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CHAPTER 2: INORGANIC ELECTROCHEMISTRY (l) A. TRANSITION METAL COMPLEX REDOX RATES I. Introduction. In this section we inorganic compounds. consider "simple" electrochemistry of We will concentrate on systems where the electron transfer event is rapid and uncomplicated by associated chemical reactions: Classification E=electrochemical step C= chemical step Reaction E, [2 . 1 ] CE [2. 2 ] EC [2. 3] but not: A+ + e = A Or: -+ B slow A+ + e = A [2 . 4 ] where E, refers to a reversible electron transfer event and refers to a quasi-reversible electron transfer event. E~, By confining our attention to a rapid, reversible, simple E, reaction we hope to see which system is amenable to analytical applications based on DP (differential pulse), SW (square wave), and/or CV (cyclic show plot voltammetric) analysis. As an example, dimensionless in Figure 2.1 (2), we (normalized) current function ~ a of a for a linear sweep experiment: [2 •5] The different lines on the plot illustrate the effect of relative • • • • • • • • • • • • • • • • • • • a= 0.5 0.4 ~-----,#--;a~:---I-----i-----t----j 0.3 ~ 0.2 1----J.-/-l.:---,~-_+-+--_+_----+_-_1 0.1 I--~t+---t+-----T~----+-----t-----j __-+--+_ _ ~+- ~e.-_+_----+_ ---- j '¥(E) o -128 128 -n(E-E,I2)' 2.1 variation of quasi-reversible different values of Q following values of A: IV, 1jl(E) ). = = ). = 10. 2 • (0.7, I, A kOjD'I2(nFjRT)'I2T)'/2. 2.) current 0.5, = 10; 0.3, II, 385 function, tP (E), as indicated) A = 1; III, for and the A = 0.1; Dashed curve is for a reversible reaction. ijnFAC o *D o 'l2(nFjRT) 1 12 T)1/2 (From Re f. 257 mV (25°) magnitude of the electron transfer rate constant (k,) to the time scale of the experiment established by the scan rate of the linea~ sweep experiment (v). = k -Y, v 50.68 'it:. where the constant 50.68 arises when we assume 0 nF/RT is 38.92 = 10 ,5 2 cm Is, V". Note from Figure 2.1 that a A full reversible linear sweep scan. of 10 is required to achieve the The advantage of a reversible easil~, system is that one gets the maximuD peak height that is related to the bulk solution concentration. values of A an::: and k" as a In Table 2.1 variou~ function of scan rate are shown. Fro: Table 2.1 we note that we need electron transfer rate constants the order of 0.05 cmls or more depending upon the scan rate, 0: whic~ controls the time scale of the experinent. Reversibility and fast electron transfer are related solvent structural changes and to structural changes expected the complex. We predict that systems reorganization should be the fastest. involving the t: i~ leas: In order to have aver', basic understanding of structural changes in inorganic complexe~ we turn our attention to crystal field theory. II. Crystal Field theory The ease of electron transfer in metal complexes proceeds, , one part, results from the spreading of charge over a large volume. in a low charge density reorganization around the complex. which If, requires little at the same time, Thi~ solven: littl~ I I I I I I I I ~ TABLE 2.1: Values of >. as a function of T) and k o • k o cm/s A 0.05 0.5 .2- 50 1.0 4.4x10· 2 1.39xl0' 4.4Xl0·' 1. 