CHAPTER II. POTENTIOMETRY AND REDOX TITRATIONS I ...

CHAPTER II. POTENTIOMETRY AND REDOX TITRATIONSI. Principles of PotentiometryPotentiometric methods of analysis are based upon measurements of the potentialof electrochemical cells under conditions of zero current, where the Nernst equationgoverns the operation of potentiometry.O + ne → RE = E° + (RT/nF)⋅In{(O)/(R)} where 2.303RT/F = 0.0592FIGURE 2-1. “Skoog” Fig. 18-1 (p. 387).This cell can be depicted asReference electrode⏐salt bridge⏐analyte solution⏐indicator electrodeE ref E j E indE ref is independent of the concentration of analyte or any other ions in the solution.E ind depends upon the activity of the analyte.E cell = E ind − E ref + E jThe salt bridge prevents components of analyte solution from mixing with those ofreference solution. The two potentials develop across the liquid junctions at eachend of the salt bridge tend to cancel one another if mobilities of cations and anionsin the bridge solution are about the same. Net E j is therefore usually less than a fewmillivolts. This uncertainty in junction potential places a limit on accuracy ofpotentiometric analysis.II. Reference ElectrodesRequirements:1. Stable2. Reversible3. Reproduciblei/. Standard Hydrogen Electrode (SHE)1

Pt2H + + 2e ←⎯→ H 2 ;E° = 0 Vii/. Calomel ElectrodeFIGURE 2-2. “Harris” Fig. 15-5 (p. 317).Hg⎪Hg 2 Cl 2 (sat’d), KCl(x M)⎟⎜Hg 2 Cl 2 + 2e = 2Hg(l) + 2Cl − ; E° = +0.2682 VE(sat’d KCl) = +0.2415 VThe potential is governed by Cl − ion activity.The most common type is saturated calomel electrode (SCE).iii/. Silver/Silver Chloride ElectrodeFIGURE 2-3. “Harris” Fig. 15-3 (p. 316).Ag⎪AgCl(sat’d), KCl(x M)⎟⎜AgCl(s) + e = Ag(s) + Cl − ;The potential is governed by Cl − ion activity.E° = +0.2223 VE(sat’d KCl) = +0.197 VIII. Indicator Electrodes(A) Metallic indicator electrodesMetal electrodes develop an electric potential in response to a redox reaction at themetal surface, e.g., Pt, Au, and C, they are relatively inert.(B) Ion-Selective Electrodes (ISE)i/. Thermodynamics of ISEsISEs do not involve redox processes and often have a thin membrane ideallycapable of binding only the intended ion.FIGURE 2-4. “Harris” Fig. 15-8 (p. 383).−RT⋅In(a 1 /a 2 ) = −nFE∆G due to activity difference∆G due to charge imbalance2

⇒ E = (0.05916/n) ⋅log(a 1 /a 2 )(n = charge of ion)ii/. Glass Electrodes for pH measurementsFIGURE 2-5. “Harris” (p. 323).FIGURE 2-6. “Harris” Fig. 15-3 (p. 316).H + + Na + Gl − = Na + + H + Gl −soln. solid soln. solidFIGURE 2-7. “Harris” Fig. 15-12 (p. 325).FIGURE 2-8. “Harris” Fig. 15-13 (p. 325).The reaction in which H + replaces metal cations in glass is an ion-exchangeequilibrium. This equilibrium constant is so large that surfaces of hydrated glassmembrane consist of entirely silicic acid (H + Gl − ).E b = E 1 − E 2 = 0.0592⋅log(a 1 /a 2 )where a 1 = activity of analyte solutiona 2 = activity of internal solutioni.e., E b = −0.0592⋅log(a 2 ) − 0.0592⋅pH = constant − 0.0592⋅pH (1)Alkaline Error: The apparent pH is lower than true pH.Some glass membranes also respond to concentration of alkaline metal ions.M + + H + Gl − = H + + M + Gl −soln. solid soln. solidwhere M + represents some singly charged cation, such as sodium ion.K ex = (a 1 b 1 ’)/(a 1 ’b 1 )where a 1 and b 1 are activities of H + and M + in solution, respectivelya 1 ’ and b 1 ’ are activities of H + and M + in gel surface, respectivelyK ex is usually small in value except when [H + ] is low and [M + ] is high.Selectivity Coefficients:The effect of an alkaline metal ion on potential across a membrane can be3

