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2.6 PROBLEMS
2.1 Devise electrochemical cells in which the following reactions could be made to occur. If liquid junctions are necessary, note them in the cell schematic appropriately, but neglect their effects.
(a) H2O ^± H+ + OH~
(b) 2H2 + O2 ^± H2O
(c) 2PbSO4 + 2H2O ±± PbO2 + Pb + 4H+ + 2SOf
(d) AnT 4- TMPD^ ±± An + TMPD (in acetonitrile, where An and AnT are anthracene and its anion radical, and TMPD and TMPD^ are AW^'^-tetramethyl-p-phenylenediamine and its cation radical. Use anthracene potentials for DMF solutions given in Appendix C.3).
(e) 2Ce3 + + 2H+ + BQ ^± 2Ce4 + + H2Q (aqueous, where BQ is p-benzoquinone and H2Q is p- hydroquinone)
(f) Ag+ + I~ <± Agl (aqueous)
(g) Fe3 + + Fe(CN)£~ <=» Fe2 + + Fe(CN)3," (aqueous) (h) Cu2+ + Pb «± Pb2 + + Cu (aqueous)
(i) AnT + BQ <=^ BOT. + An (in А^Д-dimethylformamide, where BQ, An, and AnT are defined above and BO~ is the anion radical of p-benzoquinone. Use BQ potentials in acetonitrile given in Appendix C.3).
What half-reactions take place at the electrodes in each cell? What is the standard cell potential in each case? Which electrode is negative? Would the cell operate electrolytically or galvanically in carrying out a net reaction from left to right? Be sure your decisions accord with chemical intuition.
2.2 Several hydrocarbons and carbon monoxide have been studied as possible fuels for use in fuel cells. From thermodynamic data in references 5-8 and 16, derive E°s for the following reactions at 25°C:
(a) CO(g) + H2O(/) -> CO2(g) + 2H+ + 2e (b) CH4(#)+ 2H2O(/) -* CO2(g) + 8H+ + 8e (c) C2H6(g) + 4H2O(/) -* 2CO2(#) + 14H+ + Ue (d) C2H2(g) + 4H2O(/) -> 2CO2(#) + 10H+ + 10*
Even though a reversible emf could not be established (Why not?), which half-cell would ideally yield the highest cell voltage when coupled with the standard oxygen half-cell in acid solution?
Which of the fuels above could yield the highest net work per mole of fuel oxidized? Which would give the most net work per gram?
2.6 Problems 85 2.3 Devise a cell in which the following reaction is the overall cell process (T = 298 K):
2Na+ + 2СГ -> 2Na(Hg) + Cl2 (aqueous)
where Na(Hg) symbolizes the amalgam. Is the reaction spontaneous or not? What is the standard free energy change? Take the standard free energy of formation of Na(Hg) as —85 kJ/mol. From a thermodynamic standpoint, another reaction should occur more readily at the cathode of your cell.
What is it? It is observed that the reaction written above takes place with good current efficiency.
Why? Could your cell have a commercial value?
2.4 What are the cell reactions and their emfs in the following systems? Are the reactions spontaneous?
Assume that all systems are aqueous.
(a) Ag/AgCl/K+, СГ (1 M)/Hg2Cl2/Hg
(b) Pt/Fe3+ (0.01 M), F e2 + (0.1 M), HC1 (1 M)//Cu2+ (0.1 M), HC1 (1 M)/Cu (c) Pt/H2 (1 atm)/H\ С Г (0.1 M)//H+, С Г (0.1 M)/O2 (0.2 atm)/Pt (d) Pt/H2 (1 atm)/Na+, OH~ (0.1 M)//Na+, OH" (0.1 M)/O2 (0.2 atm)/Pt (e) Ag/AgCl/K+, С Г (1 M)//K\ С Г (0.1 M)/AgCl/Ag
(f) Pt/Ce3+ (0.01 M), C e4 + (0.1 M), H2SO4 (1 M)//Fe2+ (0.01 M), Fe3 + (0.1 M), HC1 (1 M)/Pt 2.5 Consider the cell in part (f) of Problem 2.4. What would the composition of the system be at the end
of a galvanic discharge to an equilibrium condition? What would the cell potential be? What would the potential of each electrode be vs. NHE? Vs. SCE? Take equal volumes on both sides.
2.6 Devise a cell for evaluating the solubility product of PbSO4. Calculate the solubility product from the appropriate E° values (T = 298 K).
2.7 Obtain the dissociation constant of water from the parameters of the cell constructed for reaction (a) in Problem 2.1 (T = 298 K).
2.8 Consider the cell:
Cu/M/Fe2+, Fe3 +, H+//Cr/AgCl/Ag/Cu'
Would the cell potential be independent of the identity of M (e.g., graphite, gold, platinum) as long as M is chemically inert? Use electrochemical potentials to prove your point.
