Chapter 9 Problems - Problems Problems_’_———-————— Chemical Equilibrium 9.1 Equilibrium constants of gaseous reactions can be

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Unformatted text preview: Problems Problems _’________________———-————— Chemical Equilibrium 9.1 Equilibrium constants of gaseous reactions can be expressed in terms of pressures only (KP), concentrations only (Kc), or mole fractions only (Kx). For the hypothetical reaction I r aA01) : bB(g) derive the following relationships: (a) Kp = KC(RT)A"(P°)_A" and (b) KP = KXPA"(P°)‘A", where An is the difference in the number of moles of products and reactants, and P is the total pressure of the system. Assume ideal-gas behavior. 9.2 At 1024 °C, the pressure of oxygen gas from the decomposition of copper(II) oxide (CuO) is 0.49 bar: 4CuO(s) : 2Cu20(s) +0201) (a) What is the value of K p for the reaction? (b) Calculate the fraction of CuO that will decompose if 0.16 mole of it is placed in a 2.0-L flask at 1024 °C. (c) What would the fraction be if a 1.0-mole sample of CuO were used? ((1) What is the smallest amount of CuO (in moles) that would establish the equilibrium? 9.3 Gaseous nitrogen dioxide is actually a mixture of nitrogen dioxide (N02) and dinitrogen tetroxide (N204). If the density of such a mixture is 2.3 g L‘1 at 74°C and 1.3 atm, calculate the partial pressures of the gases and the value of KP for the dissociation of N204. 9.4 About 75% of the hydrogen produced for industrial use is produced by the steam-reforming process. This process is carried out in two stages called primary and secondary reforming. In the primary stage, a mixture of steam and methane at about 30 atm is heated over a nickel catalyst at 800 °C to give hydrogen and carbon monoxide: CH4(g) + H20(g) : CO(g) + 3H2(g) A.H° = 206 kJ mol-1 The secondary stage is carried out at about 1000 °C, in the presence of air, to convert the remaining methane to hydrogen: CH4(g) +§oz(g) :2 CO(g) + 2H2(g) A.H° = 35.7 kJ mol-1 (a) What conditions of temperature and pressure would favor the formation of products in both the primary and secondary stages? (b) The equilibrium constant, Kc, for the primary stage is 18 at 800 °C. (i) Calculate the value of K p for the reaction. (ii) If the partial pressures of methane and steam were both 15 atm at the start, what would the pressures of all the gases be at equilibrium? 9.5 Consider the reaction PC15(g) : PC13(Q) +C12(g) for which KP = 1.05 at 250 °C. A quantity of 2.50 g of PC15 is placed in an evacuated flask of volume 0.500 L and heated to 250 °C. (a) Calculate the pressure of PC15 if it did not dissociate. (b) Calculate the partial pressure of PC15 at equilibrium. (c) What is the total pressure at equilibrium? ((1) What is the degree of dissociation of PC15? (The degree of dissociation is given by the fraction of PC15 that has undergone dissociation.) 9.6 The vapor pressure of mercury is 0.002 mmHg at 26 °C. (a) Calculate the values of K6 and Kp for the process Hg(l) : Hg(g). (b) A chemist breaks a thermometer and spills mercury onto the 345 346 Chapter 9: Chemical Equilibrium 5.3 m wide, and 3.1 m high. Calculate the mass of d the concentration of mercury vapor in mg ‘3? (Ignore the volume of floor of a laboratory measuring 6.1 m long, mercury (in grams) vaporized at equilibrium an m‘3. Does this concentration exceed the safety limit of 0.05 mg m furniture and other objects in the laboratory.) 9.7 A quantity of 0.20 mole of carbon dioxide was heated to a certain temperature with an excess of graphite in a closed container until the following equilibrium was reached: f) c(s> +c02<g) = more Under these conditions, the average molar mass of the gases was 35 g mol‘l. (a) Calculate the mole fractions of C0 and C02. (b) What is the value of K2: if the total pressure is 11 atm? (Hint: The average molar mass is the sum of the products of the mole fraction of each gas times its molar mass.) van’t Hoff Equation 9.8 Consider the thermal decomposition of CaC03: CaC03(s) :2 Ca0(s) + C02(g) The equilibrium vapor pressures of C02 are 22.6 mmHg at 700 °C and 1829 mmHg at 950 °C. Calculate the standard enthalpy of the reaction. 