Questions and Answers of Introductory Chemical Engineering Thermodynamics

Consider the liquefaction of N2 by Joule–Thomson throttling. If the inlet to the expansion valve is at T1 = -122°C and P1 = 100 bar and the outlet is at 1 bar, determine the percentage of N2 that
A pot of boiling water is open to the atmosphere when, at time 0, the pot is sealed by a tight lid so no gas can escape. With continued heating, the water continues to boil. As best you can, estimate
The boiling point for species A at 1 bar is reported to be 250 K, and you desire to know the boiling point at 10 bar. Knowing the enthalpy of vaporization, you apply the Clausius-Clapeyron equation
The boiling point for species A at 1 bar is reported to be 250 K, and you desire to know the saturation pressure at 300 K. Knowing the enthalpy of vaporization, you apply the Clausius-Clapeyron
A well-insulated tank with a valve at the top contains saturated water at 5 MPa. The quality of the water is 0.1.(a) What is the ratio of the liquid volume to the vapor volume?(b) The valve is
Your coworker has scribbled down the saturation pressures for a pure species from the solid (sublimation) and liquid (evaporation) as follows:and,However, in his haste, he forgot to note which
(a) A pure fl uid shows the following s vs. T behavior. Draw schematically how the chemical potential would change with temperature.(b) A pure substance shows the following v vs. P behavior at
At room temperature, iron exists in the ferrite phase (α-Fe). At 912°C, it goes through a phase transformation to the austenite phase (γ-Fe). Which phase of iron has stronger bonds?Explain.
Consider the crystallization of species a. The molar Gibbs energy of pure species a vs. temperature at a pressure of 1 bar is shown below. Take the molar volume of species a in the liquid phase to
The slope of the coexistence line between the solid and liquid phases shown in Figure 6.3 is positive. Most pure species behave this way. However, species that expand on freezing (like liquid water
For two species, A and B, with a positive enthalpy change of mixing:(a) Are the like interactions or the unlike interactions stronger? Explain.(b) If pure species A and B are mixed adiabatically,
The following diagram shows the normal melting point of pure solid 1 to be Tm. Consider now that the same pure solid 1 is in a liquid mixture with four species 1, 2, 3, and 4 as shown on the right.
The normal boiling point of puThe normal melting point of pure solid 1 is Tm. Consider now that the same pure solid 1 is melting into a liquid that initially contains pure 2. How does the temperature
The normal melting point of pure solid 1 is Tm. Consider now that the same pure solid 1 is melting into a liquid that initially contains pure 2. How does the temperature at which 1 will melt into the
In Example 6.5, we found Ni nanopartibles of 2 nm radius would melt at 587 K, assuming the system contained pure Ni liquid. Consider now 2 nm Ni nanoparticles in equilibrium with a liquid mixture.
In this problem you will compare properties of species 1 as a pure liquid at 1 atm and 300 K (System I) to species 1 in a mixture with species 2, 3, and 4 at the same pressure and temperature
For a given binary system, the partial molar volume of species 1 is constant. What can you say about species 2? Explain.
(a) Use the Clausius–Clapeyron equation and data for water at 100°C to develop an expression for the vapor pressure of water as a function of temperature.(b) Plot the expression you came up with
What pressure is needed to isothermally compress ice initially at 25°C and 1 bar so that it changes phase?
One mole of a pure species exists in liquid–vapor equilibrium in a rigid container of volume V = 1 L, a temperature of 300 K, and a pressure of 1 bar. The enthalpy of vaporization and the second
Tired of studying thermo, you come up with the idea of becoming rich by manufacturing diamond from graphite. To do this process at 25°C requires increasing the pressure until graphite and diamond
You wish to know the melting temperature of aluminum at 100 bar. You fi nd that at atmospheric pressure, Al melts at 933.45 K and the enthalpy of fusion is:Heat capacity data are given by:Take the
The vapor pressure of silver (between 1234 K and 2485 K) is given by the following expression:with P in torr and T in K. Estimate the enthalpy of vaporization at 1500 K. State the assumptions that
At a temperature of 60.6°C, benzene exerts a saturation pressure of 400 torr. At 80.1°C, its saturation pressure is 760 torr. Using only these data, estimate the enthalpy of vaporization of
Pure ethanol boils at a temperature of 63.5°C at a pressure of 400 torr. It also boils at 78.4°C and 760 torr. Using only these data, estimate the saturation pressure for ethanol at 100°C.
