Extract from: Hibbert D.B., Introduction to Electrochemistry, Macmillan, London, 350pp. 1993.

Available via the institutional repository of the University of New

South Wales, UNSWorks: HUwww.unsworks.unsw.edu.auU U

© D. Brynn Hibbert 1993

Reproduced and communicated by permission of the publisher: Palgrave Macmillan.

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9 Electroanalytical chemistry: potentiometric methods

9.1 Introduction

Electroanalytical chemistry started life with one of the great analytical tools, the pH elect~ode. It has gone on to promise many wonderful things and in some ways the world still waits for the ultimate sensor. The appeal­ ing thing about electrochemical sensors, particularly potentiometric sen­ sors, is that they_have no moving parts, their output is readily assimilated by a computer and they can be made small and cheap. Although electro­ chemical detectors for chromatography are now available, electrochemis­ try is in fact in direct conflict with chromatography. In chromatography by clever separations the detection step is almost trivial, as each analyte comes through as a separate entity. ~J~ctroc_h~mistrYhQP~s-!oc!irectly J!leasure the concentration ofan analyte witl191,1tpJ:'igr Jleparati9J). This puts much greater constraints on the method: it must discriminate between analyte and the myriad of interfering compounds, it must operate over a range of concentrations and it must be quick. Research still continues attempting to find better electrodes and to develop numerical methods to allow for interferences. This chapter and the next are organised about the different electrochemi­ cal methods. In this chapter I describe techniques that are performed at equilibrium, the measurement of potentials and the conductance of solu­ tions. Then comes voltammetry, in which the potential is controlled and the current measured. Of these, polarography has a special mention, being the first and probably still most used of all voltammetric methods. Then follow amperometric and coulometric methods.

190 191 9.2 Potentiometric methods of analysis

9.2. 7 Ib~N~IQ~tJ?9L.l9tloI}IDanaly!!~(JL 9hemlstry

All potentiometric measurements rely on some difference in electrochemi­ cal potential between a...referenc~tsJ'.~~m _amLthe_ test system. This may be exploited by establishing a redox potential or a membrane potential. In any case the measured voltage of the cell will be related to the activity of the species in question by the kl~rnst equation or something very like it. In general, therefore, all potentiometric cells follow

_'_~meas = Econst ± R ~L~ Fin (a)!1 (9.1) where a is the activity_oLth_~ ~nalyte. In situations in which the ionic strength is low, the activitl__I1l~~~~ace~_by th~~c:>ncel}trat!on __~!th~uti loss of accuracy. However, this does mean that more concentrated solu­ tionsneed to. be buffered-tothesime ionic strength as the reference !~~tiort:~-usually by the addition ()fanon-interfering_elec!rolyte. There are two basic types of potentiometric sensor. The most widely used is the !9!l~.se1ecti.veelectrQ_electrode and the ftuorideelectro(je. The second class of potentiometric sensors are based oiiiradiiTonal redox reactions. These are useful for specific applications but are prone to in­ terferences, as any redox couple in the solution will compete for electrons

v

M e m X- b X- r

•n ••·.ref e I •.

Figure 9.1 Ion-selective membrane electrode 192 Introduction to electrochemistry

v

Reference electrode

Indicator electrode

Figure 9.2 Oxidation-reduction (redox) electrode from the electrode. We start with the measurement of pH, for which electrochemical methods encompass both ISEs and redox electrodes.

Sensitivity of potentiometric methods

The strength of an analytical method that follows good old Nernst is that a very wide range of concentrations are encompassed by a measurable range of voltages. For a one-electron process at 25 QC the change is 0.06 V for every tenfold change in activity. To put it another way, 1 V spans more than a 1016 change in activity. The drawback is that small errors in the measurement of the voltage lead to large errors in the calculated analyte concentration. If you work it out, 1 mV leads to about a 4% change in concentration. See Problem 9.1.

