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Chapter 6 Problems - Problems Problems...

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Unformatted text preview: Problems ' Problems ——_—_——I—_—————— AG and AA 6.1 A quantity of 0.35 mole of an ideal gas initially at 15.6 °C is expanded from 1.2 L to 7.4 L. Calculate the values of w,,-‘q, AU, AS, and AG if the process is carried out (a) isothermally and reversibly, and (b) isother'mally and irreversibly against an external pressure of 1.0 atm. 6.2 At one time, the domestic gas used for cooking, called “water gas,” was prepared as follows: H2001) + C(graphite) -+ C0(9) + H2(g) From the thermodynamic quantities listed in Appendix B, predict whether this reaction will occur at 298 K. If not, at what temperature will the reaction occur? Assume A,H° and A,S° are temperature independent. 6.3 Use the Values listed in Appendix B to calculate the value of AIG° for the following alcohol fermentation: a—D-glucose-(aq) -+ 2C2H50H(l) +2C02(g) (AfG°[<z-D-glucose(aq)] = ——914.5 k] mol‘l) 6.4 Without referring to Appendix B, calculate the quantity (A,G° — A,A°) for the following reaction at 298 K: C(S)+C02(g) -> 2C0(g) Assume ideal-gas behavior. 6.5 As an approximation, we can assume that proteins exist either in the native (or physiologically functioning) state and the denatured state. The standard molar enthalpy and entropy of the denaturation of a certain protein are 512 kJ mol‘1 and 1.60 k] K"1 mol‘l, respectively. Comment on the signs and magnitudes of these quantities, and calculate the temperature at which the denaturation becomes spontaneous. 6.6 Certain bacteria in the soil obtain the necessary energy for growth by oxidizing nitrite to nitrate: 2N0; (at!) + 02(9) —> 2N0§(aq) Given that the standard Gibbs energies of formation of N02— and NO; are —34.6 kJ mol‘1 and —110.5 kJ mol“, respectively, calculate the amount of Gibbs energy released when 1 mole of N02— is oxidized to 1 mole of NO; 6.7 Consider the synthesis of urea according to the equation 002(9) + 2NH3(9) —> (NH2)2CO(s) + H20(l) From the data listed in Appendix B, calculate the value of A,G° for the reaction at 298 K. Assuming id_eal gas behavior, calculate the value of A,G for the reaction at a pressure of 10.0 bar. The AfG° of urea is —197.15 kJ mol". 6.8 This problem involves the synthesis of diamond from graphite: C(graphite) —> C(diamond) 197 198 Chapter 6: Gibbs and Helmholtz Energies and Their Applications (a) Calculate the values of A,H° and ArS° for the reaction. Will the conversion occur spontaneously at 25 °C or any other temperature? (b) From density measurements, the molar volume of graphite is found to be 2.1 cm3 greater than that of diamond. Can the conversion of graphite to diamond be brought about at 25 °C by applying pressure on graphite? If so, estimate the pressure at which the process becomes spontaneous. [Hint: Starting from Equation 6.16, derive the equation AG = (Vdiamond —- VyaphimMP for a constant-temperature process. Next, calculate the AP value that would lead to the necessary decrease in Gibbs energy.] 6.9 How do the requirements that T and V are constant enter the derivation for AAsys < 0 for a spontaneous process? 6.10 From the standard molar enthalpy of combustion of benzene at 298 K, calculate the value of A,A for the process. Compare the value of AA" with that of A,H°. Comment on the difference. 6.11 A student placed 1 g of each of three compounds A, B, and C in a container and found that no change had occurred after one week. Offer possible explanations for the lack of reaction. Assume that A, B, and C are totally miscible liquids. 6.12 Predict the signs of AH, AS, and AG of the system for the following processes at 1 atm: (a) ammonia melts at —60 °C, (b) ammonia melts at —77.7 °C, (c) ammonia melts at —100 °C. (The normal melting point of ammonia is —77.7 °C.) 6.13 Crystallization of sodium acetate from a supersaturated solution occurs spontaneously. What can you deduce about the signs of AS and AH? 6.14 A student looked up the AfG°, AMT, and 5': values for C02_ in Appendix B. Plugging these values into Equation 6.3, he found that AfG° 7E AfH° -— T S° at 298 K.“What is wrong with his approach? 6.15 A certain reaction is spontaneous at 72 °C. If the enthalpy change for the reaction is 19 kJ, what is the minimum value of AS (in joules per kelvin) for the reaction? 6.16 A certain reaction is known to have a A,G° value of — 122 kJ. Will the reaction necessarily occur if the reactants are mixed together? iPhase Equilibria 6.17 The vapor pressure of mercury at various temperatures has been determined as follows: T/K P/mmHg 323 0.0127 353 0.0888 393.5 0.7457 413 1.845 433 4.189 Calculate the value of Am]? for mercury. 6.18 The pressure exerted on ice by a 60.0-kg skater is about 300 atrn. Calculate the depression in freezing point. The molar volumes are: 17L = 0.0180 L mol‘1 and 73 = 0.0196 L mol‘l. 6.19 Use the phase diagram of water (Figure 6.5) to predict the direction for the following changes: (a) at the triple point of water, temperature is lowered at constant pressure, and (b) somewhere along the S—L curve of water, pressure is increased at constant temperature. 6.20 Use the phase diagram of water (Figure 6.5) to predict the dependence of the freezing and boiling points of water on pressure. 6.21 Consider the following system at equilibrium CaCO3(s) = CaO(s) +C02(g) Problems 199 How many phases are present? 