accounted for by inserting an additional term in Equation (1) to giveE b = constant + 0.0592⋅log(a 1 + K H,M b 1 ) (2)where K H,M = K ex is the selectivity coefficient for the electrode.Acid Error: The apparent pH is higher than true pH.Perhaps because glass surface is saturated with H + in strong acid and cannot beprotonated at any more sites.iii/. Glass Electrodes for Cations other than pHBy varying the chemical composition of glass, glass electrodes can be prepared thatare differentially responsive to other cations (primarily monovalent), e.g., Na + , K + ,NH + 4 , Rb + , Cs + , Li + , and Ag + .iv/. Solid State ElectrodesFIGURE 2-9. “Harris” Fig. 15-16 (p. 331).TABLE 2-10. “Harris” Table 15-5 (p. 332).e.g., Fluoride electrodeEuropium doped LaF 3 single crystal; internal electrolyte: NaF/NaCl.FIGURE 2-11. “Harris” Fig. 15-17 (p. 331).E = constant − 0.0592⋅log(a F− )At low pH, F − forms HF (pK a ≈ 3) and interferes; at pH > 8, OH − interferes.v/. Liquid-Membrane ElectrodesFIGURE 2-12. “Harris” Fig. 15-20 (p. 333).TABLE 2-13. “Harris” Table 15-6 (p. 334).e.g., Calcium ion-selective electrode based on a liquid ion exchangerTABLE 2-13. “Harris” Table 15-6 (p. 334).[(RO) 2 PO 2 ] 2 Ca = 2(RO) 2 PO − 2 (dialkylphosphate) + Ca 2+E = constant + (0.0592/2)⋅log(a 2+ Ca )4

vi/. Gas-Sensing Probese.g., FIGURE 2-14. “Harris” Fig. 15-22 (p. 335).Other acidic or basic gases, including NH 3 , SO 2 , H 2 S, NO x (nitrogen oxides), andNH 3 , can be detected in the same manner.IV. Redox TitrationsA redox titration is based on an oxidation-reduction reaction between analyte andtitrant.i./. Potentiometric TitrationsA potentiometric titration involves measurement of the potential of a suitableindicator electrode as a function of titration volume.e.g., Titration of Fe(II) with standard Ce(IV),FIGURE 2-15. “Harris” Fig. 16-1 (p. 349).Titration reaction: Ce 4+ (titrant) + Fe 2+ (analyte) → Ce 3+ + Fe 3+K ≈ 10 17 in 1 M HClO 4Reference half-reaction: 2Hg(l) + 2Cl − = Hg 2 Cl 2 (s) + 2eAt the Pt indicator electrode, there are two reactions that come to equilibrium,Indicator half-reaction: Fe 3+ + e = Fe 2+ E° = 0.767 V (1)Indicator half-reaction: Ce 4+ + e = Ce 3+ E° = 1.70 V (2)FIGURE 2-16. “Harris” Fig. 16-2 (p. 353).a) Region 1: Before the Equivalent PointPrior to equivalent point, amounts of Fe 2+ and Fe 3+ are both known, therefore, it isconvenient to calculate cell potential by using Reaction 1 instead of Reaction 2.E = E cathode − E anode = E + − E −= {0.767 − 0.0592⋅log([Fe 2+ ]/[Fe 3+ ])} − 0.241= 0.526 − 0.0592⋅log([Fe 2+ ]/[Fe 3+ ])When volume of titrant, V = V e /2, where V e = amount required to reach equivalent5