Interferences

In an ideal world there would be an electrode for each analyte that would respond only to that substance and nothing else. Alas, you do not need me to tell you that this is not the case despite the very best efforts of genera­ tions of electrochemists. If a voltage is generated at an electrode by more than one analyte, each of which follows the Nernst equation, the total potential measured is Electroanalytlcal chemIstry 193

-0.1

-0.15

-0.2

-0.25 > iU -0.3

-0.35

-0.4

-0.45 -8 -7

Figure 9.3 Plot of Ecell against log/o (aJ for a solution containing one interfering ion (X+) of activity ax. The numbers on the curves give the value of k1j ax

/z E cell = Econs' + RT / n Fin (aj + I kjj ar ) (9.2) aj is the activity of the analyte of interest and aj the activity of interfering species j that has charge z. The sum is over all interfering ions. k jj is known as the selectivity coefficient and may be determined experimentally. Values of kij are specific to each electrode and analyte solution, and Equation (9.2) hQlds only over quite small ranges of concentration. Values of k less than 1. mean that the interfering species has a smaller effect on the .voltage than the_analyte, and greater than 1 show the species has a larger effect. See Problem 9.5. . Figure 9.3 shows the effect on the plot of E cell against aj of interfering ions at different concentrations and with different kjjs (Le. different values of the product kij Qj)' See Problems 9.2 and 9.5. From the above it is clear that a reasonable amount of an interfering ion can render an ISE almost useless. Often halides and cyanide mutually interfere; silver, copper and mercury interfere with the determination of other metals, and, in general, similar ions (charge, size) interfere. Interferences can arise because of complex formation that removes the free ion (e.g. EDTA complexing most metals), Of by reactjon~t th~electrode (for example, cyanide leaches chloride from silver chloride). 194 Introduction to electrochemlstry

9.2.2 Potentiometric measurement of pH

DefinitiQn QtpH

The quantity pH is defined as the negative logarithm to the base 10 of the hydrogen ion activity (pAnything is the negative logarithm to the base 10 of Anything):

pH = -loglO(aH +) (9.3)

~ 14 The equilibrium constant of H20 H+ + OH- is 10- at 25 QC (the pK of water is 14), so the pH of water should be 7. Interestingly enough, nice and simple as the definition is, because of the impossibility of measuring single ion activities it is useless as it stands. 'But', you will say, 'what about the pH meter?' This is an electrochemical device that gives a direct reading of pH, but it is only relative to a defined solution of known pH (the buffer you use to calibrate the instrument). The problem arises in making a cell for which the measured voltage reflects only the change in hydrogen ion activity. Cells may have liquid junction potentials, although these can be minimised, and the activities of the different species will vary with ionic strength. Luckily, analytical chemists are very practical people, and the International Union of Pure and Applied Chemistry (IUPAC) has agreed an operational definition of pH derived from the electrochemical method of measurement:

pH = pHbuf + (E - Ebuf) F / R TIn (10) (9.4) E is the potential of an electrode that responds to H+, and the subscript buf refers to a standard reference buffer solution of known or defined pH. The National Bureau of Standards in the USA defines the pHs of buffers from measurements of the potential of a cell containing a hydrogen electrode

and silver-silver chloride reference electrode: Pt, H 2 I buffer, Cl- I AgCI, Ag. This has the advantage of not having a liquid junction potential. Assumptions are made about activity coefficients and the defined pH is

hopefully near enough the true -loglO (aH +). There are seven NBS primary standard buffer solutions. These are given in Table 9.1. A review of different electrodes that have been used for the measurement of pH is given in Table 9.2.

Measurement by redox electrodes

Although seldom used, the quinhydrone electrode is a good example of a redox electrode that can be used for the measurement of pH. Quinhydrone is the name of an equimolar mixture of quinone and hydroquinone. In solution at a platinum electrode the redox equilibrium in Figure 9.4 is established. Both quinone and hydroquinone are sparingly soluble in Electroanalytical chemistry 195

Table 9.1 NBS primary buffer standard solutions

Buffer Composition (m = molality) pH (25 QC) Potassium hydogen tartrate (KHTar) Saturated KHTar 3.557 Potassium dihydrogen citrate

(KH2Cit) 0.05 m KH2Cit 3.776 Potassium hydrogen phthalate (KHPhth) 0.05 m KHPhth 4.004

Phosphate 0.025 m KHzP04 6.863 (equimolal) 0.025 m NaH2P04

Phosphate 0.008 695 m KHzP04 7.415 (35: 1) 0.03043 m NaH2P04 Borax 0.01 m NazB40 7 .1O H 20 9.183 Carbonate 0.025 m NaHC03 10.014

0.025 m NaZC03

Table 9.2 Characteristics of electrodes used for the measurement of pH Electrode pH range (error) Interferences Remarks Hydrogen 0-14 Redox, air, heavy Nernstian. Slow (0.002) metals equilibrium. Reducing. Quinhydrone 0-7 Alkali, redox, Nernstian to pH7. (0.002) complexing agents, Quinhydrone contaminates proteins solution. Antimony­ 4-10 Strong acid, alkali, Not Nernstian. Must be antimony oxide (0.2) HzS, Cu2+ calibrated. Glass 0-12 Strong alkali, Nernstian over wide range (0.002) dehydrating agents but needs calibration. Can be used in presence of redox couples.