An alternative criteria for chemical equilibrium between two phases of pure species i can be written:Apply the thermodynamic web to show that the partial derivative of this function with respect to
At 922 K, the enthalpy of liquid Mg is 26.780 [kJ/mol] and the entropy is 73.888 [J/(mol K)].Determine the Gibbs energy of liquid Mg at 1300 K. The heat capacity of the liquid is constant over this
Solid sulfur undergoes a phase transition between the monoclinic (m) and orthorhombic (o) phases at a temperature of 368.3 K and pressure of 1 bar. Calculate the difference in Gibbs energy between
At 900 K, solid Sr has values of enthalpy and entropy of 20.285 [kJ/(mol)] and 91.222 [J/(mol K)], respectively. At 1500 K, liquid Sr has values of enthalpy and entropy of 49.179 [kJ/mol]and 116.64
At 1100 K, solid SiO2 has values of enthalpy and entropy of 2856.84 3kJ/mol4 and 124.51 [J/(mol K)], respectively. At 2500 K, liquid SiO2 has values of enthalpy and entropy of 2738.44 [kJ/mol] and
Determine the second virial coeffi cient, B, for CS2 at 100°C from the following data. The saturation pressure of carbon disulfi de (CS2) has been fi t to the following equation: In Pat CS = 62.7839
Calculate the Gibbs energy of the liquid and vapor phases of water for the following conditions:(a) Saturated water at 100°C(b) 100°C and 50 kPa Are these results consistent with Equation (6.3)
The saturation pressure of pure solid species A is given by:where PAsat is in [bar] and T is in [K]. You wish express the vapor pressure of the liquid in the form:You know the enthalpy of fusion is
At 1 bar, silver melts at 1233.95 K. The density of the liquid and solid are:You may assume these values are constant in this problem. The entropy at the normal melting point is:The molecular weight
You need to fi nd the triple point of pure species A and are unable to fi nd its value in any reference books. You can fi nd the following data for A. It sublimes at 200 K and 0.1 bar, and it boils
You need to fi nd the enthalpy of sublimation of solid A at 300 K. The following equilibrium vapor pressure measurements have been made on pure A: (1) at 250 K, the pressure is 0.258 bar and (2) at
A TP diagram of carbon is presented in the following fi gure. The following data are available at 25°C.Answer the following questions:(a) Identify the region where diamond is the thermodynamically
Consider the use of CF2Cl2 as a dispersing agent for aerosol spray cans. Estimate the pressure a can has to withhold at 40°C. Its enthalpy of vaporization at its normal boiling point (244 K)
At 1 atm titanium melts at 1941 K and boils at 3560 K. Its triple point pressure is 5.3 Pa.Using only these data, estimate the enthalpy of vaporization of titanium. You will need to think about a
You wish to determine the enthalpy of vaporizaton of species A. You are able to fi nd the following data: Species A has a normal boiling point of 207.3 K, and at 20.0 atm, it boils at 301.5 K.The
In Example 6.2, we developed an expression for gd - gn vs. T for the protein lysozyme (l)between its native phase, n, and its denatured phase, d, where unfolding occurs. Develop the same expression
Consider an ideal gas mixture at 83.14 kPa and 500 K. It contains 2 moles of species A and 3 moles of species B. Calculate the following:VA, VB, vA, vB, VA, VB, V, v, ΔVmix, Δvmix.
For a given binary system at constant T and P, the molar volume (in cm3 /mol) is given by v = 100y + 80y + 2.5yayb (a) What is the pure species molar volume for species a, va? (b) Come up with an
Consider a mixture of species 1, 2, and 3. The following equation of state is available for the vapor phase:where,and y1, y2, and y3 are the mole fractions of species 1, 2 and 3, respectively.
The molar enthalpy of a ternary mixture of species a, b, and c can be described by the following expression: h = -5000x - 3000x2200x500xxx [J/mol] (a) Come up with an expression for H (b) Calculate H
Plot the partial molar volumes of CO2 and C3H8 in a binary mixture at 100°C and 20 bar as a function of mole fraction CO2 using the van der Waals equation of state.
The Gibbs energy of a binary mixture of species a and species b at 300 K and 10 bar is given by the following expression:(a) For a system containing 1 mole of species a and 4 moles of species b, fi
Consider a binary mixture of species 1 and species 2. A plot of the partial molar volumes in [cm3/mol] of species 1 and 2, V1 and V2, vs. mole fraction of species 1 is shown below. For a mixture of 1
Enthalpies of mixing for binary mixtures of cadmium (Cd) and tin (Sn) have been fi t to the following equation at 500°C:where, XCd and XSn are the cadmium and tin mole fractions, respectively.
