- Consider a mixture of nitrogen(1) + n-butane(2) for each of the options: (i) 395K and 2 MPa; (ii) 460 K and 3.4 MPa; (iii) 360 K and 1 MPa.(a) Calculate the fugacity coefficients for each of the
- Thermodynamic data for Gibbs energy of formation is shown below (kJ/mol for molal standard states) at 298.15 K. A saturated solution of NaCl is approximately an ideal solution.(a) Use the Gibbs
- Suppose 0.1 mol of CO2 were mixed with 0.9 mol of Cl2 and 1 liter of water. What would be the concentrations of the aqueous species and the mole fractions in the vapor phase at 0.8 atm in that case?
- Corrosion resistant alloys (such as nickel alloys and stainless steels) can be susceptible to crevice corrosion in solutions where no corrosion is observed in the bulk solution. For example, nickel
- Ruthenium (Ru) is a strong oxidation catalyst for organic compounds typically in the form RuO4(aq) represented as H2RuO5(aq), but it is a stoichiometric catalyst because it is reduced during the
- The human body processes ethanol by oxidizing it to acetaldehyde via the NADox/NADred dehydrogenase redox reaction. The reaction isThe values for properties in the order the species appear in the
- The first step in biological glycolysis (the catabolic reaction for glucose consumption) involves addition of a phosphate to create glucose 6-phosphate2–. If the reaction were to occur in aqueous
- When we discussed H3PO4 in Section 18.9, we developed a recurring relation for the dissociation in Eqn. 18.50. Later we gave with verbal argument a binding polynomial in Eqn. 18.90.(a) Write the
- Write a binding polynomial for CO2 in aqueous systems and determine the transformed standard state Gibbs energy of total CO2 at pHc = 7 and I = 0.25 m. Give the distribution of aqueous species at
- (a) Write the binding polynomial for ATP at 298.15K in terms of binding constants in the absence of Mg for application between 3 < pHc < 14. Assume ideal solutions. (b) Convert the binding constants
- Beginning with the untransformed Gibbs energies of formation, document the intermediate calculations for the value of apparent Gibbs energy of formation of ADP at the conditions of Example 18.10,
- Repeat problem 18.18, but use ADP.Data from problem 18.18(a) Write the binding polynomial for ATP at 298.15K in terms of binding constants in the absence of Mg for application between 3 < pHc < 14.
- Repeat problem 18.20, but use H3PO4.Data from problem 18.20Beginning with the untransformed Gibbs energies of formation, document the intermediate calculations for the value of apparent Gibbs energy
- At pHc = 7, I = 0.25, beginning with the untransformed Gibbs energies of formation, document the intermediate calculations for the value of apparent Gibbs energy of formation of CO2 at the conditions
- Plot P against V at 647.3 K for water with the ESD equation using the characterization analogous to Eqns. 15.73–15.76. Apply the equal area rule and determine the vapor pressure at that
- Work problem 11.26 using the(a) Wilson equation(b) NRTL equation(c) UNIQUAC equationData from problem 11.26Fit the specified model to the methanol(1) + benzene(2) system T-x-y data at 760 mmHg by
- (a) A gas-phase A+B system solvates A + B ⇆ AB with Ka = 0.5 at 298.15 K. Calculate the compressibility factor, apparent fugacity coefficients, and the true vapor phase mole fractions in a mixture
- Consider a dilute isothermal mixing process of acetic acid(1) in benzene(2). For the dilute region (say, up to 5 mol% acid), draw schematically curves for the following:Briefly justify your schematic
- Acetic acid dimerizes in the vapor phase. Show that the fugacity of the dimer is proportional to the square of the fugacity of the monomer.