0=( )=0 + 2W + 28 ;:=: HO-@- OH

Figure 9.4 The reaction of the quinone-hydroquinone half-cell

water, which causes the actIvItIes of these species to remain constant. Against a reference electrode the potential of this half-cell is

Ecell = Econs, + RT / Fin (a H +) = Econs' - 0.059 pH (9.5) 196 Introduction to electrochemistry at 25°C. In case you are wondering why there is not a '2' in RT / F because there are two electrons in the reaction, it cancels with the aH + squared. In fact the potential of all hydrogen ion sensing electrodes varies as 2.303 RT / F volts per pH unit. The antimony-antimony oxide electrode H+ I

Sb20 3 , Sb is also pH-sensitive. The half-cell reaction is ~ 3 Sb20 3 + 6 H+ + 6 e 2 Sb + + 3 H20 The electrode is formed by dipping an antimony wire into the solution of interest. A thin film of antimony oxide forms and this with the underlying metal constitutes the pH electrode. Although it follows Equation (9.5), the constant cannot be calculated and so each electrode must be calibrated before use. Almost anything interferes with the measurement: strong acid or alkali, dissolved oxygen, heavy metals and hydrogen sulphide, to name but a few.

The glass electrode

The glass electrode is a half-cell separated from a reference half-cell by a glass membrane (see Figure 9.5). At each side of the membrane an ion­ exchange equilibrium is established between ions in the glass (Na+, K+, Ca2 +, Li+, Ba2+, the exact mix of ions depending on the glass) and H+ in the solution. Most of the action occurs within 100 nm of the surface, where the glass is seen as a hydrated gel. Inside the glass is quite dry and unaffected by the solutions. The internal solution is usually 0.1 mol dm-3 HCI and contact is made through a silver-silver chloride electrode that is reversible to chloride ion. The reference electrode is often a calomel electrode. The cell is therefore

3 Ag, AgClI HCI (0.1 mol dm- ) I glass I test soln I KCI (saturated) I

Hg2Cl2 , Hg

Silver wire coated with silver chloride

0.1 mol dm-3 hydrochloric acid Glass membrane saturated with silver chloride

Figure 9.5 Essential features of a glass electrode Electroanalytical chemistry 197

The potential of the glass electrode is given by Equation (9.5) with Econsl now including equilibrium constants for the ion-exchange process. At pH > 10 (i.e. very alkaline solutions) glass membranes also respond to changes in the concentration of univalent metal ions, which leads to a negative error in the measurement of pH. There is also a negative error in very acidic solutions. Because there is no electron exchange in the electrode, the presence of redox couples has no effect on the glass electrode; in fact there are remarkably few interferences. It is important to calibrate glass electrodes frequently, and the potential must be measured with a high-impedance meter.

An ion-selective. electrogei~..~. membrane electrode that responds selec­ !ive-ly·t(;-oIle (or several) ionic species. The word 'me.Olbrane' here covers any ~JmaratorJletween two solutions, one containing the analyte and one a reference solution. IUPAC classes ISEs according to the type of mem­ brane as homogeneous membrane electrode, heterogeneous membrane electrode, liquid ion-exchanger electrode or glass electrode. A list of electrodes is given in Table 9.3.

Table 9.3 Ions that are determined by ion-selective electrodes. The composition of the membrane is given in parentheses Homogeneous Heterogeneous Liquid Glass ion­ exchanger H+ F-(LaF3) F-(LaF3) Cl­ X-(AgX)* X-(AgX) ClO';­ Na+ S2-(Ag S) NO- K+ 2 S2-(Ag2S) 3 2 CN-(Agl, Ag2S) K+ Ca + Ag+(AgX) Ag+(AgX) Ca2 + NH: 2 2 Cu +(Ag2S + CuS) SO;-(BaS04) Pb + Ag+ 2 Pb +(Ag2S + PbS) PO~-(BiP04) BF';- Li+ 2 Cd +(Ag2S + CdS) •X = Cl, Br, I.

