CHAPTER II. POTENTIOMETRY AND REDOX TITRATIONS

Transcription

1 CHAPTER II. POTENTIOMETRY AND REDOX TITRATIONS I. Principles of Potentiometry Potentiometric methods of analysis are based upon measurements of the potential of electrochemical cells under conditions of zero current, where the Nernst equation governs the operation of potentiometry. O + ne R E = E + (RT/nF) In{(O)/(R)} where 2.303RT/F = FIGURE 2-1. Skoog Fig (p. 387). This cell can be depicted as Reference electrode salt bridge analyte solution indicator electrode E ref E j E ind E 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 j The salt bridge prevents components of analyte solution from mixing with those of reference solution. The two potentials develop across the liquid junctions at each end of the salt bridge tend to cancel one another if mobilities of cations and anions in the bridge solution are about the same. Net E j is therefore usually less than a few millivolts. This uncertainty in junction potential places a limit on accuracy of potentiometric analysis. II. Reference Electrodes Requirements: 1. Stable 2. Reversible 3. Reproducible i/. Standard Hydrogen Electrode (SHE) 1

2 Pt 2H + + 2e H 2 ; E = 0 V ii/. Calomel Electrode FIGURE 2-2. Harris Fig (p. 317). Hg Hg 2 Cl 2 (sat d), KCl(x M) Hg 2 Cl 2 + 2e = 2Hg(l) + 2Cl ; E = V E(sat d KCl) = V The potential is governed by Cl ion activity. The most common type is saturated calomel electrode (SCE). iii/. Silver/Silver Chloride Electrode FIGURE 2-3. Harris Fig (p. 316). Ag AgCl(sat d), KCl(x M) AgCl(s) + e = Ag(s) + Cl ; The potential is governed by Cl ion activity. E = V E(sat d KCl) = V III. Indicator Electrodes (A) Metallic indicator electrodes Metal electrodes develop an electric potential in response to a redox reaction at the metal surface, e.g., Pt, Au, and C, they are relatively inert. (B) Ion-Selective Electrodes (ISE) i/. Thermodynamics of ISEs ISEs do not involve redox processes and often have a thin membrane ideally capable of binding only the intended ion. FIGURE 2-4. Harris Fig (p. 383). RT In(a 1 /a 2 ) = nfe G due to activity difference G due to charge imbalance 2

3 E = ( /n) log(a 1 /a 2 ) (n = charge of ion) ii/. Glass Electrodes for ph measurements FIGURE 2-5. Harris (p. 323). FIGURE 2-6. Harris Fig (p. 316). H + + Na + Gl = Na + + H + Gl soln. solid soln. solid FIGURE 2-7. Harris Fig (p. 325). FIGURE 2-8. Harris Fig (p. 325). The reaction in which H + replaces metal cations in glass is an ion-exchange equilibrium. This equilibrium constant is so large that surfaces of hydrated glass membrane consist of entirely silicic acid (H + Gl ). E b = E 1 E 2 = log(a 1 /a 2 ) where a 1 = activity of analyte solution a 2 = activity of internal solution i.e., E b = log(a 2 ) ph = constant 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. solid where 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, respectively a 1 and b 1 are activities of H + and M + in gel surface, respectively K 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 be 3

4 accounted for by inserting an additional term in Equation (1) to give E b = constant 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 be protonated at any more sites. iii/. Glass Electrodes for Cations other than ph By varying the chemical composition of glass, glass electrodes can be prepared that are differentially responsive to other cations (primarily monovalent), e.g., Na +, K +, NH + 4, Rb +, Cs +, Li +, and Ag +. iv/. Solid State Electrodes FIGURE 2-9. Harris Fig (p. 331). TABLE Harris Table 15-5 (p. 332). e.g., Fluoride electrode Europium doped LaF 3 single crystal; internal electrolyte: NaF/NaCl. FIGURE Harris Fig (p. 331). E = constant log(a F ) At low ph, F forms HF (pk a 3) and interferes; at ph > 8, OH interferes. v/. Liquid-Membrane Electrodes FIGURE Harris Fig (p. 333). TABLE Harris Table 15-6 (p. 334). e.g., Calcium ion-selective electrode based on a liquid ion exchanger TABLE 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