The Gibbs energy of a binary mixture is given by the following expression:where R is the ideal gas constant and T is in [K]. For a mixture at 298 K with the following mole fractions of a, calculate
The molar enthalpy of a binary liquid mixture of species 1 and 2 is given by:where T is the temperature in [K](a) What is the enthalpy of mixing, ΔHmix in [J], of a mixture with 2 mol of 1 and 3
The molar volume, in [cm3/mol], of a binary mixture of ethanol (1) and ethylene glycol (2)at 25°C is given in the following table.Using the graphical method, determine the partial molar volume of
The volume change of mixing, in [cm3/mol], for binary liquid mixture of sulfuric acid (1) and water (2) at 25°C is given by the following expression: _Uma = -13.1x12 - 2.25x3x2 mix
The molar enthalpy of a binary liquid mixture of species 1 and 2 is given by:where T is the temperature in [K]. This expression is valid in the temperature range from 280 K to 360 K. Please answer
You are running a manufacturing process where a mole fraction of 0.40 species 1 in a binary mixture of 1 and 2 is required at a fl ow rate of 5 mol/s and a temperature of 300 K. This is achieved by
The partial molar Gibbs energy of species 1 in a binary liquid mixture of species 1 and 2 is given by: G-500 + 2,500 In x + 833x J mol
The following expression describes the molar volume of a binary liquid mixture of species 1 and 2:Consider a mixture that contains 2 mol of species 1 and 4 mol of species 2. Answer the following
You are designing a process that requires a molten liquid solution of copper (Cu) and silver (Ag). You start with a charge of 1,000 kg of pure Cu and 2,000 kg of pure Ag at 298 K and 1 atm.You place
Consider a binary mixture of ethanol, EtOH (CH3CH2OH) and water (H2O) . A plot of the partial molar volumes of EtOH and H2O versus mole fraction EtOH (xEtOH) is provided in the following fi gure.
A group of students came across an unsuspected supply of laboratory alcohol containing 96 weight % ethanol (EtOH) and 4 weight % water (H2O) . As an experiment, they wanted to see if they could make
The Gibbs energy of mixing, Δgmix in [J/mol], of a binary liquid mixture of water (1) and 1-propanol (2) vs. mole fraction water (x1)is shown below. These data are at a temperature at 40°C. A9mix
A binary mixture of species a and b behaves as an ideal gas at 300 K and 1 bar. Calculate the partial molar Gibbs energy of species a, Ga, and the total solution Gibbs energy, g, at the following
The partial molar volumes of a binary mixture of ethanol (1) and ethylene glycol (2) at 25°C are reported in the following table. Answer the following questions: V [cm3/mol] 0 56.519 0.05 56.722
Enthalpies of solution, are reported in Table 6.1 for 1 mole of HCl diluted in n moles of H2O at 25°C:(a) Consider a mixture of 8 moles H2O and 2 moles HCl. As best you can from these data,
Aqueous HCl can be manufactured by gas-phase reaction of H2 and Cl2 to form HCl(g), followed by absorption of HCl(g) with water. Consider a steady-state process at 25°C where HCl(g)and pure water
How does the enthalpy of mixing data for H2SO4 given by Equation (6.24) compare to the enthalpy of solution data from Table 6.1? Is the agreement reasonable? What are the reasons they may be
Calculate the enthalpy of mixing for HCl from the enthalpy of solution data reported in Table 6.1. TABLE 6.1 Enthalpy of Solution of Different Species in Water at 25C Ah, J mol solute n NaOH CH5OH
What is the heat requirement to dilute an inlet aqueous stream of 50% NaOH, by weight, to a fi nal concentration of 10%?
Develop an equation for a ternary mixture analogous to Equation (6.30). Then generalize to a mixture with m components.
