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All Textbook Solutions for Fundamentals of Chemical Engineering Thermodynamics (MindTap Course List)

1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16P 17P 18P 19P 20P 21P 22P 23P 24P 25P 26P 27P 28P 29P 30P 31P 32P 1E 2E 3E 4E 5E 6E 7E 8E 9E 10P 11P 12P 13P 14P 15P The classic way to synthesize ammonia is through the gas phase chemical reaction: N2+3H22NH3 This reaction is carried out at high pressures, most often using an iron catalyst. A. Use Equation 2.32 and CP from Appendix D to determine the change in molar enthalpy when nitrogen is compressed from T = 300 K and P = 1 bar to T = 700 K and P = 200 bar. B. Repeat part A for hydrogen. C. What assumptions or approximations were made in step B? Comment on how valid you think the approximations are.17P 18P 19P 20P 21P 22P 23P 24P 25P 26P 27P 29P 10 m3 of saturated steam at T = 150C is mixed with 0.1 m3 of saturated liquid water at T = 150C. How many total kilograms of H2O does the mixture contain?2E 3E 4E 5E 6E 7E 8P 9P 10P 11P 12P 13P 14P 15P 16P 17P 18P 19P 20P 21P 22P 23P 24P 25P 26P 20 lb-mol/min of the compound enters a steady-state boiler as saturated liquid at P = 1 bar. Find the rate at which heat is added if the exiting stream is: A. Saturated vapor at P = 1 atm B. Vapor at P = 1 atm and T = 200F C. Vapor at P = 0.7 atm and T = 200F 28P 29P 30P 31P 1E 2E 3E 4E 5E 7E 8E 9P 10P 11P 12P 13P 14P 15P 16P 17P 18P 19P 20P 21P 22P 23P 24P 25P 26P 27P 28P 29P 30P 31P 32P 33P 34P 1E 3E 5E 6P 7P 8P 9P 10P 13P 14P 15P 16P 17P 18P 19P 1E 2E 3E 4E 6E 7P 8P 9P 10P 11P 12P 13P 14P 15P 16P 17P 18P 19P 20P 21P 22P 23P 24P 25P 26P 27P 28P 29P 1E 2E 3E 4E 5E 6E 7E 8P 9P 10P Imagine a compound has TC = 500 K and PC = 20 bar. Use the Peng-Robinson equation throughout this problem. A. Plot P-V_ at T = 400 K, T = 500 K, and T = 600 K, assuming the compound has = 0. B. Repeat part A for = 0.5. C. Repeat part A for = 1.0. D. What do the plots reveal about the interrelationship between and the P-V_-T behavior of a compound?Consider the chemical compound: CH3CHClCH = CHCHFCH2CH2OH Estimate the normal boiling point, critical temperature, critical pressure, and standard enthalpy of formation of the compound using the Joback method.13P 14P 15P 17P 18P 19P 20P 21P 22P 24P 25P 26P 1E 2E 3E Estimate the boiling points of toluene at pressures of P = 0.1, 0.5, 1, and 5 bar: A. The Antoine equation B. The Clausius-Clapeyron equation, with Hvap = 33.2 kJymol at the normal boiling point of T = 110.7C C. The shortcut equation 5E 6E 7E 8E 9E 10P 11P 12P 13P Compare Problems 8-12 and 8-13. You presumably approached both in exactly the same way. Are you confident in the accuracy of your answers in both cases, or are some of them more questionable than others? Explain.Ten moles of a solid is placed in a piston-cylinder device, and its pressure is maintained constant at P = 0.7 atm throughout the following process. The solid is heated to 47C, at which temperature it melts. It takes 55,000 J of heat to melt the solid completely. The liquid is heated to 75C, at which temperature it boils. It takes 429,000 J of heat to boil the liquid completely. The volume is 0.57 L when melting begins, 0.63 L when melting ends, and 0.64 L when boiling begins. Give your best estimate of each of the following properties of this compound. A. The coefficient of thermal expansion in the liquid phase B. The normal boiling point C. The normal melting point D. The triple point 16P 17P 18P 19P 20P 21P 23P 24P 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E Experimental data is available that shows the excess molar volume of acetone with three different normal alkanes at 298.15 K: n-hexane, n-heptane, and n-octane. Each of the three mixtures shows positive excess molar volumes across the entire composition range. Consider their values in Table E9-11 for an equimolar mixture. Table E9-11 Excess molar volumes for three n-alkane + acetone equimolar systems at 298.15 K. Based on data from Marino, G. et al., Temperature Dependence of Binary Mixing Properties for Acetone, Methanol, and Linear Aliphatic