Chapter 10 Problems - Problems...

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Unformatted text preview: Problems Problems _________—_—_—_——————— Emf of Electrochemical Cells 10.1 Calculate the standard emf for the following reaction at 298 K: /' Fe(s) + Tl3+ —+ Fe2+ + T1+ 10.2 Calculate the emf of the Daniell cell at 298 K when the concentrations of CuSO4 and ZnSO4 are 0.50 M and 0.10 M, respectively. What would the emf be if activities were used instead of concentrations? (The yi values for CuSO4 and ZnSO4 at their respective concentrations are 0.068 and 0.15, respectively.) 10.3 The half-reaction at an electrode is A13+(aq) + M a Al(s) Calculate the number of grams of aluminum that can be produced by passing 1.00 faraday through the electrode. 10.4 Consider a Daniell cell operating under non-standard-state conditions. Suppose that the cell’s reaction is multiplied by 2. What effect does this have on each of the following quantities in the Nemst equation? (a) E, (b) E°, (c) Q, (d) In Q, and (e) v 10.5 A student is given two beakers in the laboratory. One beaker contains a solution that is 0.15 M in Fe3+ and 0.45 M in Fe“, and the other beaker contains a solution that is 0.27 M in I‘ and 0.050 M in 12. A piece of platinum wire is dipped into each solution. (2) Calculate the potential of each electrode relative to a standard hydrogen electrode at 25 °C. (b) Predict the chemical reaction that will occur when these two electrodes are connected and a salt bridge is used to join the two solutions together. 10.6 From the standard reduction potentials listed in Table 10.1 for Cu2+|Cu and PtICu2+, Cu+, calculate the standard reduction potential for Cu+|Cu. Thermodynamics of Electrochemical Cells and the Nemst Equation 10.7 Complete the following table, indicating in the third column whether the cell reaction is spontaneous: E A,G Cell Reaction + + 0 10.8 Calculate the values of E°, A,G°, and K for the following reactions at 25 °C: (a) Zn + Sn4+ v——‘ Zn2+ + Sn2+ (b) C12 +21‘ : 20‘ +12 (c) 5Fe2+ + MnO‘ + 8H+ = Mn2+ + 4H20 + 5Fe3+ 4 10.9 The equilibrium constant for the reaction Sr + Mg2+ : Sr2+ + Mg 391 392 Chapter 10: Electrochemistry is 6.56 x 1017 at 25 °C. Calculate the value of E° for a cell made up of the Sr|Sr2+ and Mg|Mg2+ half-cells. ' 10.10 Consider a concentration cell consisting of two hydrogen electrodes. At 25 °C, the cell emf is found to be 0.0267 V. If the pressure of hydrogen gas at the anode is 4.0 bar, what is the pressure of hydrogen gas at the cathode? ' 10.11 An electrochemical cell consists of a half-cell in which a piece of platinum wire is dipped into a solution that is 2.0 M in KBr and 0.050 M in Brz. The other half-cell consists of magnesium metal immersed in a 0.38 M Mg2+ solution. (a) Which electrode is the anode and which is the cathode? (b) What is the emf of the cell? (c) What is the spontaneous cell reaction? (d) What is the equilibrium constant of the cell reaction? Assume that the temperature is 25 °C. 10.12 From the standard reduction potentials listed in Table 10.1 for Sn2+|Sn and Pb2+1Pb, calculate the ratio of [Sn2+] to [Pb2+] at equilibrium at 25 °C and the A,G° value for the reaction. 10.13 Consider the following cell: Ag(s)|AgC1(S)|NaC1(aq)ng2C12(s)ngU) (a) Write the half-cell reactions. (b) The standard emfs of the cell at several temperatures are as follows: T/K I 291 298 303 311 E°/mV 43.0 45.4 47.1 50.1 Calculate the values of AG", AS", and A,H° for the reaction at 298 K. 10.14 Calculate the emf of the following concentration cell at 298 K: Mg(s)|Mg2+(o.24 M) | |Mg2+(0.53 M)|Mg(s) 10.15 An electrochemical cell consists of a silver electrode in contact with 346 mL of 0.100 M AgNO3 solution and a magnesium electrode in contact with 288 mL of 0.100 M Mg(N03)2 solution. (a) Calculate the value of E for the cell at 25 °C. (b) A current is drawn from the cell until 1.20 g of silver have been deposited at the silver electrode. Calculate the value of E for the cell at this stage of operation. Bioelectrochemistry ' 10.16 For the reaction NAD+ + I-I~+ + 2e‘ —-> NADH E°’ is —0.320 V at 25 °C. Calculate the value of E’ at pH = 1. Assume that both NAD+ and NADH are at unimolar concentration. 