9.9 Consider the following reaction: C0281) + H2(g) ‘=‘ C0(g) + H2001) The equilibrium constant is 0.534 at 960 K and 1.571 at 1260 K. What is the enthalpy of the reaction? 9.10 The vapor pressure of dry ice (solid C02) is 672.2 torr at —80 Calculate the molar heat of sublimation of C02. 9.11 Nitric oxide from car exhaust is a primary air pollutant. Calculate the equilibrium constan the reaction °C and 1486 torr at —70°C. t for N2(g)+02(g) : ZNOC‘J) at 25 °C using the data listed in Appendix B. Assume that both A,H° and A,S° are temperature independent. Calculate the equilibrium constant at 1500 °C, which is the typical temperature inside the cylinders of a car’s engine after it has been running for some time. AG° and K 9.12 Calculate the value of ArG° for each of the following equilibrium constants: 1.0 x 10-4, 1.0 x 10‘2, 1.0, 1.0 x 102, and 1.0 x 104 at 298 K. 9.13 Use the data listed in Appendix B to calculate the equilibrium constant, KP, for the synthesis of HCl at 298 K: H2(g) + 02(9) ‘2‘ 2HC1(9) What is the value of KP if the equilibrium is expressed as inw) + %C12(g) *4 HC1(9) 9.14 The dissociation of N204 into N02 is 16.7% complete at 298 K and 1 atm: N204(9) : 2N02(9) Problems Calculate the equilibrium constant and the standard Gibbs energy change for the reaction. [Hints Let or be the degree of dissociation and show that KP = 4a2P/ (1 — (12), where P is the total pressure] ' 9.15 The standard Gibbs energies of formation of gaseous cis- and trans-Z-butene are 67.15 kJ mol‘1 and 64.10 kJ mol“, respectively. Calculate the ratio of equilibrium pressures of the gaseous / isomers at 298 K. 9.16 Consider the decomposition of calcium carbonate: CaCO3(s) : Ca0(s) + C02(g) (a) Write an equilibrium constant expression (KP) for the reaction. (b) The rate of decomposition is slow until the partial pressure of carbon dioxide is equal to 1 bar. Calculate the temperature at which the decomposition becomes spontaneous. Assume that AH" and ArS° are temperature independent. Use the data in Appendix B for your calculation. 9.17 Use the data in Appendix B to calculate the equilibrium constant (K P) for the following reaction at 25 °C: 2S02(g) +02(g) :2 2503(9) Calculate Kp for the reaction at 60 CC (a) using the van’t Hoff equation, that is, Equation 9.17; (b) using the Gibbs—Helmholtz equation, that is, Equation 6.15, to find A,G° at 60 oC and hence Kp at the same temperature; and (c) using ArG° = A,H° — TArS° to find A,G° at 60 °C and hence KP at the same temperature. State the approximations employed in each case and compare your results. (Hint: From Equation 6.15, you can derive the relationship A,- Gz ArGl 1 l _ = A _ _ _ T2 T1 rH (T2 T1) Le Chatelier’s Principle 9.18 Consider the reaction 2N02(g) = N204(g) mm = —58.04 kJ mol—1 Predict what happens to the system at equilibrium if (a) the temperature is raised, (b) the pressure on the system is increased, (c) an inert gas is added to the system at constant pressure, ((1) an inert gas is added to the system at constant volume, and (e) a catalyst is added to the system. 9.19 Referring to Problem 9.14, calculate the degree of dissociation of N204 if the total pressure is 10 atm. Comment on your result. 9.20 At a certain temperature, the equilibrium pressures of N02 and N204 are 1.6 bar and 0.58 bar, respectively. If the volume of the container is doubled at constant temperature, what would be the partial pressures of the gases when equilibrium is re-established? 9.21 Eggshells are composed mostly of calcium carbonate (CaCO3) formed by the reaction Ca2+(aq) + Cog—((111) : CaCO3(s) The carbonate ions are supplied by carbon dioxide produced during metabolism. Explain why eggshells are thinner in the summer when the rate of panting by chickens is greater. Suggest a remedy for this situation. 