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physical chemistry
Physical Chemistry 3rd edition Thomas Engel, Philip Reid - Solutions
How is the mean ionic chemical potential of a solute related to the chemical potentials of the anion and cation produced when the solute is dissolved in water?
Why are activity coefficients calculated using the Debye–Hückel limiting law always less than one?
Why is it not possible to measure the Gibbs energy of solvation of Cl− directly?
Discuss how the Debye–Hückel screening length changes as the (a) Temperature(b) Dielectric constant,(c) Ionic strength of an electrolyte solution are increased.
Use the Davies equation to calculate γ±for a 1.00 molar solution of KOH. Compare your answer with the values in Table 10.3. 0.2 m 0.7 m 0.4 m 0,8 m 0.9 m Substance 0.1 m 0.3 m 0.5 m 0.6 m 1.0 m 0.657 0.485 AGNO3 0.734 0.606 0.567 0.536 0.509 0.464 0.446 0.429 0.405 0.391 BaCl, 0.500 0.444
Calculate the pH of a buffer solution that is 0.200 molal in CH3COOH and 0.15 molal in CH3COONa using the Davies equation to calculate γ ±. What pH value would you have calculated if you had assumed that γ ± = 1?
Calculate ΔHR and ΔGR for the reaction AgNO3(aq) + KCl(aq) → AgCl(s) + KNO3(aq).
Calculate the value of m± in 5.5 × 10−3 molal solutions of (a) KCl(b) Ca(NO3)2(c) ZnSO4. Assume complete dissociation.
Calculate the ionic strength of each of the solutions in Problem P10.4.In Problem V-l, + V-H- Usolute
Calculate I, γ ±, and a± for a 0.0175 m solution of Na3PO4 at 298 K. Assume complete dissociation. How confident are you that your calculated results will agree with experimental results?
Calculate I, γ ±, and a± for a 0.0215 m solution of K2SO4 at 298 K. How confident are you that your calculated results will agree with experimental results?
Calculate the Debye–Hückel screening length 1/κ at 298 K in a 0.0075 m solution of K3PO4.
Dichloroacetic acid has a dissociation constant of Ka = 3.32 × 10-2. Calculate the degree of dissociation for a 0.105 m solution of this acid a. Using the Debye–Hückel limiting law using an iterative calculation until the answer is constant to within ± 2 in the second decimal
What information can be obtained from a tie line in a P−Z phase diagram?
Describe the system at points a and c in Figure 19.25b. How would you calculate the relative amounts of different phases present at these points?
Describe the changes in a beaker containing water and butanol that you would observe along the path f → j → k in Figure 19.24b. How would you calculate the relative amounts of different phases present along the path?
Describe the changes in a beaker containing water and butanol that you would observe along the path f → j → k in Figure 19.24b. How would you calculate the relative amounts of different phases present along the path?
Describe the changes in a beaker containing water and butanol that you would observe along the path a → b → c in Figure 19.24b. How would you calculate the relative amounts of different phases present along the path?
Describe the changes you would observe as the temperature of a mixture of triethylamine\ and water at point a in Figure 9.22 is increased until the system is at point a€³. How does the relative amount of separate phases of triethylamine and water change along this path?Figure 9.22
Describe the changes you would observe as the temperature of a mixture of phenol and water at point a in Figure 9.21 is increased until the system is at point a€². How does the relative amount of separate phases of phenol and water change along this path?Figure 9.21 a' L1 L2 ai L4 + L2 о
An ideal dilute solution is formed by dissolving the solute A in the solvent B. Write expressions equivalent to Equations (9.9) through (9.13) for this case.
Describe what you would observe if you heated the solid at the composition 40. atomic percent Si in Figure 9.26 from 300.°C to 1300.°C.
The dissolution of 7.75g of a substance in 825 g of benzene at 298 K raises the boiling point by 0.575°C. Note that K f = 5.12 K kg mol–1, Kb = 2.53 K kg mol–1, and the density of benzene is 876.6 kg m–3. Calculate the freezing point depression, the ratio of the vapor pressure above the
Calculate the activity and activity coefficient for CS2 at xCS2 = 0.722 using the data in Table 9.3 for both a Raoult’s law and a Henry’s law standard state.