10.17 From the E°’ value for the following reaction in Table 10.3, CH3CHO + 2H+ + 26— —> C2H5OH calculate the value of E’ at pH 5.0 and 298 K, given that [C2H5OH] = 5.0 x 10'6 M , and [CH3CHO] = 2.4 x 10-4 M. 10.18 Look up the E°’ values in Table 10.3 for the reactions CH3CHO + 2H+ + 2e‘ —-> CszOH NAD+ + HJr + 2e‘ —> NADH Problems Calculate the equilibrium constant for the following reaction at 298 K. CH3CHO + NADH + H+ : C2H5OH + NADJr 10.19 The following reaction, which takes place just before the citric acid cycle, is catalyzed by the enzyme lactate dehydrogenase: CH3COCOO' + NADH + HJr :‘ CH3CH(OH)COO_ + NAD+ pyruvate lactate E From the data listed in Table 10.3, calculate the value of AG°’ and the equilibrium constant for the reaction at 298 K. 10.20 Calculate the number of moles of cytochrome c3+ formed from cytochrome c2+ with the Gibbs energy derived from the oxidation of 1 mole of glucose. (A,G° = ~2879 k] for the degradation of 1 mole of glucose to C02 and H20.) 10.21 The terminal respiratory chain involves the redox couples NAD+|NADH and FADIFADHZ. Calculate the AG“ value for the following reaction at 298 K: NADH + FAD + H+ —> NAD+ + FADH2 Is this Gibbs energy change sufficient to synthesize ATP from ADP and inorganic phosphate? Draw a diagram showing the experimental arrangement for measuring the emf of a cell consisting of these two couples. 10.22 The oxidation of malate to oxaloacetate is a key reaction in the citric acid cycle: malate + NAD+ —> oxaloacetate + NADH + H+ Calculate the value of A,G°’ and the equilibrium constant for the reaction at pH 7 and 298 K. 10.23 Calculate the value of A,G°’ for the oxidation of succinate to fumarate by cytochrome c at 298 K. 10.24 Flavin adenine dinucleotide (FAD) participates in several biological redox reactions according to the half-reaction FAD + 2H+ + 2e‘ —> FADHZ If the value of E°’ of this couple is —0.219 V at 298 K and pH 7, calculate its reduction potential at this temperature and pH when the solution contains (a) 85% of the oxidized form and (b) 15% of the oxidized form. 10.25 According to the chemiosmotic theory, the synthesis of 1 mole of ATP is coupled to the movement of 4 moles of H+ ions from the low-pH side of the membrane to the high-pH side. (a) Derive an expression for AG for the movement of 4H+. (b) Calculate the change in pH across the membrane that is required at 25 °C to synthesize one mole of ATP from ADP and Pi under standard-state conditions. ArG‘” = 31.4 kJ for the synthesis of 1 mole of ATP. 10.26 The nitrite in soil is oxidized to nitrate by the bacteria nitrobacter agilis in the presence of oxygen. The half-reduction reactions are NO; + 2H+ + 2e" —> NO; + H20 E°’ = 0.42 V §02 + 2H+ + 2e— —) H20 E” = 0.82 v Calculate the yield of ATP synthesis per mole of nitrite oxidized, assuming an efliciency of 55%. (The A,G°’ value for ATP synthesis from ADP and Pi is 31.4 k] mol"1.) 394 Chapter 10: Electrochemistry Membrane Potentials 10.27 Describe an experiment that would show that the nerve cell membrane is much more permeable to K+ than to Na+. 10.28 A membrane permeable only to K+ ions is used to separate the following two solutions: a [KCl] = 0.10 M [NaCl] = 0.050 M ,3 [KCl] = 0.050 M [NaCl] = 0.10 M Calculate the membrane potential at 25 °C, and determine which solution has the more negative potential. 10.29 Referring to Figure 10.14b, carry out the following operations: (a) Calculate the membrane potential due to K+ ions at 25 °C. (b) Given that biological membranes typically have a capacitance of approximately 1 ,uF cm‘z, calculate the charge in coulombs on a unit area (1 cm2) of the membrane. (See Appendix 8.1 for units of capacitance.) (c) Convert the charge in (b) to number of K1L ions. ((1) Compare the result in (c) with the number of K+ ions in 1 cm3 of the solution in the left compartment. What can you conclude about the relative number of K+ ions needed to establish the membrane potential? Additional Problems 10.30 Look up the values of E" for the following half-cell reactions: Ag+ + e‘ —> Ag AgBr + e“ —+ Ag + Br— Describe how you would use these values to determine the solubility product (Ksp) of AgBr at 25 °C. 10.31 A well-known organic redox system is the quinone—hydroquinone couple. In an aqueous solution at a pH below 8, we have ' O OH + 2H+ + 29" ——> © E°=0.699V O OH Quinone Hydroquinone (0) (HQ) This system can be prepared by dissolving quinhydrone, QH (a complex consisting of equimolar amounts of Q and HQ), in water. A quinhydrone electrode can be constructed by immersing a piece of platinum wire in a quinhydrone solution. (a) Derive an expression for the electrode potential of this couple in terms of E ° and the hydrogen-ion concentration. (b) When the quinone—hydroquinone couple is joined to a saturated calomel electrode, the emf of the cell is found to be 0.18 V. In this arrangement, the saturated calomel electrode acts as the anode. Calculate the pH of the quinhydrone solution. Assume the temperature is 25 °C. 10.32 A 25.0-mL quantity of a 0.10 M Fe2+ solution is titrated against a 0.10 M Ce4+ solution added from a buret. What is the emf after the addition of 30.0 mL of the Ce4+ solution? The temperature is at 298 K. 10.33 One way to prevent a buried iron pipe from rusting is to connect it with a piece of wire to a magnesium or zinc rod. What is the electrochemical principle for this action? Problems 10.34 Aluminum has a more negative standard reduction potential than iron. Yet aluminum does not form rust or corrode as easily as iron. Explain. 