9.22 Photosynthesis can be represented by 6C02(g) + 6H20(l) : C6H1206(s) + 602(g) 'A,H° = 2801 kJ mol-1 348 Chapter 9: Chemical Equilibrium Explain how the equilibrium would be affected by the following changes: (a) the partial pressure of C02 is increased, (b) 02 is removed from the mixture, (c) C6H1205 (glucose) is removed from the mixture, (d) more water is added, (e) a catalyst is added, (f) the temperature is decreased, and (g) more sunlight shines on the plants. 9.23 When a gas was heated at atmospheric pressure and 25 °C, its color deepened. Heating above 150 °C caused the color to fade, and at 550 °C the color was barely detectable. At 550 °C, however, the color was partially restored by increasing the pressure of the system. Which of the following scenaribs best fits the above description? Justify your choice. (a) A mixture of hydrogen and bromine, (b) pure bromine, (c) a mixture of nitrogen dioxide and dinitrogen tetroxide. (Hint: Bromine is reddish, and nitrogen dioxide is brown. The other gases are colorless.) 9.24 Industrially, sodium metal is obtained by electrolyzing molten sodium chloride. The reaction at the cathode is Na+ + e‘ —» Na. We might expect that potassium metal could also be prepared by electrolyzing molten potassium chloride. Potassium metal is soluble in molten potassium chloride, however, and is therefore hard to recover. Furthermore, potassium vaporizes readily at the operating temperature, creating hazardous conditions. Instead, potassium is prepared by the distillation of molten potassium chloride in the presence of sodium vapor at 892 °C: Na(g) + KC1(l) = NaCl(l) + K(g) Considering that potassium is a stronger reducing agent than sodium, explain why this approach works. (The boiling points of sodium and potassium are 892 °C and 770°C, respectively.) 9.25 People living at high altitudes have higher hemoglobin content in their red blood cells than those living near sea level. Explain. Binding Equilibria 9.26 Derive Equation 9.23 from 9.21. 9.27 The calcium ion binds to a certain protein to form a l : 1 complex. The following data were obtained in an experiment: Total Ca2+/uM 60 120 180 240 480 Ca2+ bound to Protein/uM 31.2 51.2 63.4 70.8 83.4 Determine graphically the dissociation constant of the Ca2+—protein complex. The protein concentration was kept at 96 uM for each run. (1 1.1M = 1 x 10‘6 M 9.28 An equilibrium dialysis experiment showed that the concentrations of the free ligand, bound ligand, and protein are 1.2 x 10’5 M, 5.4 x 10‘6 M, and 4.9 x 10‘6 M, respectively. Calculate the dissociation constant for the reaction PL : P + L. Assume there is one binding site per protein molecule. Bioenergetics 9.29 The reaction L-glutamate + pyruvate —> ot-ketoglutarate + L-alanine is catalyzed by the enzyme L-glutamate-pyruvate aminotransferase. At 300 K, the equilibrium constant for the reaction is 1.11. Predict whether the forward reaction (left to right) will occur spontaneously if the concentrations of the reactants and products are [L-glutamate] = 3.0 x 10‘5 M, [pyruvate] = 3.3 x 10‘4 M, [a-ketoglutarate] = 1.6 x 10‘2 M, and [L-alanine] = 6.25 x 10—3 M. ‘ Problems 9.30 As mentioned in the chapter, the standard Gibbs energy for the hydrolysis of ATP to ADP at 310 K is approximately —30.5 k] mol‘l. Calculate the value of ArG°’ for the reaction in the muscle ofa polar sea fish at —l.5 °C. (Hint: A,H°’ = —20.1 k] mol‘l.) 9.31 Under standard-state conditions, one of the steps in glycolysis does not occur spontaneously: glucose + HPOE‘ —> glucose-6-phosphate + H20 A,G°’ = 13.4 kJ mol‘1 Can the reaction take place the cytoplasm of a cell where the concentrations are [glucose] = 4.5 x 10‘2 M, [HPOE‘] = 2.7 x 10‘3 M, and [glucose-6-phosphate] : 1.6 x 10‘4 M and the temperature is 310 K? 9.32 The formation of a dipeptide is the first step toward the synthesis of a protein molecule. Consider the following reaction: glycine + glycine —> glycylglycine + H20 Use the data in Appendix B to calculate the value of Ar G°’ and the equilibrium constant at 298 K, keeping in mind that the reaction is carried out in an aqueous buffer solution. Assume that the value of A,G°’ is essentially