DNA is capable of forming complex helical structures. An unusual triple-helix structure of poly(dA).2poly(dT) DNA was studied by P. V. Scaria and R. H. Shafer [Journal of Biological Chemistry 266 (1991): 5417] where the intercalation of ethidium bromide was studied using UV absorption and circular
Assume that 1-bromobutane and 1-chlorobutane form an ideal solution. At 273 K, P* chloro = 3790. Pa and P* bromo = 1394 Pa. When only a trace of liquid is present at 273 K, y chloro = 0.750. a. Calculate the total pressure above the solution.b. Calculate the mole fraction of
In an ideal solution of A and B, 3.00mol are in the liquid phase and 5.00mol are in the gaseous phase. The overall composition of the system is ZA = 0.375 and xA = 0.250. Calculate yA.
The vapor pressures of 1-bromobutane and 1-chlorobutane can be expressed in the formAndAssuming ideal solution behavior, calculate x bromo and y bromo at 305 K and a total pressure of 9750. Pa. At 305 K, Po bromo = 7113 Pa and Po chloro = 18552 Pa. 1584.8 Poromo = 17.076 - In т 111.88 K Pa 2688.1
A volume of 5.50 L of air is bubbled through liquid toluene at 298 K, thus reducing the mass of toluene in the beaker by 2.38 g. Assuming that the air emerging from the beaker is saturated with toluene, determine the vapor pressure of toluene at this temperature
A sample of glucose (C6H12O6) of mass 13.2 g is placed in a test tube of radius 1.25 cm. The bottom of the test tube is a membrane that is semi-permeable to water. The tube is partially immersed in a beaker of water at 298 K so that the bottom of the test tube is only slightly below the level of
A solution is prepared by dissolving 45.2 g of a nonvolatile solute in 119 g of water. The vapor pressure above the solution is 22.51 Torr and the vapor pressure of pure water is 23.76 Torr at this temperature. What is the molecular weight of the solute?
An ideal solution is formed by mixing liquids A and B at 298 K. The vapor pressure of pure A is 151 Torr and that of pure B is 84.3 Torr. If the mole fraction of A in the vapor is 0.610, what is the mole fraction of A in the solution?
Two liquids, A and B, are immiscible for xA = xB = 0.5, for T < 75.0????C and completely miscible for T > 75.0????C. Sketch the phase diagram, showing as much information as you can from these observations.
The densities of pure water and ethanol are 997 and 789 kg m−3, respectively. For x ethanol = 0.35, the partial molar volumes of ethanol and water are 55.2 and 17.8 × 10−3 L mol−1, respectively. Calculate the change in volume relative to the pure components when 2.50 L of a solution with x
The data from Problem P9.20 can be expressed in terms of the molality rather than the mole fraction of Br2 . Use the data from the following table and a graphical method to determine the Henry€™s law constant for Br2in CCl4at 25°C in terms of molality. тв, (mol kg-l) 0.026 0.028
The partial pressures of Br2 above a solution containing CCl4as the solvent at 25°C are found to have the values listed in the following table as a function of the mole fraction of Br2in the solution [Lewis G. N., and Storch, H. J. American Chemical Society 39 (1917): 2544]. Use these data
A and B form an ideal solution. At a total pressure of 0.720 bar, yA = 0.510 and xA = 0.420. Using this information, calculate the vapor pressure of pure A and of pure B.
Given the vapor pressures of the pure liquids and the overall composition of the system, what are the upper and lower limits of pressure between which liquid and vapor coexist in an ideal solution?
The binding of NADH to human liver mitochondrial isozyme was studied [Biochemistry 28 (1989): 5367] and it was determined that only a single binding site is present with K = 2.0 × 107 M−1. What concentration of NADH is required to occupy 10% of the binding sites?
Calculate the solubility of H2S in 1 L of water if its pressure above the solution is 2.75 Pa. The density of water at this temperature is 997kg m−3.
At 39.9°C, a solution of ethanol (x1 = 0.9006, P*1 = 130.4 Torr) and isooctane (P*2 = 43.9 Torr) forms a vapor phase with y1 = 0.6667 at a total pressure of 185.9 Torr. a. Calculate the activity and activity coefficient of each component. b. Calculate the total pressure that the solution
The heat of fusion of water is 6.008 × 103 J mol−1 at its normal melting point of 273.15 K. Calculate the freezing point depression constant K f.