The partial molar volume of benzene (1) in cyclohexane (2) at 30°C is given by the following expression:Find an expression for the partial molar volume of cyclohexane. The density of cyclohexane at
Using data from Table 6.1, fi nd the partial molar enthalpy of water in a mixture of ethanol (1) and water (2) at 25°C with x1 = 0.33. Use the same reference state as used in the steam tables.Steam
Consider the isothermal mixing of 20% solute 1 by weight and 80% water, 2, at 25°C. What is the heat transferred for the following mixtures? (a) pure HSO4 (1) and HO (2) (b) 18 M HSO4 (1) and HO
The following data are available for a binary mixture of ethanol and water at 20°C:(a) Make a plot of the partial molar volumes of ethanol and water vs. mole fraction ethanol.(b) What is Δvmix for
The following data have been reported for the density, r, vs. mole fraction ethanol of binary mixtures of ethanol (1) and formamide (2) at 25°C and 1 bar. X1 0 0.1000 0.1892 0.2976 0.3907 0.5009
Consider a binary mixture of ideal gases, a and b, at temperature T and pressure P. Come up with an expression forin terms of T, P, and ya. What is the value of (AGmix) a
Consider a system in which liquid water is in phase equilibrium with wet air at 25°C and 1 bar. What is the partial molar Gibbs energy of the water in the vapor phase? You may assume the liquid is
We have seen that the Gibbs energy determines whether a process can occur spontaneously. This concept can be applied to understand aspects of biological systems. Use the Gibbs energy to show why the
We can use the principles of phase equilibrium to learn about the stability of proteins in biological systems. In this example, we consider the phase equilibrium of the protein lysozyme (l) between
Trimethyl gallium, Ga(CH3 ) 3, can be used as a feed gas to grow fi lms of GaAs. Estimate the enthalpy of vaporization of Ga(CH3) 3 from the data of saturation pressure vs. temperature given in Table
The fi eld of nanotechnology is an emerging area for chemical and biological engineers. Consider nickel nanoparticles for use as a catalyst to grow carbon nanotubes. The normal melting temperature,
Mathematically verify that integration of Equation (6.16) leads to Equations (6.18) or (6.17) (a) starting with the expression for dK; (b) based on applying Euler’s theorem to Equation (6.13).
Label the volumes depicted in Figure 6.6 according to the different types of thermodynamic properties depicted in this section. 50 ml Pure ethanol + Figure 6.6 Mixing of ethanol and water. 20 ml Pure
An experiment is performed to measure the enthalpy of mixing of chloroform, CHCl3, and acetone, C3H6O. In this experiment, pure species inlet streams of different compositions are mixed together in
An insulated piston–cylinder assembly contains two compartments divided by a partition. As shown in Figure E6.9A, the top compartment initially contains 2 moles of pure liquid 1, whereas the bottom
Table 6.1 presents data for the enthalpy of solution, for nitric acid in water at 18°C. Find the corresponding values for the enthalpy of mixing vs. mole fraction of solute. Ahs, S
Develop an expression for the entropy change of mixing for a binary ideal gas mixture.
Consider a binary mixture of 10 mole% chloroform (1) in acetone (2) at 333 K and 10 bar. The second virial coeffi cients for this system are reported to be B11 = 2910, B22 = -1330, and B12 = 22005
Develop expressions for the partial molar enthalpies of sulfuric acid and water in a binary mixture at 21°C. The pure species enthalpies are 1.596 [kJ/mol] and 1.591 [kJ/mol], respectively, and the
Verify that the expressions developed in Example 6.12 for the partial molar enthalpies of sulfuric acid and water in a binary mixture at 21°C satisfy the Gibbs–Duhem equation.
Develop an expression for the partial molar enthalpy of sulfuric acid in water at 21°C using Equation (6.30). dk K=kx2 drz (6.30)
Graphically determine values for the partial molar enthalpies of sulfuric acid and water in an equimolar mixture at 21°C by plotting Equation (E6.13A). h = 1.596XHSO, +1.591xHO - 74.40xHSOHO (1 -
Consider a system at temperature T and pressure P with m species present in π phases. How many measurable properties need to be determined (e.g., T, P, and xi) to constrain the state of the entire
Consider a bottle of water that you have just opened in the room in which you are sitting. How does the fugacity of water in the liquid in the bottle compare to the fugacity of water in the vapor
A gas mixture of species 1 and 2 at 300 K and 30 bar perfectly obeys the Lewis fugacity rule. What is the enthalpy of mixing? Choose one of the following answers, and explain your reasoning. (Δhmix
In which of the following mixtures do you expect species 1 to be better represented by the Lewis fugacity rule? Explain.Mixture A: n-pentane (1) and n-hexane (2)or, Mixture B: water (1) and n-hexane
Explain why the mixing rules for the van der Waals constants a and b have different forms.
It is 10 a.m. and already getting hot. You are wondering why you agreed to do fi eld work for the summer in Houston. On the radio, the weatherperson declares, “It will be another scorcher today
Henry’s law is often a convenient reference state for the dilute components in the liquid phase in equilibria calculations.(a) Consider a solution of acetone (1) in water (2) vs. a solution of
Consider a binary liquid mixture of species a and b. The activity coeffi cients for this mixture are adequately described by the two-suffi x Margules equation.(a) If Δhmix = 0, what can you say
The development of fugacity is stated to be inductive. Explain what you think is meant by that.

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