39 1 4.4XI0· 3 1.29xIO< 4.4X10 0.1 4.4xl0·4 1.29xIO" 4.4xl0· 3 v(V/s): 2 1.39xIO·' 1.39xl0· 2 change in internal bond structure occurs (little lability causir: bond length changes and/or ligand replacement), the electrc transfer reaction should be rapid and reversible. Crystal field theory presumes that the main interactic between the metal ion and the ligands is electrostatic in nature Assuming an octahedral complex (6 coordinate), incoming 1 igan::: ~ c approach along the x, y and z axis (Figure 2.2), perturbing the y2 and the d z 2 (Figure 2.3) ra is ing them in energy (Figure 2.4) Orbitals lying off axis and are lowered, orbi tals into 3 (d xy ' resul ting degenerate d xz ' in dyJ are less perturbed in ener:: splitting t2~ (J, (d,y' of d,z' the d\,z) 5 degenerate orbitals and The total energy splitting between orbitals is arbitrarily at 10Dq. The absolute value of this energy difference is S'C° relat~ to the charge transfer bands observed'spectrochemically in the 4C: 700 nm region. lowered t that the 2g e~ By noting that the sum of the orbitals must equal zero, energy is divided between 2g t~ simple arithmetic thus she. the eg orbitals orbitals as weighted values of +6Dq and -4Dq, x = the t orbitals with and the respectively. : L,,' orbi ta 1 energy and y the e] orb i tal energy: = 30 - 3x 2x = 3y 2x x + Y = 10 30 Y = 10 -x x = 6 so 3y = 30 - 3x Y = 4 5x As an example, let us examine chromium. . . conf1.gurat1.on 0 f 3 d 5 4s , 4p 0 . Cr has an electro~. Notice that the electronic conf igurat:..: x y )' ..r:y : z / / x x y .v xz 2.2 Complete set of d orbitals orbitals are shaded and the in an octahedral t2~ vz field. The e g orbitals are unshaded. The (From torus of the d: 2 orbital has been omitted for clarity. Re f. 3.) ~3 I - 2; ....{. "0 !--/? ...... I\j . It • I • I \ 2.3 Spatial arrangement of the five d orbitals. (From Ref. 3.) fie, j _~ _ _ eg 1 1 / / / 6Dq / / / ----I IODq=Ll ---\-"--- \ 4Dq \ \ 1 \ \----(2g 2.4 Splitting of the degeneracy octahedral ligand field. of the (From Ref. five 3.) d orbitals by an 1S written to imply that the 4s orbitals are higher in energy than the 3d orbitals, from the 4s therefore electrons orbital. The orbital removed from Cr come configuration is first obtained by placing the d electrons in the lowest possible orbitals shown in Figure 2.5. Two examples are diagrammed. That in which the incoming ligand greatly perturbs the d orbitals (high field ligand) and that which only weakly total energy perturbs the d orbitals (low field crystal fielc ligand) . The of the stabilization energy, CFSE. splitting between the t 29 two states is the Note that for the low field case, the and e g orbital levels is less and it is energetically more favorable to fill the upper e g orbital for the d 4 complex than to pair up the electrons in the lower t The low field complex for Cr 2 • field (d J ) orbital. 29 has higher spin than the hig:-. (more unpaired electrons). The energy for the high ligand field Cr 2• complex 1S compute:: from four t electrons 29 electrons minus the energy, wi thin the same orbit. The P, required to pair u:= energ ies of the varies electronic configurations can be calculated as shown in Table 2.2. Similar analysis can be made of other metal ions. work through C0 2 +/ ]+ (F igure 2. 6) and Fe 2 >J+ (Figure 2. 7). electronic 3d 6 4so. Fe]· have configuration of 3d 7 4s", so Co 2 • is 3d 7 4So Fe has the electronic configuration of 3d6 4s 2 , the configurations of 3d" and 3d 5 • The electronic configurations are shown in Table 2.3. We shal~ Co has tr.