10.35 Given that the ArS° value for the Daniel] cell is —21.7 J K'1 mol“, calculate the temperature coefficient (6E°/6 T) P of the cell and the emf of the cell at 80 °C. 10.36 For years it was not clear whether mercury(1) ions existed in solution as Hg+ or as Hg§+. To distinguish between these two possibilities, we could set up the following system: Hg(l)|soln A| Isoln B|Hg(l) where solution A contained 0.263 g mercury(l) nitrate per liter and solution B contained 2.63 g mercury(l) nitrate per liter. If the measured emf of such a cell is 0.0289 V at 18 °C, what can you deduce about the nature of the mercury ions? 10.37 Given the following standard reduction potentials, calculate the ion-product Kw value ([H+][OH']) at 25 °C: 2H+(aq) + 2e' —> H2(g) E0 = 0.00 V 2H20(l) + 2e- —> H2(g) + on—(aq) E” = —0.828 V 10.38 Given that 2Hg2+(aq) + 2e‘ —+ Hg§+(aq) E° = 0.920 v Hg§+(aq) + 2e" —> 2Hg(l) E° = 0.797 v calculate the values of ArG° and K for the following process at 25 °C: Hg§+(aq) —* Hg2+(aq) + HgU) (The above reaction is an example of a disproportionation reaction, in which an element in one oxidation state is both oxidized and reduced.) 10.39 The magnitudes of the standard electrode potentials of two metals, X and Y, are x2++2e— —» X |E°|=0.25V Y2++2e- —> Y |E°| =0.34V where the I | notation denotes that only the magnitude (but not the sign) of the E° value is shown. When the half-cells of X and Y are connected, electrons flow from X to Y. When X is connected to a SHE, electrons flow from X to SHE. (3) Which value of E0 is positive and which is negative? (b) What is the standard emf of a cell made up of X and Y? 10.40 An electrochemical cell is constructed as follows. One half-cell consists of a platinum wire immersed in a solution containing 1.0 M Sn2+ and 1.0 M Sn“, and the other half-cell has a thallium rod immersed in a solution of 1.0 M Tl+. (a) Write the half—cell reactions and the overall reaction. (b) What is the equilibrium constant at 25 °C? (c) What is the cell voltage if the Tl+ concentration is increased tenfold? 10.41 Given the standard reduction potential for Au3+ in Table 10.1 and Au+(aq) +e' —> Au(s) E° = 1.69 V answer the following questions. (3) Why does gold not tarnish in air? (b) Will the following disproportionation occur spontaneously? 3Au+(aq) —+ Au3+(aq) +2Au(s) 395 396 Chapter 10: Electrochemistry 10.42 10.43 10.44 10.45 10.46 (c) Predict the reaction between gold and fluorine gas. Consider the Daniel] cell shown in Figure 10.1. In the diagram, the anode appears to be negative and the cathode positive (electrons are flowing from the anode to the cathode). Yet the anions in solution are moving toward the anode, which must therefore seem positive to the anions. Because the anode cannot simultaneously be negative and positive, give an explanation for this apparently contradictory situation. Calculate the pressure of H2 (in bar) required to maintain equilibrium with respect to the following reaction at 25 °C: Pb(s) + 2H+(aq) : Pb2+(aq) + H2(g) given that [Pb2+] = 0.035 M and the solution is buffered at pH 1.60. Use the data in Appendix B and the convention that AfG°[H+(aq)] = 0 to determine the standard reduction potentials for sodium and fluorine. (Like sodium, fluorine also reacts violently with water.) * Use the data in Table 10.1 to determine the value of AfG° for Fe2+(aq). Consider the following cell: Pt|H2(1 bar)lHCl(m)|AgCl(s)|Ag At 25 “C, the emf values at various molalities are given by m/(mol kghl) 0.124 0.0539 0.0256 0.0134 0.00914 0.00562 0.00322 E/V 0.342 0.382 0.418 0.450 0.469 0.493 0.521 (a) Determine the value of E° graphically. Compare your value of E° with that listed in Table 10.1. (b) Calculate the mean activity coeflicient (Vi) for HCl at 0.124 m. .;.,ta\mr.vtw~bv<<~wvb'v\w ...
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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 10 Problems - Problems...

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