A saturated solution of Na2SO4, with excess of the solid, is present at equilibrium with

Define the following terms: phase, constituent, component, and degree of freedom.

What factors determine the number of theoretical plates required to achieve a desired degree of separation in fractional distillation?

Draw phase diagrams for the following types of systems. Label the regions and intersections of the diagrams, stating what materials (possibly compounds or azeotropes) are present and whether they are solid liquid or gas. (a) Onecomponent, pressuretemperature diagram, liquid density greater than that of solid. (b) Two-component, temperaturecomposition, solidliquid diagram, one compound AB formed that melts congruently, negligible solidsolid solubility.

Draw phase diagrams for the following types of systems. Label the regions and intersections of the diagrams, stating what materials (possibly compounds or azeotropes) are present and whether they are solid liquid or gas. (a) Two-component, temperaturecomposition, solidliquid diagram, one compound of formula AB2 that melts incongruently, negligible solidsolid solubility; (b) two-component, constant temperature composition, liquidvapour diagram, formation of an azeotrope at xB = 0.333, complete miscibility.

Label the regions of the phase diagram in Fig. 6.37. State what substances (if compounds give their formulas) exist in each region. Label each substance in each region as solid, liquid, or gas.

Label the regions of the phase diagram in Fig. 6.38. State what substances (if compounds give their formulas) exist in each region. Label each substance in each region as solid, liquid, or gas.

At 90C, the vapour pressure of methylbenzene is 53.3 kPa and that of 1,2-dimethylbenzene is 20.0 kPa. What is the composition of a liquid mixture that boils at 90C when the pressure is 0.50 atm? What is the composition of the vapour produced?

At 90C, the vapour pressure of 1,2-dimethylbenzene is 20 kPa and that of 1,3-dimethylbenzene is 18 kPa. What is the composition of a liquid mixture that boils at 90C when the pressure is 19 kPa? What is the composition of the vapour produced?

The vapour pressure of pure liquid A at 300 K is 76.7 kPa and that of pure liquid B is 52.0 kPa. These two compounds form ideal liquid and gaseous mixtures. Consider the equilibrium composition of a mixture in which the mole fraction of A in the vapour is 0.350. Calculate the total pressure of the vapour and the composition of the liquid mixture.

The vapour pressure of pure liquid A at 293 K is 68.8 kPa and that of pure liquid B is 82.1 kPa. These two compounds form ideal liquid and gaseous mixtures. Consider the equilibrium composition of a mixture in which the mole fraction of A in the vapour is 0.612. Calculate the total pressure of the vapour and the composition of the liquid mixture.

It is found that the boiling point of a binary solution of A and B with xA = 0.6589 is 88C. At this temperature the vapour pressures of pure A and B are 127.6 kPa and 50.60 kPa, respectively. (a) Is this solution ideal? (b) What is the initial composition of the vapour above the solution?

It is found that the boiling point of a binary solution of A and B with xA = 0.4217 is 96C. At this temperature the vapour pressures of pure A and B are 110.1 kPa and 76.5 kPa, respectively. (a) Is this solution ideal? (b) What is the initial composition of the vapour above the solution?

Dibromoethene (DE, p*DE = 22.9 kPa at 358 K) and dibromopropene (DP, p*DP = 17.1 kPa at 358 K) form a nearly ideal solution. If zDE = 0.60, what is (a) ptotal when the system is all liquid, (b) the composition of the vapour when the system is still almost all liquid?

Benzene and toluene form nearly ideal solutions. Consider an equimolar solution of benzene and toluene. At 20C the vapour pressures of pure benzene and toluene are 9.9 kPa and 2.9 kPa, respectively. The solution is boiled by reducing the external pressure below the vapour pressure. Calculate (a) the pressure when boiling begins, (b) the composition of each component in the vapour, and (c) the vapour pressure when only a few drops of liquid remain. Assume that the rate of vaporization is low enough for the temperature to remain constant at 20C.