Describe what you would observe if you heated the liquid mixture at the composition corresponding to point i in Figure 9.24b from a temperature below Tato 118°C.Figure 9.24b 118 Vapor 100 Ть Tj L + VI 94 6, L1 Ta e a L,+L2 Zbutanol (b) T/°C
A and B form an ideal solution at 298 K, with xA = 0.320, P*A = 84.3 Torr, and P*B = 41.2 Torr.a. Calculate the partial pressures of A and B in the gas phase.b. A portion of the gas phase is removed and condensed in a separate container. Calculate the partial pressures of A and B in equilibrium
At −47°C, the vapor pressure of ethyl bromide is 10.0 Torr and that of ethyl chloride is 40.0 Torr. Assume that the solution is ideal. Assume there is only a trace of liquid present and the mole fraction of ethyl chloride in the vapor is 0.80 and answer these questions:a. What is the total
At high altitudes, mountain climbers are unable to absorb a sufficient amount of O2 into their bloodstreams to maintain a high activity level. At a pressure of 1 bar, blood is typically 95% saturated with O2, but near 18,000 feet where the pressure is 0.50 bar, the corresponding degree of
The volatile liquids A and B, for which P*A = 165 Torr and P*B = 85.1. Torr are confined to a piston and cylinder assembly. Initially, only the liquid phase is present. As the pressure is reduced, the first vapor is observed at a total pressure of 110. Torr. Calculate xA.
At 303 K, the vapor pressure of benzene is 120. Torr and that of hexane is 189 Torr. Calculate the vapor pressure of a solution for which x benzene = 0.28 assuming ideal behavior.
The osmotic pressure of an unknown substance is measured at 298 K. Determine the molecular weight if the concentration of this substance is 31.2 kg m−3 and the osmotic pressure is 5.30 × 104 Pa. The density of the solution is 997 kg m−3.
A solution is made up of 222.9 g of ethanol and 130.8 g of H2O. If the volume of the solution is 403.4 cm3 and the partial molar volume of H2O is 17.0 cm3 mol−1, what is the partial molar volume of ethanol under these conditions?
The partial molar volumes of water and ethanol in a solution with xH2O = 0.45 at 25°C are 17.0 and 57.5 cm3 mol–1, respectively. Calculate the volume change upon mixing sufficient ethanol with 3.75 mol of water to give this concentration. The densities of water and ethanol are 0.997 and 0.7893g
At 350. K, pure toluene and hexane have vapor pressures of 3.57 × 104 Pa and 1.30 × 105 Pa, respectively.a. Calculate the mole fraction of hexane in the liquid mixture that boils at 350. K at a pressure of 1atm.b. Calculate the mole fraction of hexane in the vapor that is in equilibrium
Two liquids, A and B, are immiscible for T < 75.0°C and for T > 45.0°C and are completely miscible outside of this temperature range. Sketch the phase diagram, showing as much information as you can from these observations.
The statement “The boiling point of a typical liquid mixture can be reduced by approximately 100°C if the pressure is reduced from 760. to 20. Torr” is found in Section 9.4. What figure(s) in Chapter 9 can you identify to support this statement in a qualitative sense?
What can you say about the composition of the solid below the eutectic temperature in Figure 9.26 on a microscopic scale? 1500 1300 1100 Liquid 900 700 Liquid + Solid 500 363°C 300 18.6% Solid 100 20 40 60 80 100 Atomic percent silicon T/°C
You boil an ethanol–benzene mixture with x ethanol = 0.35. What is the composition of the vapor phase that first appears? What is the composition of the last liquid left in the vessel?
At a given temperature, a nonideal solution of the volatile components A and B has a vapor pressure of 795 Torr. For this solution, yA = 0.375. In addition, xA = 0.310, P*A = 610. Torr, and P*B = 495 Torr. Calculate the activity and activity coefficient of A and B.
Ratcliffe and Chao [Canadian Journal of Chemical Engineering 47 (1969): 148] obtained the following tabulated results for the variation of the total pressure above a solution of isopropanol (P*1= 1008 Torr) and n-decane (P*2= 48.3 Torr) as a function of the mole fraction of the n-decane in the
Explain why colligative properties depend only on the concentration, and not on the identity of the molecule.
The entropy of two liquids is increased if they mix. How can immiscibility be explained in terms of thermodynamic state functions?
Why is the preferred standard state for the solvent in an ideal dilute solution the Raoult’s law standard state? Why is the preferred standard state for the solute in an ideal dilute solution the Henry’s law standard state? Is there a preferred standard state for the solution in which x solvent
Is a whale likely to get the bends when it dives deep into the ocean and resurfaces? Answer this question by considering the likelihood of a diver getting the bends if he or she dives and resurfaces on one lung full of air as opposed to breathing air for a long time at the deepest point of the dive.
Using the differential form of G, dG = V dP – S dT, show that if ΔG mixing = nRT Σi xi ln xi, then ΔH mixing = ΔV mixing = 0.