Homogeneous membrane electrode

A homogeneous membrane is one made from a single crystal or pressed disk of an insoluble salt (e.g. AgCl). The membrane is inserted into the end of a tube (see Figure 9.6), which is then filled with an internal reference solution and contact made via a reference electrode that is 198 Introduction to electrochemistry

Internal reference electrode

Solid state membrane (or heterogeneous membrane in supporting matrix)

Figure 9.6 Construction of a solid statf!lmembrane electrode reversible to one ion in the reference solution. For example, the fluoride 3 electrode LaF3 has an internal solution of 0.1 mol dm- sodium fluoride and 0.1 mol dm-3 sodium chloride, and an internal reference electrode of silver-silver chloride. The membrane usually can conduct the ion in ques­ tion. For example, LaF3 conducts fluoride and only fluoride. Thus, it is remarkably free from interference. The cell that is formed in determining fluoride by a lanthanum fluoride ISE coupled to a calomel reference electrode is

3 3 Ag, AgCI(s) I Cl- (0.1 mol dm- ), F- (0.1 mol dm- )I LaP3 1 test

solution 11 Cl- (satd) I Hg2C1 2 , Hg The potential depends on the ratio between concentrations of fluoride in the test solution and internal reference solution: (9.6)

Because cF -. ref is constant, Equation (9.6) at 25 QC becomes

Ecell = const + 0.059 pF (9.7)

6 where pF = -loglO (cF- ). The fluoride electrode can measure F- from 10- mol dm 3 up to saturated solution. At pH < 3 the formation of HF interferes with the determination and the only other ion the fluoride electrode responds to}s.hydro~ide. For this reason test solutkms ..are.Qften buffered. See Problem 9.3. Silver halides and silver sulphide conduct silver ions and thus are used in silver ion sensors. However, they are most useful as halide and sulphide sensors, respectively. Their response to the anion arises from the low solubility of the salt. For example, the potential of a silver chloride elec­ trode is, by Equation (9.1), Electroonolyticol chemistry 199

E AgC1 = Econst + RT / Fin (a Ag+) (9.8) However, in a solution containing predominantly chloride ions the activity of silver ions will be determined by the solubility product of silver chloride, aAg+ = K sp / acl-. Equation (9.8) becomes

E AgC1 = Econst + RT / Fin (Ksp / aCI-) = const - RT / Fin (acl-) (9.9) and so this electrode also responds to chloride.

Heterogeneous membrane electrode

In a heterogeneous membrane electrode the active ingredient is dispersed in a material to give the membrane better mechanical properties. For example, silicone rubber and polyvinyl chloride have been used. The active material comprises at least 50% of the membrane, as it is essential that the particles be in electrical contact.

Liquid ion-exchanger electrode

Many ions are complexed by organic compounds that are soluble in organic solvents but not in water. A porous hydrophobic membrane soaked in an organic solution of such a compound and having a reference (aqueous) solution on one side and the test solution on the other will function as an ion-selective electrode. A traditional design is shown in Figure 9.7. A common membrane material is cellulose acetate. The exchanger picks up the ion it is sensing and transports it through the membrane, thus

Organic liquid ion exchanger (MR2 in l-pentanol)

Ag, AgCI

Aqueous solution saturated with AgCI + MCI2

Porous membrane holding liquid ion exchanger

Figure 9.7 Construction ofa liquid ion-exchanger ion-selective electrode 200 Introduction to electrochemistry

establishing an equilibrium between the ion in the test solution and that in an internal reference solution. Because of the way that equilibrium is established, the response of liquid ion exchangers can be somewhat slow. Being insoluble in water, the exchanger and the complex are confined to the membrane. A modern design uses a polyvinyl chloride (PVC) membrane in which the ion exchanger is introduced in a suitable solvent. When the solvent is allowed to evaporate, the membrane with its ion exchanger may then be used as the membrane ISEs described above. They may also be coated onto a metal wire or graphite rod. It is not clear how the internal reference potential arises, but these devices are small and cheap, and work surpris­ ingly well. Anion exchangers are either long-chain alkylammonium salts or salts of a non-labile metal complex MLi+, where L is orthophenanthroline. Perchlorate, nitrate and tetrafluoroborate ion are selectively determined by different complexes of this type. Cation exchangers are usually long­ chain alkyl anions such as bis(n-decyl)phosphate [(C lOH z1 )zPOz]Z-, which is an exchanger for calcium. This electrode is Nernstian with a slope of 0.0294 3 5 3 V/pCa for concentration from 1 mol dm- to 10- mol dm- • Neutral exchangers depend on the shape and size of cavities in large molecules such as the naturally occurring antibiotic valinomycin or syn­ thetic crown ethers. The valinomycin electrode is specific for K+ (k: Na+ = 5 3 x 10-\ H+ = 5 X 10- ).