The following temperature/composition data were obtained for a mixture of octane (O) and methylbenzene (M) at 1.00 atm, where x is the mole fraction in the liquid and y the mole fraction in the vapour at equilibrium. /C 110.9 112.0 114.0 115.8 117.3 119.0 121.1 123.0 xM 0.908 0.795 0.615 0.527 0.408 0.300 0.203 0.097 yM 0.923 0.836 0.698 0.624 0.527 0.410 0.297 0.164 The boiling points are 110.6C and 125.6C for M and O, respectively. Plot the temperature/composition diagram for the mixture. What is the composition of the vapour in equilibrium with the liquid of composition (a) xM = 0.250 and (b) xO = 0.250?

The following temperature/composition data were obtained for a mixture of two liquids A and B at 1.00 atm, where x is the mole fraction in the liquid and y the mole fraction in the vapour at equilibrium. /C 125 130 135 140 145 150 xA 0.91 0.65 0.45 0.30 0.18 0.098 yA 0.99 0.91 0.77 0.61 0.45 0.25 The boiling points are 124C for A and 155C for B. Plot the temperature composition diagram for the mixture. What is the composition of the vapour in equilibrium with the liquid of composition (a) xA = 0.50 and (b) xB = 0.33?

State the number of components in the following systems. (a) NaH2PO4 in water at equilibrium with water vapour but disregarding the fact that the salt is ionized. (b) The same, but taking into account the ionization of the salt.

State the number of components for a system in which AlCl3 is dissolved in water, noting that hydrolysis and precipitation of Al(OH)3 occur.

Blue CuSO45H2O crystals release their water of hydration when heated. How many phases and components are present in an otherwise empty heated container?

Ammonium chloride, NH4Cl, decomposes when it is heated. (a) How many components and phases are present when the salt is heated in an otherwise empty container? (b) Now suppose that additional ammonia is also present. How many components and phases are present?

A saturated solution of Na2SO4, with excess of the solid, is present at equilibrium with its vapour in a closed vessel. (a) How many phases and components are present. (b) What is the variance (the number of degrees of freedom) of the system? Identify the independent variables.

Suppose that the solution referred to in Exercise 6.8a is not saturated. (a) How many phases and components are present. (b) What is the variance (the number of degrees of freedom) of the system? Identify the independent variables.

Methylethyl ether (A) and diborane, B2H6 (B), form a compound that melts congruently at 133 K. The system exhibits two eutectics, one at 25 mol per cent B and 123 K and a second at 90 mol per cent B and 104 K. The melting points of pure A and B are 131 K and 110 K, respectively. Sketch the phase diagram for this system. Assume negligible solidsolid solubility.

Sketch the phase diagram of the system NH3/N2H4 given that the two substances do not form a compound with each other, that NH3 freezes at 78C and N2H4 freezes at +2C, and that a eutectic is formed when the mole fraction of N2H4 is 0.07 and that the eutectic melts at 80C.

Figure 6.39 shows the phase diagram for two partially miscible liquids, which can be taken to be that for water (A) and 2-methyl-1-propanol (B). Describe what will be observed when a mixture of composition xB = 0.8 is heated, at each stage giving the number, composition, and relative amounts of the phases present.

Figure 6.40 is the phase diagram for silver and tin. Label the regions, and describe what will be observed when liquids of compositions a and b are cooled to 200 K.

Indicate on the phase diagram in Fig. 6.41 the feature that denotes incongruent melting. What is the composition of the eutectic mixture and at what temperature does it melt?

Indicate on the phase diagram in Fig. 6.42 the feature that denotes incongruent melting. What is the composition of the eutectic mixture and at what temperature does it melt?

Sketch the cooling curves for the isopleths a and b in Fig. 6.41.

Sketch the cooling curves for the isopleths a and b in Fig. 6.42.

Use the phase diagram in Fig. 6.40 to state (a) the solubility of Ag in Sn at 800C and (b) the solubility of Ag3Sn in Ag at 460C, (c) the solubility of Ag3Sn in Ag at 300C.