- By assuming that the equilibrium constant for each successive hydrogen bond is equal in the generalized association approach developed in this chapter, what assumptions are being made about the Gibbs
- The value of the excess Gibbs energy at 298 K for an equimolar chloroform(1) + triethylamine(2) system is GE = 0.91 kJ/mol. Assuming only a 1-1 compound is formed, model the excess Gibbs energy with
- Suppose that, due to hydrogen bonding, the system A + B forms a 1-1 complex in the vapor phase when mixed. Neither pure species self-associates in the vapor phase. The equilibrium constant for the
- At 143.5°C, the vapor pressure of acetic acid is 2.026 bar. The dimerization constant for acetic acid vapor at this temperature is 1.028 bar-1. The molar liquid volume of acetic acid at this
- An A + B mixture exhibits solvation in the liquid phase, which is to be represented using ideal chemical theory. Because of a Lewis acid/base interaction, the system is expected to form a 1-1
- Water and acetic acid do not form an azeotrope at 760 mmHg. The normal boiling point of acetic acid is 118.5°C. Therefore, at 118.5°C and 760 mmHg, the mixture will exhibit only vapor behavior
- (a) The molar Gibbs energy of mixing (per mole of superficial solution) for a liquid binary systemexpressed extensively, this becomesIntroduce the concepts of chemical theory into Eqn. 19.131 to
- Furnish a proof that the concentration of true species i is maximum at composition xA* = ai/ (ai + bi), xB* = bi/(ai + bi) where ai and bi are given in Eqn. 15.1. Β = || ΣΣΑ,Β, 15.1
- Show that the result for Zassoc is obtained by taking the appropriate derivative of Aassoc.
- Fit the data from problem 13.8 to the following model by regression over all points, and compare with the experimental data on the same plot, using the(a) Wilson equation(b) NRTL equation(c) UNIQUAC
- Use the ESD equation to model the monomer, dimer, and trimer in the vapor and liquid phases of saturated water at 373 K, 473 K, and 573 K. How does the monomer fraction of saturated vapor change with
- Apply the ESD equation to the methanol + benzene system and compare to the data in Perry’s Handbook based on matching the bubble pressure at the azeotropic point. Prepare a T-x-y diagram and
- Derive the equations for determining the critical point of the ESD equation based on εHB and KAD being zero by noting that dF/dZ = 0 and d2F/dZ2 = 0, where F = Z3 + a2Z2 + a1Z + a0 when hydrogen
- Use the ESD equation to estimate the mutual LLE solubilities of methanol and n-hexane at 285.15 K, 295.15 K, and 310.15 K. Use the value of kij = 0.03 as fitted to a similar system in Fig. 19.12
- The hydrogen halides are unusual. For example, here are the critical properties of various hydrogen halides:Experimental data for the vapor pressure and the apparent molecular weight of HF vapor are
- (a) Compute the values of Ka', a/bRTc, xMc, and bρc for methanol and ethanol according to the van der Waals hydrogen bonding equation of state.(b) Assuming an enthalpy of hydrogen bonding of 24
- Derive the association model for the Peng-Robinson model, using the van’t Hoff formula with ΔCP/R = -1. Extend the homomorph concept by applying ωPR = ωhomo, where ωhomo is the acentric factor
- Acetic acid has a much stronger tendency to dimerize than any alcohol. Therefore, it is not reasonable to assume that Ka2 = Ka3 = … for acetic acid. The assumption is reasonable for Ka3 = Ka4 =
- A rigid container is filled with liquid acetone at 20°C and 1 bar. Through heat transfer at constant volume, a pressure of 100 bar is generated. CP = 125 J/mol-K. (Other properties of acetone are
- Extend the ESD equation to compounds with more than one bonding segment.(a) Consider ethylene glycol as a compound with both an associating head and tail. Extend the mixture analysis to treat this
- 1 m3 of CO2 initially at 150°C and 50 bar is to be isothermally compressed in a frictionless piston/cylinder device to a final pressure of 300 bar. Calculate the volume of the compressed gas, ΔU,
- This problem explores emissions during heating of hexane(1) and toluene(2) in a tank with a fixed roof that is vented to the atmosphere through an open pipe in the roof. Atmospheric pressure is 760
- Ninov et al. (J. Chem. Eng. Data, 40:199, 1995) have shown that the system diethylamine(1) + chloroform(2) forms an azeotrope at 1 bar, 341.55 K and x1 = 0.4475. Is this a maximum boiling or minimum
- Acrolein + water exhibits an atmospheric (1 bar) azeotrope at 97.4 wt% acrolein and 52.4 °C.(a) Determine the values of Aij for the van Laar equation that match this bubble-point pressure at the
- The compositions of coexisting phases of ethanol(1) + toluene(2) at 55°C are x1 = 0.7186, and y1 = 0.7431 at P = 307.81 mmHg, as reported by Kretschmer and Wiebe, 1949. J. Amer. Chem. Soc., 71:1793.