point, [Fe 2+ ] = [Fe 3+ ] and E + = E° for the Fe 3+ /Fe 2+ couple.The point at which V = V e /2 is analogous to the point at which pH = pK a when V =V e /2 in an acid-base titration.b) Region 2: At the Equivalent PointExactly enough Ce 4+ has been added to react with all the Fe 2+ . Virtually all ceriumis in the form Ce 3+ and virtually all iron is in the form Fe 3+ . Tiny amounts of Ce 4+and Fe 2+ are present at equilibrium.i.e., [Ce 3+ ] = [Fe 3+ ] and [Ce 4+ ] = [Fe 2+ ].At any time, Reactions 1 and 2 are both in equilibrium at the Pt electrode.Hence, both reactions contribute to the cell potential at the equivalent point,E + = 0.767 − 0.0592⋅log([Fe 2+ ]/[Fe 3+ ]) (1)E + = 1.70 − 0.0592⋅log([Ce 3+ ]/[Ce 4+ ]) (2)Adding Equations 1 and 2,2E + = 2.46 7 − 0.0592⋅log([Fe 2+ ][Ce 3+ ]/[Fe 3+ ][Ce 4+ ])Because [Ce 3+ ] = [Fe 3+ ] and [Ce 4+ ] = [Fe 2+ ] at the equivalent point,2E + = 2.46 7 ⇒ E + = 1.23 VThe cell voltage potential isE = E + − E(calomel) = 1.23 − 0.241 V = 0.99 VIn this particular titration, the equivalence-point potential is independent ofconcentrations and volumes of reactants.c) Region 3: After the Equivalent PointNow both [Ce 3+ ] and [Ce 4+ ] are known, it is convenient to calculate cell potentialby using Reaction 2 instead of Reaction 1.E = {1.70 − 0.0592⋅log([Ce 3+ ]/[Ce 4+ ])} − 0.241= 1.46 − 0.0592⋅log([Ce 3+ ]/[Ce 4+ ])}At the special point when V = 2V e , [Ce 3+ ] = [Ce 4+ ] and E + = E° for the Ce 4+ /Ce 3+couple.After the equivalence point, the cell potential levels off near 1.46 V.6

e.g., Titration of Tl + by IO − 3 in 1.00 M HCl.Titration reaction: IO − 3 + 2Tl + + 2Cl − + 6H + → ICl − 2 + 2Tl 3+ + 3H 2 OIndicator half-reaction: IO − 3 + 2Cl − + 6H + + 4e = ICl − 2 + 3H 2 O E° = 1.24 VIndicator half-reaction: Tl 3+ + 2e = Tl +E° = 0.77 VFIGURE 2-17. “Harris” Fig. 16-3 (p. 353).When the stoichiometry of the reaction is not 1:1, the curve is not symmetric. Still,negligible error is introduced if center of steepest portion is taken as end-point.Less change in voltage near equivalence point as compared to last titration curve!i.e., clearest results are achieved with strongest oxidizing and reducing agents.ii/. Redox IndicatorsA redox indicator changes color when it goes from its oxidized to its reduced state.TABLE 2-18. “Harris” Table 16-2 (p. 355).To predict the potential range over which the indicator color will change, write aNernst equation for the indicator.In(oxidized) + ne = In(reduced)E = E° − (0.0592/n)⋅log{[In(reduced)]/[In(oxidized)]}The color of In(reduced) will be observed when[In(reduced)]/[In(oxidized)] ≥ 10/1and the color of In(oxidized) will be observed when[In(reduced)]/[In(oxidized)] ≤ 1/10i.e., The color change will occur over the rangeE = (E° ± 0.0592/n) Ve.g., ferroin, E° = 1.147 VFIGURE 2-19. “Harris” (p. 354).The color change is expected to occur in the approximate range 1.088 V to 1.206 Vwith respect to standard hydrogen electrode.7

The larger the difference in standard potential between titrant and analyte, thesharper the break in titration curve at equivalent point. A redox titration is usuallyfeasible if the difference between analyte and titrant is ≥ 0.2 V. If the difference informal potentials is ≥ 0.4 V, then a redox indicator usually gives a satisfactory endpoint. Otherwise, the end point should be detected potentiometrically.iii/. Gran PlotThe Gran plot uses data from well before the equivalent point (V e ) to locate V e .Potentiometric data close to V e are the least accurate because electrodes are slow toequilibrate with species in solution when one member of a redox couple is nearlyused up.e.g., For the oxidation of Fe 2+ to Fe 3+ , the potential prior to V e isE = [E°’ − 0.0592⋅log([Fe 2+ ]/[Fe 3+ ])] − E ref (1)If volume of analyte is V 0 and volume of titrant is V, and if the reaction goes “tocompletion” with each addition of titrant, then[Fe 2+ ]/[Fe 3+ ] = (V e − V)/V (2)Substituting (2) into (1) and rearranging,V⋅10 −nE/0.0592 = −(V − V e )⋅10 −n(E ref − E°’)/0.0592A graph of V⋅10 −nE/0.0592 versus V should be a straight line whose x-intercept is V e .FIGURE 2-20. “Harris” Fig. 16-4 (p. 356).iv/. Adjustment of Analyte Oxidation StateSometimes it is necessary to adjust oxidation state of analyte before it can betitrated. Preadjustment must be quantitative and the excess preadjustment reagentmust be removed or destroyed.a) Preoxidation1. Peroxydisulfate (Persulfate)S 2 O 2− 8 is a strong oxidant that requires Ag + as a catalyst.S 2 O 2− 8 + Ag + → SO 2− 4 + SO − 4 + Ag 2+8