Alkanes (C6C8), J. Chem. Eng. Data, 2001, 46, 728, (2010). From an interactions perspective, describe the trend in the data in Table E9-11.12P 13P 14P 15P 16P 17P The molar volume for a mixture of methanol (1) + water (2) at 298.15 K and 1 bar is given as V_=18.102+18.491x1+4.1506x12 where V_ is in units of cm3/mol. A. What is the partial molar volume of methanol at this T and P when x1 = 0.4? B. What is the pure component molar volume of methanol at this T and P? C. What is the pure component molar volume of water at this T and P? D. Lets assume you have an equimolar mixture of water and methanol. What will be the molar volume of this mixture according to the functional form given in the problem? What will be the Consider the following three liquid mixtures. A. Water + n-propane B. n-hexane + benzene C. Ortho-xylene + para-xylene Which mixtures, if any, do you expect to behave as an ideal solution and why? For those that you do not expect to behave as an ideal liquid solution, explain why.20P 21P 22P 23P Estimate the partial molar enthalpy of sulfuric acid at 140F at the following two compositions using Figure P9-22. A. 30% by wt sulfuric acid B. 80% by wt sulfuric acid You have 100 grams of water at 25C in a container that holds exactly 200 ml. What mass of methanol do you need to add to the system such that the container is filled without overflowing? See the solution of Example 9.5 for additional details.26P 27P 28P Experimental data for the excess molar volume of 1-propanol (1) + 1-hexene (2) system at 298.15 K is provided in Table P9-29. If the pure component densities at 298.15 K are 0.79965 g/cm3 for 1-propanol and 0.66828 g/cm3 for 1-hexene, do the following. A. Plot the solution molar volume as a function of composition of 1-propanol. B. Fit the solution molar volume to an appropriate functional form. C. Determine the partial molar volume for both substances when the system is equimolar. TABLE P9-29 Excess molar volume of 1-propanol (1) + 1-hexene (2) system at 298.15 K (Treszczanowicz, 2010).A Pxy plot means that the pressure is constant. True or False?If you have a Txy plot at a given pressure and have a state point at that same pressure, but above the top-most curve, what is the phase of the state point? What do you call that top-most curve?What two pure component properties are you able to determine from a Pxy plot (or Pxy data table)?On a Txy plot, where does the single vapor phase exist? Select the correct answer from the choices given. A. Above the dew-point curve B. Below the dew-point curve C. Above the bubble-point curve D. Below the bubble-point curve For a mixture of n-butane (1) + n-pentane (2) at 25C, what would be the predicted bubble-point pressure using Raoults Law if your mixture was 20% n-butane by mole? Would you expect Raoults Law to be a good model for this system? Why or why not?6E 7E For a mixture of methyl ethyl ketone (1) + water (2) at 45C, what would be the predicted bubble-point pressure using Raoults Law if your mixture was 20% water by mole? Would you expect Raoults Law to be a good model for this system? Why or why not? Methyl ethyl ketone For the methanol (1) + acetone (2) system at 101.325 kPa, what is the K-factor for each substance at 332 K? What is the relative volatility at 332 K? Use Figure 10-16.10E There are four types of VLE calculations for mixtures: A. Bubble-point temperature B. Bubble-point pressure C. Dew-point temperature D. Dew-point pressure For each of the calculations, list the variables being fixed and the variables being calculated for a binary mixture.For the n-pentane (1) + methanol (2) system at 422.6 K (Wilsak et al., 1987), answer the following questions based on Figure P10-13. A. List the boiling point for the pure components (n-pentane and methanol) at 422.6 K. B. Does this mixture show positive, negative, or no deviations from Raoults Law? Explain why, both graphically and from an interactions standpoint.Consider the n-pentane (1) + methanol (2) system at 422.6 K in Figure P10-13. Four numbered black dots are provided on the Pxy diagram, and they are all at 422.6 K. For each of the