the same at 310 K. What conclusion can you draw about your result? ' 9.33 From the following reactions at 25 °C: fumarate2_ + NH: —> aspartate' A,G°’ = —36.7 kJ mol—1 fumarate2~ + H20 —> malate2_ ArG‘” = —2.9 kJ mol—1 calculate the standard Gibbs energy change and the equilibrium constant for the following reaction: malate2_ + NH;r —> aspartate‘ + H20 9.34 A polypeptide can exist in either the helical or random coil forms. The equilibrium constant for the equilibrium reaction of the helix to the random coil transition is 0.86 at 40 °C and 0.35 at 60 °C. Calculate the values of A,H° and AS" for the reaction. Additional Problems 9.35 List two important differences between a steady state and an equilibrium state. 9.36 At a certain temperature, the equilibrium partial pressures are PNH, = 321.6 atm, PN2 = 69.6 atm, and PH2 = 208.8 atm, respectively. (a) Calculate the value of KP for the reaction described in Example 9.1. (b) Calculate the thermodynamic equilibrium constant if mm = 0.782, yNZ = 1.266, and sz = 1.243. 9.37 Based on the material covered so far in the text, describe as many ways as you can for calculating the A,G° value of a process. 9.38 The solubility of n-heptane in water is 0.050 g per liter of solution at 25 °C. What is the Gibbs energy change for the hypothetical process of dissolving n—heptane in water at a concentration of 2.0 g L‘1 at the same temperature? (Hint: First calculate the value of A,G° from the I equilibrium process and then the AG value using Equation 9.6.) 9.39 In this chapter, we introduced the quantity A,G°’, which is the standard Gibbs energy change for a reaction in which the reactants and products are in their biochemical standard states. The discussion focused on the uptake or liberation of H+ ions. The A,G°’ can also be applied to reactions involving the uptake and liberation of gases such as 02 and C02. In these cases, the biochemical standard states are Po2 = 0.2 bar and Pco2 = 0.0003 bar, where 0.2 bar and 349 350 Chapter 9: Chemical Equilibrium 0.0003 bar are the partial pressures of 02 and C02 in air, respectively. Consider the reaction A(aq) + B(aq) -+ C(aq) + C02(9) where A, B, and C are molecular species. Derive a relation between ArG° and A,G°’ for this reaction at 310 K. 9.40 The binding of oxygen to hemoglobin (Hb) is quite complex, but for our purpose we can represent the reaction as Hb(aq) +02(g) —> Hb02(aq) If the value of ArG° for the reaction is —11.2 kJ mol'1 at 20 °C, calculate the value of A,G°’ for the reaction. (Hint: Refer to the result in Problem 9.39.) 9.41 The KSp value of AgCl is 1.6 x 10’10 at 25 °C. What is its value at 60°C? 9.42 Many hydrocarbons exist as structural isomers, which are compounds that have the same molecular formula but different structures. For example, both butane and isobutane have the same molecular formula: C4H10. Calculate the mole percent of these molecules in an equilibrium mixture at 25 °C, given that the standard Gibbs energy of formation of butane is —15.9 kJ mol‘1 and that of isobutane is —18.0 k] mol‘l. Does your result support the notion that straight-chain hydrocarbons (that is, hydrocarbons in which the C atoms are joined in a line) are less stable than branch-chain hydrocarbons? 9.43 Consider the equilibrium system 3A : B. Sketch the change in the concentrations of A and B with time for the following situations: (a) initially only A is present; (b) initially only B is present; and (c) initially both A and B are present (with A in higher concentration). In each case, assume that the concentration of B is higher than that of A at equilibrium. ...
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This note was uploaded on 07/25/2008 for the course CEM 383 taught by Professor Mccracken during the Fall '07 term at Michigan State University.

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Chapter 9 Problems - Problems Problems_’_———-————— Chemical Equilibrium 9.1 Equilibrium constants of gaseous reactions can be

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