Use the phase diagram in Fig. 6.41 to state (a) the solubility of B in A at 500C and (b) the solubility of AB2 in A at 390C, (c) the solubility of AB2 in B at 300C.

Figure 6.43 shows the experimentally determined phase diagrams for the nearly ideal solution of hexane and heptane. (a) Label the regions of the diagrams as to which phases are present. (b) For a solution containing 1 mol each of hexane and heptane, estimate the vapour pressure at 70C when vaporization on reduction of the external pressure just begins. (c) What is the vapour pressure of the solution at 70C when just one drop of liquid remains. (d) Estimate from the figures the mole fraction of hexane in the liquid and vapour phases for the conditions of part b. (e) What are the mole fractions for the conditions of part c? (f) At 85C and 760 Torr, what are the amounts of substance in the liquid and vapour phases when zheptane = 0.40?

Uranium tetrafluoride and zirconium tetrafluoride melt at 1035C and 912C, respectively. They form a continuous series of solid solutions with a minimum melting temperature of 765C and composition x(ZrF4) = 0.77. At 900C, the liquid solution of composition x(ZrF4) = 0.28 is in equilibrium with a solid solution of composition x(ZrF4) = 0.14. At 850C the two compositions are 0.87 and 0.90, respectively. Sketch the phase diagram for this system and state what is observed when a liquid of composition x(ZrF4) = 0.40 is cooled slowly from 900C to 500C.

Methane (melting point 91 K) and tetrafluoromethane (melting point 89 K) do not form solid solutions with each other, and as liquids they are only partially miscible. The upper critical temperature of the liquid mixture is 94 K at x(CF4) = 0.43 and the eutectic temperature is 84 K at x(CF4) = 0.88. At 86 K, the phase in equilibrium with the tetrafluoromethane-rich solution changes from solid methane to a methane-rich liquid. At that temperature, the two liquid solutions that are in mutual equilibrium have the compositions x(CF4) = 0.10 and x(CF4) = 0.80. Sketch the phase diagram.

Describe the phase changes that take place when a liquid mixture of 4.0 mol B2H6 (melting point 131 K) and 1.0 mol CH3OCH3 (melting point 135 K) is cooled from 140 K to 90 K. These substances form a compound (CH3)2OB2H6 that melts congruently at 133 K. The system exhibits one eutectic at x(B2H6) = 0.25 and 123 K and another at x(B2H6) = 0.90 and 104 K.

Refer to the information in Exercise 6.15(b) and sketch the cooling curves for liquid mixtures in which x(B2H6) is (a) 0.10, (b) 0.30, (c) 0.50, (d) 0.80, and (e) 0.95.

Refer to the information in Exercise 6.15(a) and sketch the cooling curves for liquid mixtures in which \(x\left(\mathrm{CF}_4\right)\) is (a) 0.10, (b) 0.30, (c) 0.50, (d) 0.80, and (e) 0.95.

Hexane and perfluorohexane show partial miscibility below \(22.70^{\circ} \mathrm{C}\). The critical concentration at the upper critical temperature is x=0.355, where x is the mole fraction of \(\mathrm{C}_6 \mathrm{~F}_{14}\). At \(22.0^{\circ} \mathrm{C}\) the two solutions in equilibrium have x=0.24 and x=0.48, respectively, and at \(21.5^{\circ} \mathrm{C}\) the mole fractions are 0.22 and 0.51. Sketch the phase diagram. Describe the phase changes that occur when perfluorohexane is added to a fixed amount of hexane at (a) \(23^{\circ} \mathrm{C}\), (b) \(22^{\circ} \mathrm{C}\).

Two liquids, A and B, show partial miscibility below 52.4C. The critical concentration at the upper critical temperature is x = 0.459, where x is the mole fraction of A. At 40.0C the two solutions in equilibrium have x = 0.22 and x = 0.60, respectively, and at 42.5C the mole fractions are 0.24 and 0.48. Sketch the phase diagram. Describe the phase changes that occur when B is added to a fixed amount of A at (a) 48C, (b) 52.4C.

