Questions and Answers of Introduction To Chemical Engineering Thermodynamics

With V̅2 = V2, Eq. (15.66) for the osmotic pressure may be represented as a power series in x1:Reminiscent of Eqs. (3.33) and (3.34), this series is called an osmotic virial expansion. Show that the
Suppose that the adsorbate equation of state is given by z = (1 − bn)−1 , where b is a constant. Find the implied adsorption isotherm, and show under what conditions it reduces to the Langmuir
Suppose that the adsorbate equation of state is given by z = 1 + βn , where β is a function of T only. Find the implied adsorption isotherm, and show under what conditions it reduces to the
Make a thermodynamic analysis of the refrigeration cycle of Ex. 9.1(b).Ex. 9.1(b)(b) Calculate ω and m ∙ for a vapor-compression cycle (Fig. 9.2) if the compressor efficiency is 0.80.(Fig. 9.2)
Two special models of liquid-solution behavior are the regular solution, for which SE = 0 everywhere, and the a thermal solution, for which HE = 0 everywhere.(a) Ignoring the P-dependence of GE, show
Make a thermodynamic analysis of the refrigeration cycle described in one of the parts of Prob. 9.9. Assume that the refrigeration effect maintains a heat reservoir at a temperature 5°C above the
A binary liquid mixture is only partially miscible at 298 K. If the mixture is to be made homogeneous by increasing the temperature, what must be the sign of HE?
Make a thermodynamic analysis of the process described in Ex. 9.3. Tσ = 295 K.Ex. 9.3Natural gas, assumed here to be pure methane, is liquefied in a Claude process. Compression is to 60 bar and
A colloidal solution enters a single-effect evaporator at 100°C. Water is vaporized from the solution, producing a more concentrated solution and 0.5 kg·s−1 of steam at 100°C. This steam is
With reference to Ex. 10.4(a) Apply Eq. (10.7) to Eq. (A) to verify Eqs. (B) and (C).(b) Show that Eqs. (B) and (C) combine in accord with Eq. (10.11) to regenerate Eq. (A).Eq. (10.11)(c) Show that
If LiCl⋅2H2O(s) and H2O(l) are mixed isothermally at 25°C to form a solution containing 10 mol of water for each mole of LiCl, what is the heat effect per mole of solution?
If a liquid solution of HCl in water, containing 1 mol of HCl and 4.5 mol of H2O, absorbs an additional 1 mol of HCl(g) at a constant temperature of 25°C, what is the heat effect?
What is the heat effect when 20 kg of LiCl(s) is added to 125 kg of an aqueous solution containing 10-wt-% LiCl in an isothermal process at 25°C?
An LiCl/H2O solution at 25°C is made by adiabatically mixing cool water at 10°C with a 20-mol-% LiCl/H2O solution at 25°C. What is the composition of the solution formed?
A 20-mol-% LiCl/H2O solution at 25°C is made by mixing a 25-mol-% LiCl/H2O solution at 25°C with chilled water at 5°C. What is the heat effect in joules per mole of final solution?
A 20-mol-% LiCl/H2O solution is made by six different mixing processes:(a) Mix LiCl(s) with H2O(l).(b) Mix H2O(l) with a 25-mol-% LiCl/H2O solution.(c) Mix LiCl ⋅H2O(s) with H2O(l).(d) Mix LiCl(s)
A stream of 12 kg·s−1 of Cu(NO3)2⋅6H2O and a stream of 15 kg·s−1 of water, both at 25°C, are fed to a tank where mixing takes place. The resulting solution passes through a heat exchanger
The pressure above a mixture of ethanol and ethyl acetate at 70°C is measured to be 86 kPa. What are the possible compositions of the liquid and vapor phases? Problems 12.3 through 12.8 refer to the
Of the following binary liquid/vapor systems, which can be approximately modeled by Raoult’s law? For those that cannot, why not? Table B.1 (App. B) may be useful.(a) Benzene/toluene at 1(atm).(b)
The pressure above a mixture of ethanol and ethyl acetate at 70°C is measured to be 78 kPa. What are the possible compositions of the liquid and vapor phases? Problems 12.3 through 12.8 refer to the
Consider an ethanol(1)/ethyl acetate(2) mixture with x1 = 0.70, initially at 70°C and 100 kPa. Describe the evolution of phases and phase compositions as the pressure is gradually reduced to 70 kPa.