· and Co]· i:: so Fe 2• ai.:: correspondii.:: .... I I I I I I I I ~ ~ FIGURE 2.5 - i -- - i i - - i - - t6Dq J.4Dq - t - - t - - -- it J. i 2.5 i Diagram of Cr of a high represents ligands. I LOW FIELD LIGAND HIGH FIELD LIGAND 2 + and Cr3+ d orbital spl i tting of in the presence field the and low degenerate field energy 1 igand. level The of the dotted 1 ine unperturbed it TABLE 2.2 Crystal Field Stabilization Energies in Dq units a) 4 high field Cr 2 + ( d ) 4 (-4 Dq) + o (+6Dq) + IP b) high field cr)+ (d j ) ] (-4Dq) + o (+6Dq) + OP c) low field cr 2 + (d 4 ) ] (-4 Dq) + 1 (+6Dq) + OP d) j low field Cr J + (d ] (-4 Dq) + O(+6Dq) + OP ) / > , L· = -16Dq+P -12Dq = -6Dq -12Dq -- I I I , I I ~ , HIGH FIELD LIGAND ~ - - FIGURE 2.6 LOW FIELD LIGAND I t -- I ---- -- -t - t t t t t 2.6 -it - t t ~ t i i ~ ~ --------- ~ ~ -- -i - i - - i ~ ~ ~ ~ Diagram of Co 2 , and Co J • d orbital splitting in the presence of a high and low field level of the perturbation. five ligand. degene=ate ener~y Dotted line marks the orbitals absence in the of ....... FIGURE 2.7 LOW FIELD LIGAND HIGH FIELD LIGAND i i -i - -i - -- -- - - - - -i - i -- i ~ i i i 2.7 ~ - i - ~ i i ~ Diagram of Fe a 2 + ~ ~ and Fe). d orbital spl i tting in the presence high and low field ligand. level - - - - - - - - - -i - -i - i of the five degenerate Dotted 1 ine marks the orbitals in the 0: energ~· absence 0: perturbation. ~L ./ -- ,. I~ 30 I I I I I I I I I I I I I I I I I I I III. Ease of oxidation/Reduction from CFSE theory t-ie may make some inferences ::::nsider ~~esence the reduction/oxidation of First, (Cr N3 +). chromium let's In the of a high field ligand there is little major change in the electronic configuration, change in the complex, reactions. so, in the absence of other we might expect that there is little structural considerations, ~n from Table 2.3. thus facilitating rapid electron transfer This, of course, presumes that the CFSE energy shown Table 2.3 is of a similar order of magnitude for. the divalent and trivalent complexes (Dq similar). quite always a electrostatic complexes lot larger for considerations. should be more the In fact, trivalent This stable compared to divalent complexes. to the Dq values are suggests complex that sUbstitution Figure 2.8 (4) due to trivalent reactions as confirms these expectations by showing that the on/off rate of inner sphere water molecules is much slower for trivalent complexes than for divalent complexes. Thus, reduction of a trivalent complex to a divalent complex should always be checked for lability and attack of the reduced complex. Such attack would convert our simple E reaction to an EC reaction (see equation 2.3). This analysis holds up even more when looking at a complex in which the ligand produces a weak interacting field with Cr Table 2.3). Here we see that a change in orbital configuration accompanies a change in the redox state. orbital field (see state are noted complexes, Similar changes in the for the oxidation/reduction of Co high as compared to -1.7 ./ I Fe or Ru high field complexes. TABLE 2.3 Table of Electronic Configurations and CFSE For Several Metal Ions Cr '-"-.) "1-' electronic configuration Jd 5 4s'4p(J #d e High Field Electronic Config Low Field Energy Electronic Config -lGDq+P t g) e g1 -120q t,u -180q+JP t'Q ell -24Dq+JP t 29 e g cr 2 ' Jd 4 4So Jp o d4 t 2g 4 Cr]' 3d)4So Jp O d) t,u Co Jd 7 4S' Cot. 3d 7 4S° d Co]' 3do 4S° db t Fe 3do4 S° Fe" 3do4 S° d6 t 29° -240q+JP t Fe)' 3d 5 4so d5 t y5 -200q+2P t 2g ) e g 2 Ru 55'4d 7 Ru 2 ' 5s o4d 6 dO t 296 R,,/' 5s 0 4d 5 d5 t 2g 5 l t l b 2tl 2g e g1 h 29 ~ -6Dq ) -12Dq 5 2 -BD:}~2P 4 , -4cqtP 4 e g2 -4D:J+P OOq '-- Na+ K+Cs+ u+ Be 2 + ~!' ~Rb~ Ca 2 + s,-2 + Ba 2 + Mg2+ f i" c~+ Ru3+ , Fe 3 + a3+ /V 3+ A1 3 + \_,,) 3 Ti 3 + In + Yb 3 +_ 03+- Gd 3+ "I~ ,- 0~ V2 + Ru 2 + ~ Pt 2 + 10- 6 10- 4 Ni 2 + , Co2 + Fe 2 + Cu 2 + c,-2 + 2 " 1 Mn + Zn 2 + Cd 2 + Hi+ Pd 2 + 10- 2 100 102 104 106 loS ---... -.:\ 1'\.