four points, report the following information: A. Equilibrium phases (liquid, vapor, or both liquid and vapor) B. Composition of the equilibrium phases C. Amount of the equilibrium phases, assuming 1 mole of the system (overall)15P Consider the 1-hexene (1) + n-hexane (2) system at 328.15 K. Using Raoults Law, predict the system pressure and vapor-phase composition for this mixture and provide a Pxy plot for this mixture. Compare the results of your modeling with the set of experimental data provided for this system in Table P10-16. Plot the data (as points) on the same plot as your model. Is this system properly modeled by Raoults Law? Why or why not? Table P10-16 Experimental data for the 1-hexene (1) + n-hexane (2) system at 328.15 K.Consider the methanol (1) + ethanol (2) system at 101.325 kPa. Using Raoults Law, predict the system temperature and vapor-phase composition for this mixture and provide a Txy plot for this mixture. Compare the results of your modeling with the set of experimental data provided for this system in Table P10-17. Plot the data (as points) on the same plot as your model. Is this system properly modeled by Raoults Law? Why or why not? TABLE P10-17 Experimental data for the methanol (1) + ethanol (2) system at 101.325 kPa.Consider the n-hexane (1) + ethanol (2) system at 1 bar. Using Raoults Law, predict the system temperature and vapor-phase composition for this mixture and provide a Txy plot for this mixture. Compare the results of your modeling with the set of experimental data provided for this system in Table P10-18. Plot the data (as points) on the same plot as your model. Is this system properly modeled by Raoults Law? Why or why not? Table P10-18 Experimental data for then n-hexane (1) + ethanol (2) system at 1 bar.Consider the tetrahydrofuran (1) + n-hexane (2) system at 313.15 K. Using Raoults Law, predict the system pressure and vapor-phase composition for this mixture and provide a Pxy plot for this mixture. Compare the results of your modeling with the set of experimental data provided for this system in Table P10-19. Plot the data (as points) on the same plot as your model. Is this system properly modeled by Raoults Law? Why or why not? Tetrahydrofuran Table P10-19 Experimental data for the tetrahydrofuran (1) + n-hexane (2) system at 313.15 K.Consider the benzene (1) 1 m-xylene (2) system at 310.15 K. Using Raoults Law, predict the system pressure and vapor-phase composition for this mixture and provide a Pxy plot for this mixture. Compare the results of your modeling with a set of experimental data provided for this system from Table P10-20. Plot the data (as points) on the same plot as your model. Is this system properly modeled by Raoults Law? Why or why not? m-xylene Table P10-20 Experimental data for the benzene (1) + m xylene (2) system at 310.15 K.21P One hundred mol/min of an equimolar mixture of 1-propanol (1) + 2-propanol (2) at 75C and 200 kPa is sent to flash distillation unit operating at 75C and 75 kPa. What is the resulting composition and molar flow rate of the stream(s) exiting the flash distillation unit if you model the system using Raoults Law?One hundred mol/min of an equimolar mixture of 1-propanol (1) + 2-propanol (2) at 75C and 200 kPa is sent to flash distillation unit operating at 75C and 55 kPa. What is the resulting composition and molar flow rate of the stream(s) exiting the flash distillation unit if you model the system using Raoults Law?Twenty kmol/hr of an equimolar mixture of n-pentane (1) + 2-propanol (2) at 50C and 200 kPa is sent to a flash distillation unit operating at 50C and 75 kPa. Report the following information assuming Raoults Law is valid. Show that the mixture will flash in the flash distillation unit Report the flow rate and composition of the overhead (i.e.,vapor) stream Report the flow rate and composition of the bottoms (i.e., liquid) stream Which assumption that you made in solving this problem would you characterize as least valid and why?A vapor mixture containing 5 moles of benzene and 5 moles of toluene at 0.5 bar and 100C is isothermally compressed to 