5 vi/. Gas-Sensing Probes e.g., FIGURE Harris Fig (p. 335). Other acidic or basic gases, including NH 3, SO 2, H 2 S, NO x (nitrogen oxides), and NH 3, can be detected in the same manner. IV. Redox Titrations A redox titration is based on an oxidation-reduction reaction between analyte and titrant. i./. Potentiometric Titrations A potentiometric titration involves measurement of the potential of a suitable indicator electrode as a function of titration volume. e.g., Titration of Fe(II) with standard Ce(IV), FIGURE Harris Fig (p. 349). Titration reaction: Ce 4+ (titrant) + Fe 2+ (analyte) Ce 3+ + Fe 3+ K in 1 M HClO 4 Reference half-reaction: 2Hg(l) + 2Cl = Hg 2 Cl 2 (s) + 2e At the Pt indicator electrode, there are two reactions that come to equilibrium, Indicator half-reaction: Fe 3+ + e = Fe 2+ E = V (1) Indicator half-reaction: Ce 4+ + e = Ce 3+ E = 1.70 V (2) FIGURE Harris Fig (p. 353). a) Region 1: Before the Equivalent Point Prior to equivalent point, amounts of Fe 2+ and Fe 3+ are both known, therefore, it is convenient to calculate cell potential by using Reaction 1 instead of Reaction 2. E = E cathode E anode = E + E = { log([fe 2+ ]/[Fe 3+ ])} = log([fe 2+ ]/[Fe 3+ ]) When volume of titrant, V = V e /2, where V e = amount required to reach equivalent 5

6 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 Point Exactly enough Ce 4+ has been added to react with all the Fe 2+. Virtually all cerium is 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 + = log([fe 2+ ]/[Fe 3+ ]) (1) E + = log([ce 3+ ]/[Ce 4+ ]) (2) Adding Equations 1 and 2, 2E + = log([fe 2+ ][Ce 3+ ]/[Fe 3+ ][Ce 4+ ]) Because [Ce 3+ ] = [Fe 3+ ] and [Ce 4+ ] = [Fe 2+ ] at the equivalent point, 2E + = E + = 1.23 V The cell voltage potential is E = E + E(calomel) = V = 0.99 V In this particular titration, the equivalence-point potential is independent of concentrations and volumes of reactants. c) Region 3: After the Equivalent Point Now both [Ce 3+ ] and [Ce 4+ ] are known, it is convenient to calculate cell potential by using Reaction 2 instead of Reaction 1. E = { log([ce 3+ ]/[Ce 4+ ])} = 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

7 e.g., Titration of Tl + by IO 3 in 1.00 M HCl. Titration reaction: IO 3 + 2Tl + + 2Cl + 6H + ICl 2 + 2Tl H 2 O Indicator half-reaction: IO 3 + 2Cl + 6H + + 4e = ICl 2 + 3H 2 O E = 1.24 V Indicator half-reaction: Tl e = Tl + E = 0.77 V FIGURE Harris Fig (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 Indicators A redox indicator changes color when it goes from its oxidized to its reduced state. TABLE Harris Table 16-2 (p. 355). To predict the potential range over which the indicator color will change, write a Nernst 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)] 10/1 and the color of In(oxidized) will be observed when [In(reduced)]/[In(oxidized)] 1/10 i.e., The color change will occur over the range E = (E ± /n) V e.g., ferroin, E = V FIGURE Harris (p. 354). The color change is expected to occur in the approximate range V to V with respect to standard hydrogen electrode. 7

8 The larger the difference in standard potential between titrant and analyte, the sharper the break in titration curve at equivalent point. A redox titration is usually feasible if the difference between analyte and titrant is 0.2 V. If the difference in formal potentials is 0.4 V, then a redox indicator usually gives a satisfactory end point. Otherwise, the end point should be detected potentiometrically. iii/. Gran Plot The 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 to equilibrate with species in solution when one member of a redox couple is nearly used up. e.g., For the oxidation of Fe 2+ to Fe 3+, the potential prior to V e is E = [E 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 to completion with each addition of titrant, then [Fe 2+ ]/[Fe 3+ ] = (V e V)/V (2) Substituting (2) into (1) and rearranging, V 10 ne/ = (V V e ) 10 n(e ref E )/ A graph of V 10 ne/ versus V should be a straight line whose x-intercept is V e. FIGURE Harris Fig (p. 356). iv/. Adjustment of Analyte Oxidation State Sometimes it is necessary to adjust oxidation state of analyte before it can be titrated. Preadjustment must be quantitative and the excess preadjustment reagent must be removed or destroyed. a) Preoxidation 1. Peroxydisulfate (Persulfate) S 2 O 2 8 is a strong oxidant that requires Ag + as a catalyst. S 2 O Ag + SO SO 4 + Ag 2+ 8