[\ ~ ,:./\. 2.8 Characteristic rate constants (s") for sUbstitution of inner sphere water molecules on various metal ions. (From Ref. 4.) 10 10 Recall that the e" orbital is most directly in the path of the oncoming ligands and so we might expect large differences in bond lengths in going from the d 4 to the d 3 complexes of Cr when in the low field system. Consequently, we might also expect that the rate of electron transfer should be low. Marcus theory (5, 6, 7, 8) predicts that the rate of a self exchange reaction, k,,: A + A k" = A + A" [2 •7 J should relate to the rate of electron transfer at an electrode, heterogeneous electron transfer, k o : [2.8: via the relationship: k" == Zel ( ~,,_ ) '/2 Zsoin where and Zel Z'OII1 are the collisional frequency factors generall::o taken to be 10 3 to 10 4 cm/s and 10~' M·'s·'. The frequency factors tell you how many times the reactants collide at the electrodE surface or together in solution before an electron transfer even: occurs. Zsoln is estimated from the thermal velocity of the react in::: molecules: ZSOln - (kT/27Tm) [2.1C 1/2 where k is the gas constant, T is the temperature, and m is t~~ effective mass of molecules (9). From equation [2.9J we note tha: the will rate constant. of electron transfer mirror the self exchans:: Table 2.4 (4) and Appendix 8.1 show some data for of self exchange for several metal complexes. rate~ Note that the sel: I I I I I I , , I Some Outer-Sphere Electron-Exchange Reactions Reacting pair Electron configuration Rate (L mol-I S-I at 2SOC) [Fe(bi py )3]2 + 13 + Difference in M-L bond lengths (A) 0.00 ± 0.01 [Mn(CN)6]~-/3 [Mo(CN)s]~-/3 " " [W(CN)S]"-/3 [IrCI 6P-/2 Very small t~g/ t~g [Os(bipy) ]2+/3+ t~g/tig [Fe(CN)6]~-/3 t~g/ tig [Ru( en)3]H /3.+ t~g/ ti g 4 x Hr' [Ru(NH3)6]2+f3+ [Ru(H 20)6]2+/3+ [Fe(H 20)6]2+f3+ tt/d g 4 x 1()3 t 2geg t 2g eg [MnO~J2-/I " [C oen 3J2+/3+ [CO(NH 3)6]2+f3+ -lOS . t~g / t~g 4 2/ 3 20C 2 4 >1()3 0.04 ± 0.01 0.09 ± 0.02 0.14 ± 0.02 } -10- 4 0.18 :±: 0.02 [CO(~O~)3]4-/3 aNot octahedral, but the change in electronic configuration occurs in a nonbonding orbital. exchange rate of the cobalt complexes is a good deal slower t~ that of the Fe and Ru complexes which involve only a tha~ electron~ (orbitals out of the path of the incoming ligand). From Table 2.4 we can also observe the effect of moving the periodic table. same group, do~~ Note that even though Fe and Ru are in tt~ their electronic configurations In the presence of low field ligand (water) are different. ~ Fe behaves as a low fiel: complex with electrons in the e g orbitals while Ru behaves as a hig. field complex with electrons conf ined to the t?_ orbitals. This':'" ,~ because size and electron cloud density effects change as one down the periodic chart. The l~lger mOVE~ d orbitals of Ru are greatly perturbed by the incoming ligand and greater mo~~ stabilizatic~ results. The magnitude of Dq increases down the periodic char~ Complexes of the almos~ 2nd exclusively low spin and 3rd row (high field) transition series in nature (3). are Because Fe hc.' a low field configuration with electron density in the e g orbitals the bond length changes in the oxidation/reduction reaction greater and, the self exchange rates are much therefore, a~·: slo~E~ than for the aquo complex of ruthenium. IV. Summary - reversibility in Metal Complexes We look for