What is the composition of the azeotrope for the ethanol(1)/ethyl acetate(2) system? Would this be called a high-boiling or low-boiling azeotrope? Problems 12.3 through 12.8 refer to the Pxy diagram
Consider an ethanol(1)/ethyl acetate(2) mixture with x1 = 0.80, initially at 70°C and 80 kPa. Describe the evolution of phases and phase compositions as the pressure is gradually increased to 100
Consider a closed vessel initially containing 1 mol of pure ethyl acetate at 70°C and 86 kPa. Imagine that pure ethanol is slowly added at constant temperature and pressure until the vessel contains
Consider an ethanol(1)/ethyl acetate(2) mixture with x1 = 0.70, initially at 70°C and 100 kPa. Describe the evolution of phases and phase compositions as the temperature is gradually increased to
A mixture of ethanol and ethyl acetate is heated in a closed system at 100 kPa to a temperature of 77°C, and two phases are observed to be present. What are the possible compositions of the liquid
A mixture of ethanol and ethyl acetate is heated in a closed system at 100 kPa to a temperature of 74°C, and two phases are observed to be present. What are the possible compositions of the liquid
Air, even more than carbon dioxide, is inexpensive and nontoxic. Why is it not the gas of choice for making soda water and (cheap) champagne effervescent? Table 13.2 may provide useful data.Table
Consider an ethanol(1)/ethyl acetate(2) mixture with x1 = 0.20, initially at 70°C and 100 kPa. Describe the evolution of phases and phase compositions as the temperature is gradually increased to
Humidity, relating to the quantity of moisture in atmospheric air, is accurately given by equations derived from the ideal-gas law and Raoult’s law for H2O.(a) The absolute humidity h is defined as
A single-stage liquid/vapor separation for the benzene(1)/ethylbenzene(2) system must produce phases of the following equilibrium compositions. For one of these sets, determine T and P in the
Do all four parts of Prob. 13.7, and compare the results. The required temperatures and pressures vary significantly. Discuss possible processing implications of the various temperature and pressure
The following is a set of VLE data for the system methanol(1)/water(2) at 333.15 K:(a) Basing calculations on Eq. (13.24), find parameter values for the Margules equation that provide the best fit of
The following is a rule of thumb: For a binary system in VLE at low pressure, the equilibrium vapor-phase mole fraction y1 corresponding to an equimolar liquid mixture is approximatelywhere Psati is
Flash calculations are simpler for binary systems than for the general multicomponent case because the equilibrium compositions for a binary are independent of the overall composition. Show that, for
The excess Gibbs energy for binary systems consisting of liquids not too dissimilar in chemical nature is represented to a reasonable approximation by the equation:where A is a function of
The following is a set of VLE data for the system acetone(1)/methanol(2) at 55°C:(a) Basing calculations on Eq. (13.24), find parameter values for the Margules equation that provide the best fit of
If Eq. (13.24) is valid for isothermal VLE in a binary system, show that:Eq (13.24) (2). dP dP 2-Psat sat X=1 0= Ix (1xp
The following is a set of activity-coefficient data for a binary liquid system as determined from VLE data:Inspection of these experimental values suggests that they are noisy, but the question is
VLE data for methyl tert-butyl ether(1)/dichloromethane(2) at 308.15 K are as follows:The data are well correlated by the three-parameter Margules equation [an extension of Eq. (13.39)]:Implied by
For the ethanol(1)/chloroform(2) system at 50°C, the activity coefficients show interior extrema with respect to composition [see Fig. 13.4(e)].(a) Prove that the van Laar equation cannot represent
Following are VLE data for the system acetonitrile(1)/benzene(2) at 45°C:The data are well correlated by the three-parameter Margules equation (see Prob. 13.37).(a) Basing calculations on Eq.