- The system α-epichlorohydrin(1) + n-propanol(2) exhibits an azeotrope at 760 mmHg and 96°C containing 16 mol% epichlorohydrin. Use the van Laar theory to estimate the composition of the vapor in
- A vapor/liquid experiment for the carbon disulfide(1) + chloroform(2) system has provided the following data at 298 K: P1sat = 46.85 kPa, P2sat = 27.3 kPa, x1 = 0.2, y1 = 0.363, and P = 34.98 kPa.
- The following free energy model has been suggested for a particularly unusual binary liquid-liquid mixture. Derive the expression for the activity coefficient of component 1, AGE nRT (0₁ 0₂2)
- The Scatchard-Hildebrand model can be extended to multicomponent mixtures in the following manner. Setting aij = (aiiajj)½ and aii/Vi = Viδ2 Eqn. 12.7 can be rewritten asRecognizing that the
- The (1) + (2) system forms an azeotrope at x1 + 0.75 and 80°C. At 80°C, P1sat = 600 mmHg, P2sat = 900 mmHg. The liquid phase can be modeled by the van Laar model.(a) Estimate the activity
- Ethanol(1) + benzene(2) form azeotropic mixtures. Compare the specified model to the experimental data of Brown and Smith cited in problem 10.2.(a) Prepare a y-x and P-x-y diagram for the system at
- Using the van Laar model and the data from problem 11.3, estimate the total pressure and composition of the vapor in equilibrium with a 20 mol% ethanol(1) solution in water(2) at 78.15°C.Data from
- The CRC Handbook lists the azeotrope for the acetone + chloroform system as 64.7°C and 20 wt% acetone.(a) Use the van Laar model to estimate the T-x-y diagram at 1 bar.(b) Use the SSCED model to
- Fit the data from problem 11.11 to the following model by regression over all points, and compare with the experimental data on the same plot, using(a) The Scatchard-Hildebrand model with k12 = 0(b)
- A liquid mixture of 50 mol% chloroform(1) and 50% 1,4-dioxane(2) at 0.1013 MPa is metered into a flash drum through a valve. The mixture flashes into two phases inside the drum where the pressure and
- Fit the data from problem 11.25 to the following model by regression over all points, and compare with the experimental data on the same plot, using(a) – (d) as in problem 12.8.(e) Plot the T-x-y
- Fit the data from problem 11.27 to the following model by regression over all points, and compare with the experimental data on the same plot, using(a) – (e) as in problem 12.8.Data from problem
- Fit the data from problem 11.26 to the following model by regression over all points, and compare with the experimental data on the same plot, using(a) – (e) as in problem 12.8.Data from problem
- Starting from the excess Gibbs energy formula for Flory’s equation, derive the formula for the activity coefficient of component 1 in a binary mixture.