reversible electron transfer events complexes lower in the periodic chart and in which t~ in met:::. electrons a=, removed exclusively (Fe, Os, Ru). B. TRANSITION METAL REDOX POTENTIALS Having looked at the complexes and gained some rough feel their reversibility, can we also get a feel for the fc~ absolu:· ~ I I , , e~ergetics required to cause the electron transfer to occur? :s, can we get a feel for the redox potentials? Let's consider some redox potentials for ~rite That The answer is yes. CoJ~'. We can first the Nernst equation for simple reduction of trivalent Co to divalent Co: E = EO - RT ln [Co 2,] [2.11] [Coo.] nF Next we note the complex formation reactions for both the di- and tri-valent complexes: Co J+ + 6L := CoL/· Kill C0 2 + + 6L := coLt 1\1 -w'here Kill r <;:0 L,~~""l [Co'""] [Lf [2.12] [COL)~_ [2.13] := = [Co""] [L]" and K I are the formation constants reactions [2.13]. By combining equations [2.11-2.13] and [2.12] and separating out constants: E = { EO - RT ln K II } - ~I nF RT ln ~ ~ [ C0 4'·] [2.14] The term in the {} on the right hand side of equation [2,14] is the formal potential, trivalent species potential will simple cation. EO', for is more the Co complex. strongly shift negative Note that when complexed from the formal (stabilized) the the potential of the These trends are observed for the cobalt metal complexes as shown in Table 2.5. Dq is a measure of the strength of the ligand in creating the ligand field, of ligand strength. as is If', a ranking In general ligands follow the order of: TABLE 2.5 Formal Potential, CFSE, and f, ligand strength factors 3 for Co ' Complexes EC Reaction Co 3+ + e = Co 2 , Co (ox) / +e = Co (ox) 3 e = Co (phen) 32+ e = Co(bpy)/+ Co(bpy)/+ + 3 Co(NH 3)6 + + e 2 = Co(NH 3)6 + 2 co(en)/+ + e = Co(en)3 + Co (CN) / e = + D9(3+) IkJ-mol- 1 .f 1.808 4 Co (phen) /+ + (vs NHE) Co (CN) 5 3 0.57 .99 0.37 to 0.42 1. 0.31 to 0.37 1. 3 = 3~ 0.1 278 1. 2:: -0.26 278 1. 2:: -0.83 401 1. 7 • • • • • • • • •, • ~here ox is oxalate, en is is phenanthroline. ethylenedia~ine, bpy is bipyridine, phen Similar trends can be cODpiled from Appendix B.2. From the EO' values for Co we see that in the absence of any ligand and for the oxalate complex, the divalent state is preferred over the trivalent complex. This might be expected from the relative second and third ionization potentials of cobalt which increase indicating the greater difficulty in removing a second or third electron from the atom. ammonia, and cyano As the ligand strength increases to complexes, the trivalent complex can stabilized in solution (oxidation potentials shift negative). be The chelate complexes of bipyridine and phenanthroline do not follow the sequence perfectly due to the unique structural effects of the chelating ligand. The reason the trivalent complex can be favored is related to the large energy gain from the complex in the trivalent state (from -18Dq to -24Dq for the high field complexes) . C. ANALYTICAL APPLICATIONS: STRIPPING ANALYSIS The aquated complexes of the metal ions lie between high and low field complexes. divalent That is, we can not assume that both the and trivalent complex of the aquated specie should be particularly well stabilized in a similar electronic configuration involving only a transfer of a t;~ electron. Thus we might infer that the reversible reduction of the aquated metal ions would be poor and not a good candidate for electrochemistry as an analytical method. Tables 2.6 (3) and 2.7 (6) ( . )1 show the data