Equations analogous to Eqs. (10.15) and (10.16) apply for excess properties. Because ln γi is a partial property with respect to GE∕RT, these analogous equations can be written for ln γ1 and ln
An unusual type of low-pressure VLE behavior is that of double azeotropy, in which the dew and bubble curves are S-shaped, thus yielding at different compositions both a minimum-pressure and a
For one of the binary systems listed in Table 13.10, based on Eq. (13.19) and the Wilson equation, prepare a Pxy diagram for t = 60°C.Problems 13.43 through 13.54 require parameter values for the
Rationalize the following rule of thumb, appropriate for an equimolar binary liquid mixture: GE (equimolar) RT 1
For one of the binary systems listed in Table 13.10, based on Eq. (13.19) and the Wilson equation, prepare a txy diagram for P = 101.33 kPa.Problems 13.43 through 13.54 require parameter values for
For one of the binary systems listed in Table 13.10, based on Eq. (13.19) and the NRTL equation, prepare a Pxy diagram for t = 60°C.Problems 13.43 through 13.54 require parameter values for the
For one of the binary systems listed in Table 13.10, based on Eq. (13.19) and the NRTL equation, prepare a txy diagram for P = 101.33 kPa.Problems 13.43 through 13.54 require parameter values for the
For one of the binary systems listed in Table 13.10, based on Eq. (13.19) and the Wilson equation, make the following calculations:(a) BUBL P : t = 60°C, x1 = 0.3.(b) DEW P : t = 60°C, y1 = 0.3.(c)
For one of the binary systems listed in Table 13.10, based on Eq. (13.19) and the Wilson equation, make the following calculations:(a) BUBL T : P = 101.33 kPa, x1 = 0.3.(b) DEW T : P = 101.33 kPa, y1
Work Prob. 13.49 for the NRTL equation.Prob. 13.49For one of the binary systems listed in Table 13.10, based on Eq. (13.19) and the Wilson equation, make the following calculations:(a) BUBL T : P =
For the acetone(1)/methanol(2)/water(3) system, based on Eq. (13.19) and the Wilson equation, make the following calculations:(a) BUBL P : t = 65°C, x1 = 0.3, x2 = 0.4.(b) DEW P : t = 65°C, y1 =
Work Prob. 13.51 for the NRTL equation.Prob. 13.51For the acetone(1)/methanol(2)/water(3) system, based on Eq. (13.19) and the Wilson equation, make the following calculations:(a) BUBL P : t = 65°C,
Work Prob. 13.53 for the NRTL equation.Prob. 13.53For the acetone(1)/methanol(2)/water(3) system, based on Eq. (13.19) and the Wilson equation, make the following calculations:(a) BUBL T : P = 101.33
For the acetone(1)/methanol(2)/water(3) system, based on Eq. (13.19) and the Wilson equation, make the following calculations:(a) BUBL T : P = 101.33 kPa, x1 = 0.3, x2 = 0.4.(b) DEW T : P = 101.33
Possible correlating equations for ln γ1 in a binary liquid system are given here. For one of these cases, determine by integration of the Gibbs/Duhem equation [Eq. (13.11)] the corresponding
Table 13.10 gives values of parameters for the Wilson equation for the acetone(1)/methanol(2) system. Estimate values of ln γ∞1 and ln γ∞2 at 50°C. Compare with the values suggested by Fig.