Both SO − 4 + Ag 2+ are powerful oxidants. Excess reagent is destroyed by boiling.boilingS 2 O 2− 8 + 2H 2 O ⎯⎯→ 4SO 2− 4 + O 2 + 4H +The SO − 4 + Ag 2+ mixture oxidizes Mn 2+ to MnO − 4 , Ce 4+ to Ce 3+ , Cr 3+ to Cr 2 O 2− 7 ,and VO 2+ to VO + 2 .2. Silver(II)Silver(II) oxide (AgO) dissolves in concentrated mineral acids to give Ag 2+ , withoxidizing power similar to S 2 O 2− 8 + Ag + combination. Excess Ag 2+ can beremoved by boiling.boiling4Ag 2+ + 2H 2 O ⎯⎯→ 4Ag + + O 2 + 4H +3. Sodium BismuthateSolid NaBiO 3 has an oxidizing strength similar to that of Ag 2+ and S 2 O 2− 8 .Excess solid oxidant is removed by filtration.4. Hydrogen PeroxideH 2 O 2 is a good oxidant in basic solution. It can transform Co 2+ to Co 3+ , Fe 2+ toFe 3+ , and Mn 2+ to MnO 2 . In acidic solution it can reduce Cr 2 O 2− 7 to Cr 3+ andMnO − 4 to Mn 2+ . Excess H 2 O 2 spontaneously disproportionates in boiling water.boiling2H 2 O 2 ⎯⎯→ O 2 + 2H 2 Ob) Prereduction1. Stannous ChlorideSnCl 2 can be used to prereduce Fe 3+ to Fe 2+ in hot HCl. Excess reductant isdestroyed by adding excess HgCl 2 .Sn 2+ + 2HgCl 2 → Sn 4+ + Hg 2 Cl 2 + 2Cl −9

2. Chromous ChlorideCrCl 2 is a powerful reductant. Excess Cr 2+ is oxidized by atmospheric O 2 .3. Sulfur Dioxide and Hydrogen SulfideSO 2 and H 2 S are mild reducing agents that can be expelled by boiling in acidicsolution.4. A Column Packed with a Solid Reducing AgentJones Reductor – contains zinc coated with zinc amalgam.Zn 2+ + 2e = Zn(s) E° = −0.764 VZn is such a powerful reducing agent that the Jones reductor is not veryselective.Walden Reductor – filled with solid Ag and 1 M HCl.Walden reductor is more selective since reduction potential for Ag⎪AgCl(0.222 V) is high enough that species such as Cr 3+ and TiO 2+ are not reducedand therefore do not interfere in analysis of a metal such as Fe 3+ .Another selective reductor uses granular Cd metal. Passing NO −3Cd-filled column reduces NO − 3 to NO − 2 .through aiv/. Application of Standard OxidantsTABLE 2-21. “Skoog” Table 17-3 (p.366).a) Oxidation with Potassium PermanganateIn strongly acidic solution (pH ≤ 1),MnO − 4 + 8H + + 5e = Mn 2+ + 4H 2 Ovioletcolorless(permanganate) (manganous)In neutral or alkaline solution,E° = 1.507 V10

MnO − 4 + 4H + + 3e = MnO 2 (s) + 2H 2 O E° = 1.692 Vbrown(manganese dioxide)In strongly alkaline solution (2 M NaOH),MnO − 2−4 + e = MnO 4 E° = 0.56 Vgreen(manganate)KMnO 4 usually serves as its own indicator. If the titrant is too dilute to be seen, anindicator such as ferroin can be used.Preparation and Standardization:KMnO 4 is not a primary standard. Aqueous KMnO 4 is unstable by virtue of thereaction4MnO − 4 + 2H 2 O = 4MnO 2 (s) + 3O 2 + 4OH −which is slow in the absence of MnO 2 , Mn 2+ , heat, light, acids, and bases andshould be stored in a dark glass bottle.KMnO 4 can be standardized by titration of sodium oxalate (Na 2 C 2 O 4 ).2MnO − 4 + 5H 2 C 2 O 4 + 6H + = 2Mn 2+ + 10CO 2 + 8H 2 Ob) Oxidation with Cerium(IV)Ce 4+ + e = Ce 3+ E° = 1.44 V (in 1 M H 2 SO 4 )Ce 4+ is yellow and Ce 3+ is colorless, but the color change is not distinct enough forcerium to be its own indicator.The oxidizing strengths of KMnO 4 and Ce 4+ are comparable, but Ce 4+ in sulfuricacid is very stable.Primary-standard-grade salt of Ce(IV) is available.c) Oxidation with Potassium DichromateIn acidic solution,Cr 2 O 2− 7 + 14H + + 6e = 2Cr 3+ + 7H 2 OE° = 1.36 V11