For a pure substance, the liquid and gaseous phases can only coexist for a single value of the pressure at a given temperature. Is this also the case for an ideal solution of two volatile liquids?
Explain the usefulness of a tie line on a Pˆ’Z phase diagram such as that of Figure 9.4.Figure 9.4 100 Liquid 80 60 Liquid + vapor 40 Vapor 20 0.2 0.4 0.6 0.8 Zbenzene Pressure/Torr
Explain why chemists doing quantitative work using liquid solutions prefer to express concentration in terms of molality rather than molarity.
In the description of Figure 9.24b, the following sentence appears: €œAt the point when the L2phase disappears, the temperature increases beyond 94°C and the vapor composition changes along the iˆ’ j curve.€ Why does the vapor composition change along the
Fractional distillation of a particular binary liquid mixture leaves behind a liquid consisting of both components in which the composition does not change as the liquid is boiled off. Is this behavior characteristic of a maximum or a minimum boiling point azeotrope?
Why is the magnitude of the boiling point elevation less than that of the freezing point depression?
Autoclaves that are used to sterilize surgical tools require a temperature of 120.°C to kill some bacteria. If water is used for this purpose, at what pressure must the autoclave operate?
At a given temperature, a liquid can coexist with its gas at a single value of the pressure. However, you can sense the presence of H2O(g) above the surface of a lake by the humidity, and it is still there if the barometric pressure rises or falls at constant temperature. How is this possible?
Are the two P€“T phase diagrams below likely to be observed for a pure substance? If not, explain all features of the diagram that will not be observed.a.b. Liquid Solid Vapor Vapor Liquid Solid
Show the paths n †’ o †’ p †’ q and a †’ b †’ c †’ d †’ e †’ f of the P€“V€“T phase diagram of Figure 8.15 in the
Use the vapor pressures for hexane given in the following table to estimate the temperature and pressure of the triple point and also the enthalpies of fusion, vaporization, and sublimation. Phase T (K) 168 P (Pa) 0.1296 Solid Solid Liquid Liquid 178 1.111 1.400 x 104 4.822 x 104 290. 320.
Figure 8.7 is not drawn to scale. What would be the relative lengths on the qPaxis of the liquid + solid, liquid, and liquid + gas segments for water if the drawing were to scale and the system consisted of H2O?Figure 8.7 Ть AHusion AHaporization Solid Liquid + Solid Liquid Liquid + Gas Gas Яр
Why do the temperature versus heat curves in the solid, liquid, and gas regions of Figure 8.7 have different slopes?Figure 8.7 Ть AHusion AHaporization Solid Liquid + Solid Liquid Liquid + Gas Gas Яр Temperature
Why is it reasonable to show the μ versus T segments for the three phases as straight lines as is done in Figure 8.1? More realistic curves would have some curvature. Is the curvature upward or downward on a μ versus T plot? Explain your answer.Figure 8.1 Solid Liquid I
You have a compound dissolved in chloroform and need to remove the solvent by distillation. Because the compound is heat sensitive, you hesitate to raise the temperature above 5.00°C and decide on vacuum distillation. What is the maximum pressure at which the distillation takes place?
Answer the following questions using the P–T phase diagram for carbon sketched below.a. Which substance is denser, graphite or diamond? Explain your answer.b. Which phase is more dense, graphite or liquid carbon? Explain your answer.c. Why does the phase diagram have two triple points? Explain
It has been suggested that the surface melting of ice plays a role in enabling speed skaters to achieve peak performance. Carry out the following calculation to test this hypothesis. At 1 atm pressure, ice melts at 273.15 K, 6010. Jmol-1, ΔH fusion = the density of ice is 920. kgm−3, and the
A cell is roughly spherical with a radius of 20.0 × 10−6 m. Calculate the work required to expand the cell surface if the radius increases by a factor of three. Assume the cell is surrounded by pure water and that T = 298.15 K.
A P€“T phase diagram for potassium is shown below.a. Which phase has the higher density, the fcc or the bcc phase? Explain your answer.b. Indicate the range of P and T in the phase diagram for which fcc and liquid potassium are in equilibrium. Does fcc potassium float on or sink in liquid
Within what range can you restrict the values of P and T if the following information is known about CO2? Use Figure 8.12 to answer this question.a. As the temperature is increased, the solid is first converted to the liquid and subsequently to the gaseous state.b. An interface delineating liquid
Use the vapor pressures for tetrachloromethane given in the following table to estimate the temperature and pressure of the triple point and also the enthalpies of fusion, vaporization, and sublimation. P (Pa) T (K) Phase Solid 230. 225.7 Solid 905 250. Liquid 6440 280. Liquid 340. 62,501
In Section 8.8, it is stated that the maximum height of a water column in which cavitations does not occur is ∼9.7 m. Show that this is the case at 298 K.