1.0 bar. What is the amount and composition of the resulting phase(s)? How would the result change if, instead of 5 moles of benzene and 5 moles of toluene, you had 4 moles of benzene and 6 moles of toluene?A 50/50 (by mole) n-pentane/n-heptane liquid mixture is flashed at 7.34 psia and 325 K. Analysis of the liquid phase leaving the unit reveals that the flow rate for the liquid is 0.882 mol/s. What is the flow rate of the mixture entering the flash distillation unit? What is the flow rate and composition of the vapor leaving the flash distillation unit?A liquid mixture of diethyl ketone (1) and n-hexane (2) is fed into a flash distiller operating at 328 K and 0.4 bar. The feed rate is 2.15 mol/s and the feed is 50% (by mol) of the n-hexane. A. What is the composition and amount of the resulting equilibrium phases? B. If you take the exiting liquid phase from the flash distiller and send it into a second flash distiller operating at 328 K and 0.3 bar, what is the composition and amount of the resulting equilibrium phases? What percentage of the diethyl ketone in the initial feed entering the first flash distiller ends up in the liquid exiting the second flash distiller? C. Which assumption that you made in solving this problem would you characterize as least valid and why?A separation stream off the main reactor effluent contains almost exclusively ethyl benzene, benzene, and toluene at 1 bar and 100C. You determine that the stream flow rate is made up of 34 kg/s of benzene, 10 kg/s of toluene, and 57.75 kg/s of the other component. You send this mixture into a flash distillation unit operating at 0.6 bar and 100C. A. Estimate if this mixture flashes. B. If the mixture flashes, determine the composition and amount of the equilibrium liquid and vapor. C. You send the liquid exiting the flash distillation unit into another flash distillation unit operating at 1.5 bar and 140C. Determine if this mixture flashes. If so, determine the composition and amounts of the equilibrium phases. D. What percentage of the original benzene that left the reactor is now a vapor (you have to consider both flash units).29P 30P The derivation of the expression for the natural logarithm of the activity coefficient of component 1 for a binary mixture modeled by the 1-parameter Margules equation is given in Section 11.6. Please derive the expression for component 2.Derive the expression for the natural logarithm of the activity coefficient for component 1 in a binary mixture modeled by the 2-parameter Margules equation.3E Given an equimolar binary mixture, calculate the activity coefficients for both components from the 2-parameter Margules equation whose parameter values are A12 = 0.5 and A21 = 1.5. What would be the excess molar Gibbs free for this system?5E 6E Calculate the van Laar parameters, L12 and L21, for the benzene (1) + toluene (2) system at 25C through use of the van der Waals equation of state, What would be the value for the activity coefficients of an equimolar mixture of benzene + toluene at 25C?Calculate the van Laar parameters using the Scatchard-Hildebrand approach, M12 and M21, for the benzene (1) + toluene (2) system at 25C. What would be the value for the activity coefficients of an equimolar mixture of benzene + toluene at 25C?Explain why the integral test for thermodynamic consistency is only a necessary condition, while the direct test is a sufficient condition.10E A binary liquid containing mostly component 2 is in equilibrium with a vapor phase containing both components 1 and 2. The pressure of this two-phase system is 1 bar; the temperature is 25C. Estimate x1 and y1 if the Henrys Law constant is equal to 200 bar and the vapor pressure of component 2 at 25C is 0.1 bar.Provide an estimate of the composition of N2 dissolved in water at 298 K. Assume A = 6.52 for the 1-parameter Margules equation for this system and the partial pressure of the Nitrogen is 44.5 atm at this temperature.Resolve Example Problem 11.1, but now include the nitrogen gas into the system. Note the Henrys Law constants for nitrogen in water in Table P11-15: Table P11-15 Henrys