6.2 Below is a rough sketch of the phase diagram of carbon. (a) How many triple points are there, and what are the phases that can coexist at each triple point? (b) Which has a higher density, graphite or diamond? (c) Synthetic diamond can be made from graphite. Using the phase diagram, how would you go about making diamond? ,3’ Diamond 2x104 P/atm Graphite 3300 t/°C 6.23 What is wrong with the following phase diagram for a one-component system? 6.24 The plot in Figure 6.4 is no longer linear at high temperatures. Explain. 6.25 Pike’s Peak in Colorado is approximately 4,300 m above sea level (0°C). What is the boiling point of water at the summit? (Hint: See Problem 2.56. The molar mass of air is 29.0 g mol", and AvapH for water is 40.79 kJ mol“.) 6.26 The normal boiling point of ethanol is 78.3 °C, and its molar enthalpy of vaporization is 39.3 k] mol'l. What is its vapor pressure at 30°C? 6.27 Calculate the number of components present in each of the following situations: (a) Water, including autodissociation into H+ and OH‘ ions. (b) Consider the following reaction in a closed container: 2NH3(g) = N2(9) +3H2(9) (i) All three gases were present initially in arbitrary amounts, but the temperature is too low for the reaction to occur. ' (ii) Same as (i), but the temperature is raised sufliciently to allow for the equilibrium to be established. (iii) Initially only NH3 was present. The system is then allowed to reach equilibrium. 200 Chapter 6: Gibbs and Helmholtz Energies and Their Applications Additional Problems 6.28 Give the conditions under which each of the following equations may be applied. (a) dA < 0 (for equilibrium and spontaneity)P (b) dG < 0 (for equilibrium and spontaneity), P2 AH (T2 — T1) __ = _ _— _ RTl ———. (c) In P1 R T1T2 , (d) AG— n n P; 6. 29 When ammonium nitrate is dissolved in water, the solution becomes colder. What conclusion can you draw about AS° for the process? 6.30 Protein molecules are polypeptide chains made up of amino acids. In their physiologically functioning or native state, these chains fold in a unique manner such that the nonpolar groups of the amino acids are usually buried in the interior region of the proteins, where there is little or no contact with water. When a protein denatures, the chain unfolds so that these nonpolar groups are exposed to water. A useful estimate of the changes of the thermodynamic quantities as a result of denaturation is to consider the transfer of a hydrocarbon such as methane (a nonpolar substance) from an inert solvent (such as benzene or carbon tetrachloride) to the aqueous environment: (a) CH4 (inert solvent) —> CH4(g) (b) CH4(g) —* CH4(aq) If the values of AH ° and AG° are approximately 2.0 kJ mol‘1 and —14.5 kJ mol“, respectively, for (a) and —13.5 kJ mol‘1 and 26.5 kJ mol‘l, respectively, for (b), calculate the values of AH ° and AG° for the transfer of 1 mole of CH4 according to the equation CH4(inert solvent) —> CH4(aq) Comment on your results. Assume T = 298 K. 6.31 Find a rubber band that is about 0.5 cm wide. Quickly stretch the rubber band and then press it against your lips. You will feel a slight warming efi'ect. Next, reverse the process. Stretch a rubber band and hold it in position for a few seconds. Then quickly release the tension and press the rubber band against your lips. This time you will feel a slight cooling effect. Use Equation 6.3 to present a thermodynamic analysis of this behavior. 6.32 A rubber band under tension will contract when heated. Explain. 6.33 Hydrogenation reactions are facilitated by the use of a transition metal catalyst, such as Ni or Ft. Predict the signs of AH, AS, and A,G when hydrogen gas is adsorbed onto the surface of nickel metal. 6.34 A sample of supercooled water freezes at —10 °C. What are the signs of AH, AS, and AG for this process? All the changes refer to the system. 6.35 The boiling point of benzene is 80.1 °C. Estimate (a) its AvapH value and (b) its vapor pressure at 74°C. (Hint: Use Trouton’s rule on p. 144.) 6.36 A chemist has synthesized a hydrocarbon compound (Cx Hy). _Briefly describe what measurements are needed to determine the values of AfH°, S°, and Af G° of the compound. 6.37 A closed, 7.8-L flask contains 1.0 g of water. At what temperature will half of the water be m the vapor phase? (Hint: Look up the vapor pressures of water in the inside back matter.) 6.38 A person heated water in a closed bottle in a microwave oven for tea. After removing the bottle from the oven, she added a tea bag to the hot water. To her surprise, the water started to boil , violently. Explain what happened. 6.39 Consider the reversible, isothermal compression of 0.45 mole of helium gas from 0.50 atm and 22 L to 1.0 atm at 25 °C. (a) Calculate the values of w, AU, AH, AS, and AG for the process. (b) Can you use the sign of AG to predict whether the process is spontaneous? Explain. Problems 201 (c) What is the maximum work that can be done for the compression process? Assume ideal-gas behavior. 6.40 The molar entropy of argon (Ar) is given by §° = (36.4 + 20.81n T) J K-1 mol‘l Calculate the change in Gibbs energy when 1.0 mole of Ar is heated at constant pressure from 20 °C to 60 °C. (Hint: Use the relation flnxdx = xlnx — x.) 6.41 Derive the thermodynamic equation of state: 6 U 6P (W). — ‘P + 4%» Apply the equation to (a) an ideal gas and (b) a van der Waals gas. Cement on your results. (Hint: See Appendix 6.1 for thermodynamic relationships.) ...
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