9 Both SO 4 + Ag 2+ are powerful oxidants. Excess reagent is destroyed by boiling. boiling S 2 O H 2 O 4SO 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 Silver(II) Silver(II) oxide (AgO) dissolves in concentrated mineral acids to give Ag 2+, with oxidizing power similar to S 2 O Ag + combination. Excess Ag 2+ can be removed by boiling. boiling 4Ag H 2 O 4Ag + + O 2 + 4H + 3. Sodium Bismuthate Solid 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 Peroxide H 2 O 2 is a good oxidant in basic solution. It can transform Co 2+ to Co 3+, Fe 2+ to Fe 3+, and Mn 2+ to MnO 2. In acidic solution it can reduce Cr 2 O 2 7 to Cr 3+ and MnO 4 to Mn 2+. Excess H 2 O 2 spontaneously disproportionates in boiling water. boiling 2H 2 O 2 O 2 + 2H 2 O b) Prereduction 1. Stannous Chloride SnCl 2 can be used to prereduce Fe 3+ to Fe 2+ in hot HCl. Excess reductant is destroyed by adding excess HgCl 2. Sn HgCl 2 Sn 4+ + Hg 2 Cl 2 + 2Cl 9

10 2. Chromous Chloride CrCl 2 is a powerful reductant. Excess Cr 2+ is oxidized by atmospheric O Sulfur Dioxide and Hydrogen Sulfide SO 2 and H 2 S are mild reducing agents that can be expelled by boiling in acidic solution. 4. A Column Packed with a Solid Reducing Agent Jones Reductor contains zinc coated with zinc amalgam. Zn e = Zn(s) E = V Zn is such a powerful reducing agent that the Jones reductor is not very selective. 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 reduced and therefore do not interfere in analysis of a metal such as Fe 3+. Another selective reductor uses granular Cd metal. Passing NO 3 Cd-filled column reduces NO 3 to NO 2. through a iv/. Application of Standard Oxidants TABLE Skoog Table 17-3 (p.366). a) Oxidation with Potassium Permanganate In strongly acidic solution (ph 1), MnO 4 + 8H + + 5e = Mn H 2 O violet colorless (permanganate) (manganous) In neutral or alkaline solution, E = V 10

11 MnO 4 + 4H + + 3e = MnO 2 (s) + 2H 2 O E = V brown (manganese dioxide) In strongly alkaline solution (2 M NaOH), MnO e = MnO 4 E = 0.56 V green (manganate) KMnO 4 usually serves as its own indicator. If the titrant is too dilute to be seen, an indicator such as ferroin can be used. Preparation and Standardization: KMnO 4 is not a primary standard. Aqueous KMnO 4 is unstable by virtue of the reaction 4MnO 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 and should 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 CO 2 + 8H 2 O b) 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 for cerium to be its own indicator. The oxidizing strengths of KMnO 4 and Ce 4+ are comparable, but Ce 4+ in sulfuric acid is very stable. Primary-standard-grade salt of Ce(IV) is available. c) Oxidation with Potassium Dichromate In acidic solution, Cr 2 O H + + 6e = 2Cr H 2 O E = 1.36 V 11

12 orange green (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 ), whose oxidizing power is nil. CrO H 2 O + 3e = Cr(OH) 3 (s) + 5OH E = 0.12 V Primary-standard-grade salt of K 2 Cr 2 O 7 is available and its solutions are stable. d) Oxidation with Iodine Solutions of iodine are weak oxidizing agents that are used for the determination of strong reductants. I 2 (aq) + I = I 3 K = (iodine) (iodine) (triiodide) I 3 + 2e = 3I E = V 1. Iodimetry A reducing agent is titrated directly with iodine to produce I. 2. Iodometry An oxidizing analyte is added to excess I to produce iodine, which is then titrated with standard thiosulfate solution. Starch is the indicator of choice for iodine because it forms an intense blue complex with iodine. FIGURE Harris Fig (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 ion 12

13 4I + O 2 (g) + 4H + 2I 2 + 2H 2 O which 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 of KI. Addition of excess strong acid (to give ph 1) produces I 3 by quantitative reverse disproportionation. IO 3 + I + 6H + = 3I 3 + 3H 2 O Iodine solutions can be standardized by reaction with primary standard-grade As 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 Reductants Standard solutions of most reducing agents tend to react with atmospheric oxygen and are seldom used for direct titration of oxidizing analytes. Indirect methods are used 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 the presence of acids. b) Reduction with Thiosulfate Thiosulfate is a moderately strong reducing agent that is the almost universal titrant 13

14 for I S 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 6 S 2 O 2 3 is usually standardized by reaction with a fresh solution of I 3 prepared from KIO 3 plus KI. Acids promotes disproportionation of S 2 O 2 3, S 2 O H + = HSO 3 + S(s) (bisulfite) Hence, addition of sodium carbonate maintains the ph in an optimum range for stability of the solution. Metal ions catalyze atmospheric oxidation of S 2 O 2 3, 2Cu 2+ + S 2 O 2 3 2Cu S 4 O 6 4Cu + + O 2 + 4H + 4Cu H 2 O Thiosulfate solutions should be stored in dark. Bacteria also metabolize S 2 O 2 3 to sulfite and sulfate as well as elemental sulfur. 14