- R410a is a replacement for R22 in air conditioners and heat pumps. Air conditioners require a different refrigerant because they operate in a different temperature range. R410a avoids the problems
- Crime scene investigators have determined that an acrylic spray paint (polymethylmethacrylate, PMMA) was used to deface the Mona Lisa. Leonardo used linseed oil. We would like a solvent that
- The following lattice contains x’s, o’s, and void spaces. The coordination number of each cell is 8. Estimate the local composition (Xxo) and the parameter Ωox based on rows and columns away
- As part of a biorefining effort, butanediols are being produced by fermentation. The problem is that the isomers are all mixed up. Furthermore, 1,3-propanediol comprises roughly 30mol% of the mixture
- Show that Wilson’s equation reduces to Flory’s equation when Aij = Aji = 0. Further, show that it reduces to an ideal solution if the energy parameters are zero, and the molecules are the same
- The actone(1) + chloroform(2) system has an azeotrope at x1 = 0.38, 248 mmHg, and 35.17°C. Fit the Wilson equation, and predict the P-x-y diagram.
- Model the behavior of ethanol(1) + toluene(2) at 55°C using the UNIQUAC equation and the parameters r1 = 2.1055, r2 = 3.9228, q1 = 1.972, q2 = 2.968, a12 = 76.1573 K, and a21 = 438.005 K.
- Consider a mixture of isobutene(1) + butane(2). Consider a portion of the calculations that would need to be performed by UNIFAC or UNIQUAC.(a) Calculate the surface area and volume parameters for
- The UNIFAC and UNIQUAC equations use surface fraction and volume fractions. This problem explores the differences.(a) Calculate the surface area and volume for a cylinder of diameter d = 1.0 and
- Solve problem 10.10 using UNIFAC to model the liquid phase.Data from problem 10.10Solvent vessels must be purged before maintenance personnel enter in order to ensure that: (1) sufficient oxygen is
- Use the UNIFAC model to predict the VLE behavior of the n-pentane(1) + acetone(2) system at 1 bar and compare to the experimental data in problem 11.11.Data from problem 11.11:Fit the Margules
- The flash point of liquid mixtures is discussed in problem 10.14. For the following mixtures, estimate the flash point temperature of the following components and their equimolar mixtures using
- Activity coefficients are an implicit part of the equation of state but they can be determined explicitly by comparing the definitions of the K-ratios. Using the kij value fit at xe = 0.415, compute
- According to Gmehling et al. (1994),23 the system acetone + water shows azeotropes at: (1) 2793 mmHg, 95.1 mol% acetone, and 100°C; and (2) 5155 mmHg, 88.4 mol% acetone and 124°C. What azeotropic
- A preliminary evaluation of a new process concept has produced a waste stream of the composition given below. It is desired to reduce the waste stream to 10% of its original mass while recovering
- Flash separations are fundamental to any process separation train. A full steady-state process simulation consists largely of many consecutive flash calculations. Use UNIFAC to determine the
- Orbey and Sandler (1995. Ind. Eng. Chem. Res. 34:4351.) have proposed a correction term to be added to the excess Gibbs energy of mixing given by UNIQUAC. To a reasonable degree of accuracy the new
- Derive the form of the excess enthalpy predicted by Wilson’s equation assuming that Aij’s and ratios of molar volumes are temperature-independent.
- The energy equation for mixtures can be written for polymers in the form:By analogy to the development of the Scatchard-Hildebrand theory, this can be rearranged to:whereNdi = degree of
- (a) Rearrange Eqn. 13.22 to obtain Eqn. 13.23.(b) Use Eqns. 13.16 and 13.18 in Eqn. 13.17 and perform the integration to obtain Eqn. 13.19.(c) Use Eqns. 13.16 and 13.31 in Eqn. 13.17 and perform the
- Use the UNIFAC model to predict P-x-y data at 90°C and x1, = {0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0} for propanoic acid + water. Fit the UNIQUAC model to the predicted P-x-y data and report your UNIQUAC
- Work problem 11.25 using the(a) Wilson equation(b) NRTL equation(c) UNIQUAC equationData from problem 11.25Fit the specified model to the methanol(1) + benzene(2) system P-x-y data at 90°C by
- Using the data from problem 11.27, fit the specified model equation and then plot the P-x-y diagram at 80°C using the(a) Wilson equation(b) NRTL equation(c) UNIQUAC equationData from problem
- It has been suggested that the phase diagram of the hexane + furfural system can be adequately represented by the Margules one-parameter equation, where ln γi = xj2. 800/T (K). Estimate the
- Suppose the (1) + (2) system exhibits liquid-liquid immiscibility. Suppose we are at a state where G1/RT = 0.1 and G2/RT = 0.3. The Gibbs energy of mixing quantifies the Gibbs energy of the mixture
- Suppose the solubility of water in ethyl benzene was measured by Karl-Fisher analysis to be 1 mol%. Use UNIFAC to estimate the solubility of ethylbenzene in the water phase.