Consider the following model for GE∕RT of a binary mixture:This equation in fact represents a family of two-parameter expressions for GE∕RT; specification of k leaves A12 and A21 as the free
The following expressions have been reported for the activity coefficients of species 1 and 2 in a binary liquid mixture at given T and P:ln γ1 = x22 (0.273 + 0.096 x1) ln γ2 = x21 (0.273 − 0.096
Use Eq. (13.13) to reduce one of the following isothermal data sets, and compare the result with that obtained by application of Eq. (13.19). Recall that reduction means developing a numerical
A storage tank contains a heavy organic liquid. Chemical analysis shows the liquid to contain 600 ppm (molar basis) of water. It is proposed to reduce the water concentration to 50 ppm by boiling the
A single P-x1-y1 data point is available for a binary system at 25°C. Estimate from the data:(a) The total pressure and vapor-phase composition at 25°C for an equimolar liquid mixture.(b) Whether
Departures from Raoult’s law are primarily from liquid-phase nonidealities (γi ≠ 1). But vapor-phase nonidealities (ϕ i ≠ 1) also contribute. Consider the special case where the liquid phase
For one of the following substances, determine Psat∕bar from the Redlich/Kwong equation at two temperatures: T = Tn (the normal boiling point), and T = 0.85Tc. For the second temperature, compare
Work Prob. 13.69 for one of the following: (a) The Soave/Redlich/Kwong equation; (b) the Peng/Robinson equation.Prob. 13.69For one of the following substances, determine Psat∕bar from the
The relative volatility α12 is commonly used in applications involving binary VLE. In particular (see Ex. 13.1), it serves as a basis for assessing the possibility of binary azeotropy. (a) Develop
Generate P-x1-y1 diagrams at 100°C for one of the systems identified below. Base activity coefficients on the Wilson equation, Eqs. (13.45) to (13.47). Use two procedures: (i) modified Raoult’s
Peter, Paul, and Mary, members of a thermodynamics class, are asked to find the equilibrium composition at a particular T and P and for given initial amounts of reactants for the following gas-phase
Develop expressions for the mole fractions of reacting species as functions of the reaction coordinate for:(a) A system initially containing 2 mol NH3 and 5 mol O2 and undergoing the reaction:4NH3(g)
A system initially containing 2 mol C2H4 and 3 mol O2 undergoes the reactions:C2H4(g) + ½O2(g) → ⟨(CH2)2⟩O(g)C2H4(g) + 3O2(g)  → 2CO2(g)  + 2H2O(g)Develop expressions for
Ethylene is produced by the dehydrogenation of ethane. If the feed includes 0.5 mol of steam (an inert diluent) per mole of ethane and if the reaction reaches equilibrium at 1100 K and 1 bar, what is
A chemically reactive system contains the following species in the gas phase: NH3, NO, NO2, O2, and H2O. Determine a complete set of independent reactions for this system. How many degrees of freedom
Consider the gas-phase isomerization reaction: A→B.(a) Assuming ideal gases, develop from Eq. (14.28) the chemical-reaction equilibrium equation for the system.(b) The result of part (a) should
Consider the gas-phase oxidation of ethylene to ethylene oxide at a pressure of 1 bar with 25% excess air. If the reactants enter the process at 25°C, if the reaction proceeds adiabatically to
Hydrogen gas can be produced by the reaction of steam with “water gas,” an equimolar mixture of H2 and CO obtained by the reaction of steam with coal. A stream of “water gas” mixed with steam
The feed gas to a methanol synthesis reactor is composed of 75-mol-% H2, 15-mol-% CO, 5-mol-% CO2, and 5-mol-% N2. The system comes to equilibrium at 550 K and 100 bar with respect to the
Reaction-equilibrium calculations may be useful for estimation of the compositions of hydrocarbon feedstocks. A particular feedstock, available as a low-pressure gas at 500 K, is identified as
In chemical-reaction engineering, special measures of product distribution are sometimes used when multiple reactions occur. Two of these are yield Yj and selectivity Sj∕k. We adopt the following
“Synthesis gas” can be produced by the catalytic re-forming of methane with steam. The reactions are:CH4(g) + H2O(g) → CO(g) + 3H2g) CO(g)
A low-pressure, gas-phase isomerization reaction, A→B, occurs at conditions such that vapor and liquid phases are present.(a) Prove that the equilibrium state is univariant.(b) Suppose T is
The following problems involving chemical-reaction stoichiometry are to be solved through the use of reaction coordinates.(a) Feed to a gas-phase reactor comprises 50 kmol·h−1 of species A, and 50
The following is an industrial-safety rule of thumb: compounds with large positive ΔG f° must be handled and stored carefully. Explain.