The vapor pressure of ethanol(l) is given bya. Calculate the standard boiling temperature.b. Calculate ΔH vaporization at 298 K and at the standard boiling temperature. 3.6745 x 10 23.58 In Pa – - 46.702 K
Use the vapor pressures of tetrachloromethane given in the following table to calculate the enthalpy of vaporization using a graphical method or a least squares fitting routine. P/Pa T (K) 320. 330. P (Pa) 37130. T (K) 280. 6440. 53250. 74520. 290. 10540 300. 16580 340. 25190 310.
20.0 g of water is in a container of 20.0 L at 298.15 K. The vapor pressure of water at this temperature is 23.76 Torr.a. What phases are present?b. At what volume would only the gas phase be present?c. At what volume would only the liquid phase be present?
A reasonable approximation to the vapor pressure of krypton is given by log10(P/Torr) = b − 0.05223(a/T). For solid krypton, a = 10065 K and b = 7.1770. For liquid krypton, a = 9377.0 K and b = 6.92387. Use these formulas to estimate the triple point temperature and pressure and also the
Consider the transition between two forms of solid tin, Sn (s, gray) → Sn(s, white). The two phases are in equilibrium at 1 bar and 18°C. The densities for gray and white tin are 5750 and 7280 kgm−3, respectively, and the molar entropies for gray and white tin are 44.14 and 51.18 J
Solid iodine, I2(s), at 25.0°C has an enthalpy of sublimation of 56.30 kJ mol−1. The CP,m of the vapor and solid phases at that temperature are 36.9 and 54.4 J K−1 mol−1, respectively. The sublimation pressure at 25.0°C is 0.30844 Torr. Calculate the sublimation pressure of the solid
Calculate the vapor pressure of a droplet of benzene of radius 1.25 × 10−8 m at 38.0°C in equilibrium with its vapor. Use the tabulated value of the density and the surface tension at 298 K from Appendix B for this problem.
In this problem, you will calculate the differences in the chemical potentials of ice and super cooled water, and of steam and superheated water, all at 1 atm pressure shown schematically in Figure 8.1. For this problem, SoH2Os = 48.0 J mol-1 K-1, SoH2Oj = 70.0 J mol-1 K-1, and SoH2Og = 188.8
At 298.15 K, ΔG°f (HCOOH, g) = -351.0 kJ mol-1 and ΔG°f (HCOOH, l) 361.4 kJ mol-1. Calculate the vapor pressure of water at this temperature.
Use the vapor pressures of n-butane given in the following table to calculate the enthalpy of vaporization using a graphical method or a least squares fitting routine. P (Pa) 1000 x 104 1000 x 105 T (°C) -134.3 P (Pa) T (°C) 49.10 1.00 -0.800 -121.9 10.00 -103.9 100.0 -81.10 1000.
The variation of the vapor pressure of the liquid and solid forms of a pure substance near the triple point are given by ln P solid/Pa = -8750K/T + 34.143 and In P liquid /Pa = -4053K/T + 21.10. Calculate the temperature and pressure at the triple point.
The densities of a given solid and liquid of molar mass 122.5 gmol−1 at its normal melting temperature of 427.15 K are 1075 and 1012 kgm−3, respectively. If the pressure is increased to 120. bar, the melting temperature increases to 429.35 K. Calculate ΔH o fusion and ΔSo fusion for
In Equation (8.16), (dP/dT)vaporization was calculated by assuming that V gas m >> V liquid m. In this problem, you will test the validity of this approximation. For water at its normal boiling point of 373.12 K, ΔH vaporization = 40.656 × 103 J mol-1,Pliquid = 958.66 kg m-3, and Pgas
Carbon tetrachloride melts at 250. K. The vapor pressure of the liquid is 10,539 Pa at 290. K and 74,518 Pa at 340. K.The vapor pressure of the solid is 270. Pa at 232 K and 1092 Pa at 250. K.a. Calculate ΔH vaporization and ΔH sublimation.b. Calculate ΔH fusion.c. Calculate the normal boiling
The normal melting point of H2O is 273.15 K, and ∆H fusion = 6010 J mol-1. Calculate the change in the normal freezing point at 100. and 500. bar compared to that at 1 bar assuming that the densities of the liquid and solid phases remain constant at 997 and 917 kgm−3, respectively.
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