Sketch the phase diagram for the Mg/Cu system using the following information: f (Mg) = 648C, f (Cu) = 1085C; two intermetallic compounds are formed with f (MgCu2) = 800C and f (Mg2Cu) = 580C; eutectics of mass percentage Mg composition and melting points 10 per cent (690C), 33 per cent (560C), and 65 per cent (380C). A sample of Mg/Cu alloy containing 25 per cent Mg by mass was prepared in a crucible heated to 800C in an inert atmosphere. Describe what will be observed if the melt is cooled slowly to room temperature. Specify the composition and relative abundances of the phases and sketch the cooling curve.

Figure 6.45 shows \(\Delta_{mix } G\left(x_{\mathrm{Pb}}, T\right)\) for a mixture of copper and lead. (a) What does the graph reveal about the miscibility of copper and lead and the spontaneity of solution formation? What is the variance (F) at (i) \(1500 \mathrm{~K}\), (ii) \(1100 \mathrm{~K}\) ? (b) Suppose that at \(1500 \mathrm{~K}\) a mixture of composition (i) \(x_{\mathrm{Pb}}=0.1\), (ii) \(x_{\mathrm{Pb}}=0.7\), is slowly cooled to \(1100 \mathrm{~K}\). What is the equilibrium composition of the final mixture? Include an estimate of the relative amounts of each phase. (c) What is the solubility of (i) lead in copper, (ii) copper in lead at \(1100 \mathrm{~K}\) ?

The temperaturecomposition diagram for the Ca/Si binary system is shown in Fig. 6.46. (a) Identify eutectics, congruent melting compounds, and incongruent melting compounds. (b) If a 20 per cent by atom composition melt of silicon at 1500C is cooled to 1000C, what phases (and phase composition) would be at equilibrium? Estimate the relative amounts of each phase. (c) Describe the equilibrium phases observed when an 80 per cent by atom composition Si melt is cooled to 1030C. What phases, and relative amounts, would be at equilibrium at a temperature (i) slightly higher than 1030C, (ii) slightly lower than 1030C? Draw a graph of the mole percentages of both Si(s) and CaSi2(s) as a function of mole percentage of melt that is freezing at 1030C.

Iron(II) chloride (melting point 677C) and potassium chloride (melting point 776C) form the compounds KFeCl3 and K2FeCl4 at elevated temperatures. KFeCl3 melts congruently at 380C and K2FeCl4 melts incongruently at 399C. Eutectics are formed with compositions x = 0.38 (melting point 351C) and x = 0.54 (melting point 393C), where x is the mole fraction of FeCl2. The KCl solubility curve intersects the K2FeCl4 curve at x = 0.34. Sketch the phase diagram. State the phases that are in equilibrium when a mixture of composition x = 0.36 is cooled from 400Cto 300C.

Show that two phases are in thermal equilibrium only if their temperatures are the same.

Show that two phases are in mechanical equilibrium only if their pressures are equal.

The unfolding, or denaturation, of a biological macromolecule may be brought about by treatment with substances, called denaturants, that disrupt the intermolecular interactions responsible for the native three-dimensional conformation of the polymer. For example, urea, CO(NH2)2, competes for NH and CO groups and interferes with hydrogen bonding in a polypeptide. In a theoretical study of a protein, the temperaturecomposition diagram shown in Fig. 6.47 was obtained. It shows three structural regions: the native form, the unfolded form, and a molten globule form, a partially unfolded but still compact form of the protein. (i) Is the molten globule form ever stable when the denaturant concentration is below 0.1? (ii) Describe what happens to the polymer as the native form is heated in the presence of denaturant at concentration 0.15.