Two important classes of reactions are oxidation reactions and cracking reactions. One class is invariably endothermic; the other, exothermic. Which is which? For which class of reactions (oxidation
Equilibrium at 425 K and 15 bar is established for the gas-phase isomerization reactionn-C4H10(g)  → iso-C4Η10(g)Estimate the composition of the equilibrium mixture by two procedures:(a)
The standard heat of reaction ΔH° for gas-phase reactions is independent of the choice of standard-state pressure P°. (Why?) However, the numerical value of ΔG° for such reactions does depend on
Ethanol is produced from ethylene via the gas-phase reactionC2H4(g)  +  H2O(g)  →  C2H5OH(g)Reaction conditions are 400 K and 2 bar.(a) Determine a numerical value for the equilibrium
Reagent-grade, liquid-phase chemicals often contain as impurities isomers of the nominal compound, with a consequent effect on the vapor pressure. This can be quantified by
Data from the Bureau of Standards (J. Phys. Chem. Ref. Data, vol. 11, suppl. 2, 1982) include the following heats of formation for 1 mol of CaCl2 in water at 25°C:From these data prepare a plot of
Consider a plot of Δ̃H̃, the heat of solution based on 1 mol of solute (species 1), vs. ñ, the moles of solvent per mole of solute, at constant T and P. Figure 11.4 is an example of such a plot,
A liquid solution of LiCl in water at 25°C contains 1 mol of LiCl and 7 mol of water. If 1 mol of LiCl⋅3H2O(s) is dissolved isothermally in this solution, what is the heat effect?
Suppose that ΔH for a particular solute(1)/solvent(2) system is represented by the equation:ΔH = x1x2 ( A21x1  +  A12x2 ) (A)Relate the behavior of a plot of Δ̃H̃ vs. ñ to the features of
You need to produce an aqueous LiCl solution by mixing LiCl⋅2H2O(s) with water. The mixing occurs both adiabatically and without change in temperature at 25°C. Determine the mole fraction of LiCl
Consider a closed vessel initially containing 1 mol of pure tetrahydrofuran at 74°C and 120 kPa. Imagine that pure chloroform is slowly added at constant temperature and pressure until the vessel
For a 50-wt-% aqueous solution of H2SO4 at 350 K, what is the excess enthalpy HE in kJ·kg−1?
Saturated steam at 3 bar is throttled to 1 bar and mixed adiabatically with (and condensed by) 45-wt-% sulfuric acid at 300 K in a flow process that raises the temperature of the acid to 350 K. How
What is the composition of the vapor phase in equilibrium with a liquid phase ethanol(1)/ethyl acetate(2) mixture of the following compositions at P = 1 bar?(a) x1 = 0.1(b) x1 = 0.2(c) x1 = 0.3(d) x1
What is the composition of the liquid phase in equilibrium with a vapor phase ethanol(1)/ethyl acetate(2) mixture of the following compositions at P = 1 bar?(a) y1 = 0.1(b) y1 = 0.2(c) y1 = 0.3(d) y1
What is the composition of the vapor phase in equilibrium with a liquid phase chloroform(1)/tetrahydrofuran(2) mixture of the following compositions at P = 1 bar?(a) x1 = 0.1(b) x1 = 0.2(c) x1 =
What is the composition of the liquid phase in equilibrium with a vapor phase chloroform(1)/tetrahydrofuran(2) mixture of the following compositions at P = 1 bar?(a) y1 = 0.1(b) y1 = 0.2(c) y1 =

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