for aquo TABLE 2.6: Electron configuration and CFSE for Aqua Complexes Of Some Metal Ions Ion Electrons 10Dg/em Cr 3 + t 2Q Cr 2 • t 2g3 eg Mn 3 + t 2g3 eg Mn 2 + t 2g Fe 3 + t 2g 3 e g 2 1400 Fe 2 + t 4 2g e g2 1000 Co 3 + t 2g Co 2 + t 2g e g2 1000 3 3 1760 , , e g2 1400 2100 750 6 5 ., I I . self-exchange reactions Calculated values of .1G:~ Ao and AI for some .Inorgamc solution L1G*o A. o IJI A.I~ 1 e kcal rno\-I kcal mol-I kcal mol-I r I'.'A r/A Co(HP)~" 3.56 3.40 3.6 26.3 Fe(HP)~" 3.59 3.43 3.6 Mn(Hp)~.j. 3.66 3.46 Cr(Hp)~~ 3.58 V(HP)~' Ti(/lP)~~ Reduced form (CO'IIW 11 0 40 r /Ru.,O(CH)COOMpY)J l~ In t .dG*· d cole L1G~bS 48.4 22.3 14.3 26.1 48.4 22.2 14.2 3.6 25.7 75.2 28.8 19.8 3.40 3.6 26.2 60.4 25.3 ~21.4 3.56 3.41 3.7 26.2 12.0 13.3 17.6 3.56 3.45 3.6 26.1 22.8 15.8 17.7 5.0 5.0 12.7 18.3 11.0 20.0 16.7 7.0 7.0 0 a 2.3 4.0 '-I I 9.0 I aqueous complexes. From Table 2.6 again note the consistently greater stability (large 10Dq values) of the trivalent complex. note that reduction only the electrons, thus we might of Fe"" to predict that Fe 2 ' More importantly, involves the solely t;o; remaining aquated complexes would be sluggish at an electrode and not amenable to the assumption of reversibility at the electrode surface, hindering the analysis of currents in sweep methods. This is true. We can beat this problem by taking another Many metal tack. metallic state. ions form Hg analgams \·;hen reduced to their The amalgam formation depends upon the metallic solubility of the compound in liquid Hg. Since Hg is large and polarizable we would expect similarly large and polarizable metals to be soluble within Hg. metals in mercury (10). Table 2.8 shows the solubility of various Those metals grouped on the left-hand side have larger solubilities than those on the right-hand side. In general, those with larger solubilities fall to the right of the periodic chart and transition metal solubility in Hg, almost series. all are in Nearly all the 2nd those and Jrd row ions exhibit ing of low are first row transition metals, which will be smaller and less polarizable. Metal ions which can preconcentration in Hg are: be Bi J. , determined CU t. , Ga by analytically 3· , Ge 4 + , I n 3+ , ·2. N1 , The metals are determined via a method termed anodic stripping voltammetry (ASV). to the. electrode surface which A potential is applied reduces the metals resul ting in I I I I I I I ~ I TABLE 2.8 SolUbility of Metals in Mercury Metal Solubility (wt%) Metal Solubility (wt%) In 68.3 Cu 8xlO- J Th 42.4 Mn 6.6xlO- J Cd 5 Sb 3.8xlO· Zn 5.6 Ni 2.1X1O- J Sn 1.3 Co 3xlO· 4 Pb 1.2 Bi 1.2 4 metal-mercury amalgam formation. This process concentrates the metal ions in the small mercury drop n \. (Figure 2. ( 2) • After a loading period, the electrode potential is swept positive, causing the oxidation of the metals and their drop. removal from the mercury The resulting anodic stripping current is large due to the preceding concentration period (Figure 2.S; (10)) 2.9 are some Voltammetry typical (ASV) detection limits for Listed in Table Anodic Stripping utilizing either Differential Pulse or Linear Sweep techniques (see Introduction) (10) and also typical detection 1 imi ts (11) for spectroscopic methods flame atomic absorption spectrosccpic, atomic absorption specroscopy and 0 f anal ys is, where AAS is GFAAS is graphite furnace ICPAES is inductively coupled plasma atomic emission spectroscopy. Note that GFAA has the lowest detection limits, but is useful for analysis of single