Law constants for N2 in water. Based on data from R. Sander, Compilation of Henrys Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry, 1999. sander@mpch-mainz.mpg.de A liquid mixture of 20% by mole benzene and the rest 2-propanol is in equilibrium with its vapor at 69C. Estimate the equilibrium pressure and the composition of the vapor phase. Assume the 1-parameter Margules equation holds. At this temperature, the vapor pressure of the benzene is 530 mm Hg and that of the 2-propanol is 434 mm Hg. Note that the system does form an azeotrope at this temperature whose composition is 61% by mole benzene (at a pressure of 685 mm Hg) (Storonkin and Morachevsky, 1956) If you make an assumption, please justify your assumption based on the results.You are interested in finding the pressure at which the first bubble of vapor will form from a liquid mixture of methanol (1) and 2-methyl-1-propanol (2) (49% by mole methanol) at 50C. The Margules parameters for this mixture are A12 = 0.2565 and A21 = 0.2404 (Gmehling and Onken, 1977). Note that the vapor pressure of methanol is 422 mm Hg and that for 2-methyl-1-propanol is 56 mm Hg at 50C. Find the pressure and vapor-phase composition.For a chloroform (1) + ethanol (2) system at 55C, a Margules equation has been written as G_E/RT=(0.5579x1+1.5254x2)x1x2 (Gmehling and Onken, 1977). Calculate the pressure and vapor-phase composition of the system when x1 = .25. What would be the predicted pressure and vapor-phase composition if you treated the liquid as an ideal solution?You are interested in finding the pressure at which the first bubble of vapor will form from a liquid mixture of ethanol (1) and benzene (2) (49% by mole ethanol) at 313 K. The Margules parameters for this mixture are A12 = 2.173 and A21 = 1.539, while the Wilson parameters for this mixture are a12/R = 653.13 K and a21/R = 66.16 K. Find the pressure and vapor-phase composition using three ways. A. The 2-parameter Margules equation B. The Wilson equation C. Ideal solution The azeotrope of a binary mixture, being an important point on a mixture phase diagram, is often used for parameter estimation. To that end, use the azeotropic information for the acetone (1) + cyclohexane (2) system at 308.15 K to determine the A parameter of the 1-parameter Margules equation. Then plot the Pxy predictions from this model and compare it to the experimental data in Table P11-20. Note that you will need to plot the experimental data first to estimate the location of the azeotrope. Table P11-20 Vapor-liquid equilibrium of acetone (1) + cyclohexane (2) at 308.15 K.Consider the experimental data in Table P11-21 for the ethyl acetate (1) + cyclohexane (2) system at 293.15 K. Please fit this system to the 2-parameter Margules equation and plot the Pxy curve for the system (along with the experimental data and Raoults Law predictions). Also, plot the natural logarithm of activity coefficients and the excess molar Gibbs free energy (divided by RT) both on the same curve. Table P11-21 Vapor-liquid equilibrium of ethyl acetate (1) + cyclohexane (2) at 293.15 K.In the sizing of separation equipment, you need to know the vaporliquid equilibrium for the benzene (1) + acetonitrile (2) system. You have data for this system at 293.15 K, but not at your desired temperature, which is 318.15 K. You also know this system has an azeotrope at 293.15 K at about 12.7 kPa and 53% benzene. A. Use the Wilson equation to fit all of the experimental data in Table P11-22 at 293.15 K. B. Use the Wilson parameters determined from part (A) to predict the system behavior at 318.15 K. C. Now that you have predicted the behavior (part (B)), how well does your prediction compare with the experimental data for this azeotrope at 318.15 K, which is P = 37.1 kPa and x1 = y1 = 0.52?You are interested in evaluating how well you can predict the phase-behavior of a system using an excess molar Gibbs free energy model. Here, use the van Laar predictions (from the VDW-defined parameters) relative to fitting the data (in Table P11-23) with the van Laar model for the methanol (1) + water (2) system at 328.15 