2.9 Given the half-cell of the standard hydrogen electrode,
Pt/H2 (a = 1)/H+ (a = 1) (soln) H2 <=± 2H+(soln) + 2e(Pt)
Show that although the emf of the cell half-reaction is taken as zero, the potential difference be- tween the platinum and the solution, that is, фР 1 — 0s, is not zero.
2.10 Devise a thermodynamically sound basis for obtaining the standard potentials for new half-reac- tions by taking linear combinations of other half-reactions (T = 298 K). As two examples, calculate
£"° values for
(a) Cul + e ^ Cu + I "
(b) O2 + 2H+ + 2e ±± H2O2
given the following half-reactions and values for £ ° (V vs. NHE):
Cu2+ + 2e *± Cu 0.340
Cu2+ + I" + e <=> Cul 0.86 O2 + 4H+ + 4e ?± 2H2O 1.229 H2O2+ 2H+ + 2e ?± 2H2O 1.763
2.11 Transference numbers are often measured by the Hittorf method as illustrated in this problem. Con- sider the three-compartment cell:
L С R
©Ag/AgNO3(0.100 M)//AgNO3(0.100 M)//AgNO3(0.100 M)/Ag ©
86 • Chapter 2. Potentials and Thermodynamics of Cells
where the double slashes (//) signify sintered glass disks that divide the compartments and prevent mixing, but not ionic movement. The volume of AgNO3 solution in each compartment (L, C, R) is 25.00 mL. An external power supply is connected to the cell with the polarity shown, and current is applied until 96.5 С have passed, causing Ag to deposit on the left Ag electrode and Ag to dissolve from the right Ag electrode.
(a) How many grams of Ag have deposited on the left electrode? How many mmol of Ag have de- posited?
(b) If the transference number for Ag+ were 1.00 (i.e., tAg+ = 1.00, JN O- = 0.00), what would the concentrations of Ag+ be in the three compartments after electrolysis?
(c) Suppose the transference number for Ag+ were 0.00 (i.e., tAg+ = 0.00, ^NO3- = 1-00), what would the concentrations of Ag+ be in the three compartments after elec-
trolysis?
(d) In an actual experiment like this, it is found experimentally that the concentration of Ag+ in the anode compartment R has increased to 0.121 M. Calculate tAg+ and t^oj>
2.12 Suppose one wants to determine the contribution of electronic (as opposed to ionic) conduction through doped AgBr, a solid electrolyte. A cell is prepared with a film of AgBr between two Ag electrodes, each of mass 1.00 g, that is, ©Ag/AgBr/Ag©. After passage of 200 mA through the cell for 10.0 min, the cell was disassembled and the cathode was found to have a mass of 1.12 g. If Ag deposition is the only faradaic process that occurs at the cathode, what fraction of the current through the cell represents electronic conduction in AgBr?
2.13 Calculate the individual junction potentials at T = 298 К on either side of the salt bridge in (2.3.44) for the first two concentrations in Table 2.3.3. What is the sum of the two potentials in each case?
How does it compare with the corresponding entry in the table?
2.14 Estimate the junction potentials for the following situations (T = 298 K):
(a) HCl(0.1M)/NaCl(0.1M) (b) HC1 (0.1 M)/NaCl (0.01 M) (c) KNO3 (0.01 M)/NaOH (0.1 M) (d) NaNO3 (0.1 M)/NaOH (0.1 M)
2.15 One often finds pH meters with direct readout to 0.001 pH unit. Comment on the accuracy of these readings in making comparisons of pH from test solution to test solution. Comment on their mean- ing in measurements of small changes in pH in a single solution (e.g., during a titration).
2.16 The following values of Щ[+^ are typical for interferents / at a sodium-selective glass electrode:
K+, 0.001; NH4", 10~5; Ag+, 300; H+, 100. Calculate the activities of each interferent that would cause a 10% error when the activity of Na+ is estimated to be 10~3 M from a potentiometric mea- surement.
2.17 Would Na2H2EDTA be a good ion-exchanger for a liquid membrane electrode? How about Na2H2EDTA-R, where R designates a C2Q alkyl substituent? Why or why not?
2.18 Comment on the feasibility of developing selective electrodes for the direct potentiometric determi- nation of uncharged substances.
2.19 Consider the exhaust gas analyzer based on the oxygen concentration cell, (2.4.21). The electrode reaction that occurs at high temperature at both of the Pt/ZrO2 + Y2O3 interfaces is
O2 + 4e «± 2O2~
Write the equation that governs the potential of this cell as a function of the pressures, pe g and pa. What would the cell voltage be when the partial pressure of oxygen in the exhaust gas is 0.01 atm (1,013 Pa)?