What initial composition produces the maximum number of moles of P at equilibrium? TABLE P14-17Reactants A and B combine to form product P in the liquid phase reaction: A + B P But P reacts further to form an undesired by-product U: 2P U The Gibbs free energy and enthalpy of each compound at T = 300 K and P = 1 bar are given in Table P14-18. It is reasonable to assume that both reactions have CP = 0 and that A, B, P, and U form ideal solutions. The feed entering a steady-state reactor is 1000 mol/hr each of compounds A and B. The reactor is at a uniform pressure of 1 bar. A. Determine the equilibrium composition of the exit stream at 300 K. B. Determine the equilibrium composition of the exit stream at 600 K. C. The second reaction has a larger equilibrium constant than the first, yet there is, at equilibrium, more P than U. Why? TABLE P14-18Thermal decomposition of propane can progress by two different gas phase reaction pathways: (R1): C3H8 C2H4 + CH4 (R2): C3H8 C3H6 + H2 10 mol/s of propane enter a reactor in which R1 and R2 occur simultaneously. The exiting stream is at equilibrium. Find the composition of the exiting stream if the reactor is at A. T = 500 K and P = 1 bar. B. T = 1000 K and P = 1 bar. C. T = 1000 K and P = 5 bar.20PEthanol can be converted into either ethylene or acetaldehyde, by the following pair of reactions: C2H5OH C2H4 + H2O C2H5OH CH3CHO + H2 But ethylene and acetaldehyde can also be converted into butadiene: C2H4 + CH3CHO C4H6 + H2 A reactor initially contains 10 moles of pure ethanol. Assuming all three of these reactionsand no othersoccur, find the equilibrium composition of the reactor for the following. A. The reactor is at T = 500 K and P = 1 bar. B. The reactor is at T = 1000 K and P = 1 bar. C. The reactor is at T = 500 K and P = 5 bar. State any assumptions you make, and indicate the source of any data not obtained from the Appendices.This example revisits the pair of reactions in Example 14-2. 4NH3 + 5O2 4NO + 6H2O 2NO + O2 2NO2 100 mol/min of ammonia and 150 mol/min of oxygen enter an isobaric steady state reactor at T = 800 K. A. If the reactions progress to equilibrium at P = 1 bar and T = 800 K, what is the composition of the exiting stream, and at what rate is heat added to or removed from the reactor? B. Repeat part A for a reactor pressure of 3 bar. Assume ideal gas behavior at this pressure.You have 1.5 moles of pure water and 1 mole of CO, both at 258C and 1 bar. You want to mix them together to make carbon dioxide by the following gas phase reaction at 500 K: CO + H2O CO2 + H2 Once the reaction is at equilibrium, you want to heat up the resulting mixture to 750 K. This heating is done quickly enough that it can be assumed no reaction occurs; the equilibrium composition at 500 K is still the composition at 750 K. The entire process is to be carried out at 1 bar. What is the TOTAL heat load required for this process (from 258C to 750 K)? Will you be adding heat overall or removing heat?