K. What is your conclusion based on these results? TABLE P11-23 Vapor-liquid equilibrium of methanol (1) + water (2) at 328.15 K.Compare the van Laar predictions if using VDW-defined parameters relative to those from Scatchard-Hildebrand in order to calculate the Pxy diagram of the benzene (1) + m-xylene (2) system at 310.15 K Plot the results from both approaches as well as the experimental data from Table P11-24. Table P11-24 The vapor-liquid equilibrium of benzene (1) + m-xylene (2) at 310.15 K.You desire to flash 20 moles/min of a liquid mixture containing 20% by mole chloroform (1) and 80% by mole ethanol (2) at 332.4 K in a flash distillation unit operating at 70 kPa. You do not know a lot about this mixture at this temperature, other than the fact it exhibits an azeotrope (x1 = y1 = 0.84 at 101.3 kPa; Chen, 1995). Since this system forms an azeotrope, you know not to treat it as an ideal solution. Model the system using the 1-parameter Margules equation and estimate whether the mixture flashes at 332.4 K and 70 kPa. If it does flash, calculate the resulting flowrate and composition of the stream(s) leaving the flash distillation unit.Your company needs to evaluate the separation of an equimolar mixture of ethanol (1) + n-hexane (2) at 318.15 K. While looking at some company notebooks, you find data for this system at 318.15 K as follows: Table P11-26 Vapor-liquid equilibrium of ethanol (1) + n-hexane (2) at 318.15 K. You show this to your boss and she mentions Oh yeah . . . I remember when this was done. It was to determine infinite dilution values quickly in order to parameterize a model. I dont think we ever did that, however. You should do this to see if we can flash the mixture at 65 kPa. Since you follow the instructions of your boss, use the data in Table P11-26 to parameterize the 2-parameter Margules equation and determine if the mixture will flash at 65 kPa and 318.15 K. If it does flash, determine the amount and composition of the stream(s) exiting the unit, if the feed enters at 50 mol/min.In a process you need to evaluate the flash separation of an equimolar mixture of 1,3-dioxolane (1) + n-heptane (2) at 70C. However, you can only find experimental data at 40C. From your thermodynamics class, you remember that the Wilson equation can be used to predict behavior at one temperature if you parameterize your system at another temperature. This seems to be the perfect opportunity to use the Wilson equation. A. Using the data in Table P11-27, parameterize the system using the Wilson equation at 40C. B. Determine the parameters for this system at70C. C. Run a flash calculation at 70C and 675 mm Hg on an equimolar feed of 100 mol/min. Determine the amount and composition of the stream(s) leaving the flash distillation unit. D. After completing parts (A, B, and C), you find experimental data for this system at 70C. You notice the following: Pbubble (x1 = 0.5) = 665 mm Hg; Pdew (y1 = 0.5) = 517 mm Hg. Discuss the results from part (C) in light of this information.You desire to flash separate 10 mol/s of an equimolar liauid mixture of 1-butene (1) + n-heptane (2) at 100 kPa and 0 C. If your flash distillation unit operates at 50 kPa and 0 C, what is the flow rate and composition of the stream(s) exiting the flash distillation unit? Use the van Laar equation with van der Waals predicted parameters to account for the deviations of this mixture from the ideal solution model.In a process analysis application, you are working with the di-n-propyl ether (1) and 2-propanol (2) system at 25C. You think you have an error in the spreadsheet you have been working with, but you cant seem to find the problem. After a while, you begin to wonder if the data you are using is thermodynamically consistent. Not that you are suspicious of the data, but youve checked everything else by this point. For the data presented in Table P11-29, examine the thermodynamic consistency using both the integral test and direct test. TABLE P11-29 Vapor-liquid equilibrium of di-n-propyl ether (1) + 2-propanol (2) at 298.15 K.1E

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