orangegreen(dichromate) (chromic)Cr 2 O 2− 7 is a less powerful oxidizing agent than MnO − 4 or Ce 4+ .The orange color of Cr 2 O 2− 7 is not intense enough to serve as its own indicator.In basic solution, Cr 2 O 2− 7 is converted to yellow chromate ion (CrO 2− 4 ), whoseoxidizing power is nil.CrO 2− 4 + 4H 2 O + 3e = Cr(OH) 3 (s) + 5OH −E° = −0.12 VPrimary-standard-grade salt of K 2 Cr 2 O 7 is available and its solutions are stable.d) Oxidation with IodineSolutions of iodine are weak oxidizing agents that are used for the determination ofstrong reductants.I 2 (aq) + I − −= I 3 K = 7×10 2(iodine) (iodine) (triiodide)I − 3 + 2e = 3I −E° = 0.536 V1. IodimetryA reducing agent is titrated directly with iodine to produce I − .2. IodometryAn oxidizing analyte is added to excess I − to produce iodine, which is thentitrated with standard thiosulfate solution.Starch is the indicator of choice for iodine because it forms an intense blue complexwith iodine.FIGURE 2-22. “Harris” Fig. 16-6 (p. 356).Iodine solutions lack stability for several reasons:1. Volatility of iodine;2. Iodine slowly attacks most organic materials;3. Air-oxidation of iodide ion12

4I − + O 2 (g) + 4H + → 2I 2 + 2H 2 Owhich is promoted by acids, heat, and light.Preparation and Standardization:Standard solution of I − 3 can be prepared by adding iodate (IO − 3 ) to a small excess ofKI. Addition of excess strong acid (to give pH ≈ 1) produces I − 3 by quantitativereverse disproportionation.IO − 3 + I − + 6H + = 3I − 3 + 3H 2 OIodine solutions can be standardized by reaction with primary standard-gradeAs 4 O 6 .As 4 O 6 (s) + 6H 2 O = 4H 3 AsO 3(arsenious oxide) (arsenious acid)H 3 AsO 3 + I − 3 + H 2 O = H 3 AsO 4 + 3I − + 2H +Because the equilibrium constant is small, the concentration of H + must be kept low(e.g., by addition of sodium bicarbonate) to ensure complete reaction.v/. Application of Standard ReductantsStandard solutions of most reducing agents tend to react with atmospheric oxygenand are seldom used for direct titration of oxidizing analytes. Indirect methods areused instead.a) Reduction with Iron(II)Solutions of Fe(II) are readily prepared from iron(II) ammonium sulfate,Fe(NH 4 ) 2 (SO 4 ) 2 ⋅6H 2 O (Mohr’s salt) or form iron(II) ethylenediamine sulfate,FeC 2 H 4 (NH 3 ) 2 (SO 4 ) 2 ⋅4H 2 O (Oespar’s salt).Air-oxidation of Fe(II) takes place rapidly in neutral solutions but is inhibited in thepresence of acids.b) Reduction with ThiosulfateThiosulfate is a moderately strong reducing agent that is the almost universal titrant13

for I − 3 .2−2−2S 2 O 3 = S 4 O 6 + 2e E° = 0.08 V(thiosulfate) (tetrathionate)In neutral or acidic solutions,I 3 − + S 2 O 2− 3 = 3I − 2−+ S 4 O 6S 2 O 2− 3 is usually standardized by reaction with a fresh solution of I − 3 prepared fromKIO 3 plus KI.Acids promotes disproportionation of S 2 O 2− 3 ,S 2 O 2− 3 + H + = HSO − 3 + S(s)(bisulfite)Hence, addition of sodium carbonate maintains the pH in an optimum range forstability of the solution.Metal ions catalyze atmospheric oxidation of S 2 O 2− 3 ,2Cu 2+ + S 2 O 2− 3 → 2Cu + 2−+ S 4 O 64Cu + + O 2 + 4H + → 4Cu 2+ + 2H 2 OThiosulfate solutions should be stored in dark.Bacteria also metabolize S 2 O 2− 3 to sulfite and sulfate as well as elemental sulfur.14