The basic structural element of a membrane is a phospholipid, such as phosphatidyl choline, which contains long hydrocarbon chains (typically in the range C14C24) and a variety of polar groups, such as CH2CH2N(CH3)3 +. The hydrophobic chains stack together to form an extensive bilayer about 5 nm across, leaving the polar groups exposed to the aqueous environment on either side of the membrane (see Chapter 19 for details). All lipid bilayers undergo a transition from a state of low chain mobility (the gel form) to high chain mobility (the liquid crystal form) at a temperature that depends on the structure of the lipid. Biological cell membranes exist as liquid crystals at physiological temperatures. In an experimental study of membrane-like assemblies, a phase diagram like that shown in Fig. 6.48 was obtained. The two components are dielaidoylphosphatidylcholine (DEL) and dipalmitoylphosphatidylcholine (DPL). Explain what happens as a liquid mixture of composition xDEL = 0.5 is cooled from 45C.

The compound p-azoxyanisole forms a liquid crystal. 5.0 g of the solid was placed in a tube, which was then evacuated and sealed. Use the phase rule to prove that the solid will melt at a definite temperature and that the liquid crystal phase will make a transition to a normal liquid phase at a definite temperature

Some polymers can form liquid crystal mesophases with unusual physical properties. For example, liquid crystalline Kevlar (3) is strong enough to be the material of choice for bulletproof vests and is stable at temperatures up to 600 K. What molecular interactions contribute to the formation, thermal stability, and mechanical strength of liquid crystal mesophases in Kevlar?

Use a phase diagram like that shown in Fig. 6.36 to indicate how zone levelling may be described.

The technique of float zoning, which is similar to zone refining (Impact I6.2), has produced very pure samples of silicon for use in the semiconductor industry. Consult a textbook of materials science or metallurgy and prepare a discussion of the principles, advantages, and disadvantages of float zoning.

Magnesium oxide and nickel oxide withstand high temperatures. However, they do melt when the temperature is high enough and the behaviour of mixtures of the two is of considerable interest to the ceramics industry. Draw the temperaturecomposition diagram for the system using the data below, where x is the mole fraction of MgO in the solid and y its mole fraction in the liquid. /C 1960 2200 2400 2600 2800 x 0 0.35 0.60 0.83 1.00 y 0 0.18 0.38 0.65 1.00 State (a) the melting point of a mixture with x = 0.30, (b) the composition and proportion of the phases present when a solid of composition x = 0.30 is heated to 2200C, (c) the temperature at which a liquid of composition y = 0.70 will begin to solidify.

The bismuth-cadmium phase diagram is of interest in metallurgy, and its general form can be estimated from expressions for the depression of freezing point. Construct the diagram using the following data: \(T_{\mathrm{f}}(\mathrm{Bi})=544.5 \mathrm{~K}, T_{\mathrm{f}}(\mathrm{Cd})=594 \mathrm{~K}, \Delta_{\text {fus }} H(\mathrm{Bi})=10.88 \mathrm{~kJ} \mathrm{~mol}^{-1}\),\(\Delta_{\text {fus }} H(\mathrm{Cd})=6.07 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The metals are mutually insoluble as solids. Use the phase diagram to state what would be observed when a liquid of composition \(x(\mathrm{Bi})=0.70\) is cooled slowly from \(550 \mathrm{~K}\). What are the relative abundances of the liquid and solid at (a) \(460 \mathrm{~K}\) and (b) \(350 \mathrm{~K}\)? Sketch the cooling curve for the mixture.

Carbon dioxide at high pressure is used to separate various compounds in citrus oil. The mole fraction of CO2 in the liquid (x) and vapour (y) at 323.2 K is given below for a variety of pressures (Y. Iwai, T. Morotomi, K. Sakamoto, Y. Koga, and Y. Arai, J. Chem. Eng. Data 41, 951 (1996)). p/MPa 3.94 6.02 7.97 8.94 9.27 x 0.2873 0.4541 0.6650 0.7744 0.8338 y 0.9982 0.9980 0.9973 0.9958 0.9922 (a) Plot the portion of the phase diagram represented by these data. (b) State the compositions and relative proportions of the two phases present after an equimolar crystal phase will make a transition to a normal liquid phase at a definite temperature.