components only. ICPAES is a multicomponen~ spectroscopic technique but does not have the detection limits of ASV with DP detection. ASV can analyze simul taneously (Figure 2 ./~ . for several components Stripping M(Hg) -. M+ 11 + Hg + ne (e) (10-100 sec) - - - - - - k - - - - - - - 's------=·t~---_;~_ t 2.9 Principle of anodic stripping experiment. typical analysis. ones (a) used; potentials and Ep typical of Preelectrolysis at E,,; stirred solution. Rest period, stirrer off. (c) Anodic scan (From Re f. 2.) are Values shown are (ry = 10-100 cu 2 • (b) mV/sec). Table 2.9 Detection Limits (DL) in Anodic Stripping Voltamrnetry (ASV) DP = Differential Pulse, LS = Linear Swee~ and Spectroscopy AAS = Atomic Absorption Spectroscopy GFAA = Graphite Furnace Atomic Absorption Spect~: ICPAES = Inductively Coupled Plasma Atomic Emission Spe:' Spectroscopy Anodic stripping ion ng/ml (ppb) DP LS AAS GFAAS ICPAES 10~ 2 .01 Bi Cd 0.005 0.01 1 Cu 0.005 0.01 2 0.1 Ga 0.4 In 0.1 Pb 0.01 0.02 10 2 10 Rh Sn 2 Tl 0.01 0.04 Zn 0.04 0.04 20 0.1 30 2 5x10-5 2 I I I I <! :J. - Z to- lJJ c:: a:: u :::> Zn Cd +0.25 0 -0.25 -0.50 -0.75 -1.00 -1.25 POTENTIAL (V vs Ag/AgCU 2.10 Current-sampled polarogram (top) and anodic stripping vol tammogram (bottom) of 2.5 ppm cu;', Zn 2. , and 5 ppm Pb 2 . , Cd 2• in 0.1 M sodium acetate. rs~' Ie CHAPTER 2: PROBLEMS 2.1 a) Work out the electron configuration for OS2' and OS3' i;: the presence of CN- and in the presence of Cl-. B) Would you expect the sel f exchange rate for rapid as a CN or as a Cl complex? 2.2 a) to be OS2o(3. Justify your answer. Work out the electron con f igura t ion for Cu 2 ' and Cu" ir. the presence of CN- and in the presence of Cl-. b) Would you expect the self exchange rate for CU 2 • 11 - to be rapid as a CN or as a Cl 2.3 Would 2.4 expect cyclic voltammetry for RU(en)/- at a scan rate of 5,000, 500, 50, c::: Assume 0 Buttrey and Anson a • IS peak Justify your answer. in 5 Vis? you co~plex? .~ splitting .tiL of 2 5x10· cm /s. (12) 59 Assume no iR error. ion exchanged Co(bpy)/' into a Nafio: ion exchange polymer modifying a Pt electrode. the scan rate they mV found differential heights for the 3+/2+ vs the 2+/1+ peaks. As they varie= changes in the pea:-: The current of one of the redox couples was dependent upon physical diffusion the complex within the Nafion to the electrode surface. 0: The second redox couple was found to be dependent upon the rate of self-exchange of electrons between couples immobilized i: the Nafion. Which couple was which? I I 2.5 I You are Ru (bpy) performing t in an cycl ic aqueous vol tammetry of Cr (bpy) /. med ia a small with phenanthroline present at a fairly slow scan rate and amount (5 mV/s). Sketch the cyclic voltammograms that you might expect to see for the two different couples. 2.6 a) Jorgensen (13) has Justify your sketches. estimated 10Dq values from the formula: 10Dq = f"gano If X Co(II) g,en' and respectively, Co(phen)6 J " b) Co(III) compute have the g 10Dq values values of for 9 and 18.2, Co(phen)6;' and respectively. Using these values make some predictions as to the EO val ue of the Co (phen) 53.;;. coupl e as compared to the EO val ue of the straight 2.7 C03~' reduction at +1.8 V vs NHE. (From Bard and Faulkner (2).) a) An analysis for lead at the HMDE gives rise to a peak current of 1 ~A under conditions in which the deposition time is held constant at 5 min and s'tleep rate is 5 OmV Is. What currents would be observed for sweep rates of 25 and 100 mV/s? You may consider