- Assume solvents A and B are virtually insoluble in each other. Component C is soluble in both.(a) Use the Scatchard-Hildebrand theory to estimate the distribution coefficient at low concentrations of
- According to Perry’s Handbook, the system water + isobutanol forms an atmospheric pressure azeotrope at 67.14 mol% water and 89.92°C. Based on these data, we can estimate the van Laar coefficients
- One mole of a stream containing pentane, acetone, methanol, and water in proportions z = 0.75, 0.13, 0.11, 0.01, respectively, is to be mixed and decanted with 1 mol of pure water at 25°C. Estimate
- A new drug is to have the formula para-CH3CH2-(C6H4)-CH2CH2COOH, where (C6H4) designates a phenyl ring. A useful method for assessing the extent of partitioning between the bloodstream and body fat
- Use the SSCED model to predict the solubility of iodine in carbon tetrachloride at 298 K. Iodine’s melting point is 387 K and Hfus = 15.5 kJ/mol.
- Use the Scatchard-Hildebrand theory to generate figures of activity as a function of composition and ΔGmix as a function of composition for neopentane and dichloromethane at 0°C. Determine the
- Schulte et al. discuss a linear solvation energy relationship (LSER) method for the partitioning of 41 environmentally important compounds between hexane + water phases at 25°C. The LSER method is
- The bubble point of a liquid mixture of n-butanol and water containing 4 mol% butanol is 92.7°C at 1 bar. At 92.7°C the vapor pressure of pure water is 0.784 bar and that of pure n-butanol is 0.427
- Predict the compositions of the coexisting liquid phases for the system methanol (1) + cyclohexane (2) at 285.15 K and 310.15 K. Let α be the methanol-rich phase. Compare quickly with the data from
- Predict the compositions of the coexisting liquid phases for the system methanol (1) + cyclohexane (2) at 298 K. Let α be the methanol-rich phase.(a) Use the MAB model.(b) Use the SSCED model.(c)
- Water + hexane and water + benzene are immiscible pairs.(a) The binary system water + benzene boils at 69.4 °C and 760 mmHg. What is the activity coefficient of benzene in water if the solubility at
- Benzene and water are virtually immiscible. What is the bubble pressure of an overall mixture that is 50 mol% of each at 75°C?
- Consider the system water(1) + MEK(2) at 299.85 K. The solubilities measured by Skrzec, A.E., Murphy, N.F., 1954. Ind. Eng. Chem., 46:2245, are x1α = 0.927 and x1β = 0.364. For a binary system,
- For a binary system, iterations can be performed by finding a new value of x1αnew from only the K-ratios as shown in Eqn. 14.5. For a ternary system, we need at least one composition. Derive the
- Consider the system water(1) + methylethylketone(MEK)(2) + acetic acid(AA)(3) at 299.85 K. For a ternary LLE system, estimate tie lines at x3α = 0.005, 0.01, 0.02, using UNIQUAC, where the parameter
- Calculate the LLE in the system 1-butanol(1) + water(2) + methanol(3) at 288.15 K, using UNIQUAC with the following parameters: r = [3.4543, 0.92, 1.4311]; q = [3.052, 1.4, 1.432]; and the a values