the peak current in the linear sweep to be roughly described by equation (14) b) in Chap. 1. The same solution gives a peak current of A thick 25~A at a 100 mercury film electrode (MFE) on glassy carbon when the deposition time is 1 min, the electrode rotation rate is 2000 rpm, and the sweep rate is 50mV/s. What currents would t" observed for sweep rates of 25 and 100 mV/s under otherwis unchanged conditions? where CR mol/cm 3 , c) is the (The peak current in a MFE is (10): concentration of the metal in the . e is the thickness of the HME. Why does the current follow a direct MFE in (b), but a v 1a v dependence for (2), Kissinger and Heineman (10) Compare deposition this time situation of 1 min, Faulkne~ rotation rate of 4000 rpm? or Reiger (14). to a the sHeep (C~ t~" (Hint. dependence for the HMDE in (a)? Refer to technique oriented textbooks like Bard and d) MFE one rate observed of for 50mV/s and is related to the depositic time and the rotation rate of the electrode. The rotatic rate sets the diffusion layer, and hence current, for moveme~~ of the ion from the bulk solution to the mercury electrode The limiting current of a rotating disk electrode is (14): = 0 62 nFAC Oulk 0 Ox 2/3 1/ -1/6 W 1;2 l' L · where, in this case, 1/ is the kinematic viscosi ty of solution and w is the rotation rate of the electrode in (rad=27THz) . A typical kinematic viscosity is amount of charge deposited is Q lO~ m~s. tr.-:: rad!~ T:--. = nFN where N is the numbe: of moles deposited, and q is the integrated current fidt.) e) Suppose the film thickness were varied by the use c: different concentrations of the mercuric ion in the analyte What effect would one see on the peak current under otherwis" 2~_ I I ~ constant conditions? 2.8 Films of Pb0 2 Suggest an can be analytical deposited oxidatively determination on Sn0 2 Pb based your bulk of on ( 15) . this phenomena. 2.9 Your electrode area is 0.05 cm< and solution concentration of co(en)/· 5 mM in 0.01 M NaCl (K. :::: 11.85xl0·· n·'cm·'). Assuming that the solution res istance measured at a disk electrode is p/4a can you attribute peak splitting in cyclic voltammetry at 500 mV/s to slow electron transfer kinetics? (Hint: you will need to compute the extent of iR error at the peak current, you may wish to refer to Bard and Faulkner (2) or Reiger (14) for more detail on iR error.) LITERATURE CITED 1. For an early review see: H. Electron Taube, Transfe~ Reactions of Complex Ions in Solution, Academic Press, 1970. 2. Bard, A. J. and Faulkner, L. R. 1980, Electrochemical Methods, Wiley and Sons, p. 225. 3. Huheey, J. E. 1978, Inorg. Chem., Chap. 9. 4. Cotton, F. A. and Wilkinson, G. 1988, Advanced Inorganic: Chemistry, 5th Ed., Chap. 29. 5. Marcus, R. A. Electrochim. 6. Eberson, L., Electron-Transfer Reactions in Organic Chemistr; 7. Hush, 8. Kojima and A. J. 9. Marcus, R. A., J. Chem. Phys., 10. Heineman, Mark, N. S., Electrochim. Roston, W. in R., Bard, J. Laboratory H. Acta, 1968, 13, 995. Acta., 1968, 113, 13, 1005. Am. Chern. Soc., 1985, 97, B., 6317. 1965, 28: 962. Jr., Techniques J. in A. Wise, and D. A. Electroanalytica~ Chemistry, 1984, Marcel Dekker. 11. Skoog, D.A., Principles of Instrumental 1985, Saunders. Analysis, 3rd Ed., 12. Buttry, D. A. and Anson, F. C. J. Amer. Chern. Soc., 1983, 105, 685. 13. Jorgensen, 1969, C. K., Oxidation Numbers and Oxidation States, Springer, N.Y. 14. Rieger, P.H., Electrochemistry, 1987, Prentice Hall. 15. Laitinen, H. A. and Watkins, 1352. -" ,-," N. H. Anal. Chern., 1975, 47,