Glass electrode

The glass electrode has already been introduced as the sine qua non of pH measurement. Here I shall mention the use of the glass electrode for the measurement of metal ions. One problem with the measurement of pH by a glass electrode is the interference by metal ions, particularly at high pH. This is exploited in glass electrodes that are designed for the measurement of ions such as Li+, Ag+, NH:, Caz+, K+ and Na+. For example, a soda glass containing 18% alumina is particularly sensitive to silver and sodium. When the amount of alumina is cut to 4%, the glass acts as a general cation electrode.

Ion-selective field effect transistors

When making voltage measurements, the signal is usually fed to the gate of a MOSFET (metal oxide field effect transistor), which is the first stage of amplification of a voltmeter. The potential on this gate determines the current flowing through the device and thus amplification is achieved. The idea of an ISFET is to apply the membrane of an ISE directly to the gate of a MOSFET. A cross-section of an ISFET is shown in Figure 9.8 Electroanalytical chemistry 201

2 3

4 5

Figure 9.8 Cross-section through an ISFET: 1, silicon nitride layer; 2, PVC membrane impregnated with ion-selective compound; 3, silicon oxide; 4, n-doped zone; 5, silicon substrate

The lack of a reference electrode is not a great problem: impurities in the gate generate a reference potential, although, if one is used, a more stable signal results. The major drawback of an ISFET is that the extremely sensitive components of the MOSFET are exposed to the environment. This leads to a finite lifetime (100-300 h) and the need for conditioning of the electrode in situ before a useful signal may be recorded.

Ion-selective microelectrodes

For in vivo biological work it is necessary to make very small electrodes that are still ion-selective Figure 9.9 shows different designs of microelectrodes

6 6 6 1\

3

2

5 4 .j~ ~~ 0.5 "'" , ~m (a) lb)

Figure 9.9 Cross-section through three types of microelectrode: (a) reference electrode; (b) pH- or cation-selective electrode; (c) combined reference and liquid ion exchanger. 1, Glass capillary; 2, internal reference solution; 3, internal electrolyte; 4, cation-sensitive glass; 5, liquid ion exchanger; 6, silver-silver chloride electrode 202 Introduction to electrochemistry based on glass capillaries. If a reference electrode can be combined as in Figure 9.9 (c), a better response is obtained, as spurious electrical signals originating in the cell are less likely to be recorded. These electrodes have been used mostly for measuring potassium and other cations in cells, in the spinal cord and in the brain. Coated wire electrodes, because of their simplicity of design, have also been used as in vivo microelectrodes.

Gas-sensing membrane electrodes

Gases that dissolve in water to give acid (e.g. sulphur dioxide) or alkaline (e.g. ammonia) solutions may be sensed by a pH electrode. A thin (100 ,urn) gas-permeable membrane retains a small amount of internal electro­ lyte close to a glass pH electrode. Gas on the outside diffuses through the membrane and forms an equilibrium that determines the pH of the solu­ tion (see Figure 9.10). The ammonia probe is the most widely used gas-sensing membrane electrode, being employed to analyse fresh water, effluent and sewage. The

Reference electrode

Glass electrode

Reference --H~I electrode

Thin film of internal electrolyte

Membrane

(b) Membrane (a)

Figure 9.10 Construction of typical gas-sensing probe: (a) overall layout, (b) cross-section ofsensing tip Bec"oana/~~alchem~t~ 203

02--~ reference

Zirconia tube with Pt film

Figure 9.11 The zirconia oxygen electrode solution under test must be at pH > 12, to ensure that the ammonia is in a free state. Complexed ammonia may be released by treatment with 7 3 EDTA. The response range of the ammonia probe is 1-10- mol dm- • In the high-temperature zirconia cell a solid state membrane of zirco­ nium oxide stabilised by yttrium oxide and calcium oxide passes oxide ions between electrodes of platinum (Figure 9.11). On one side a reference pressure of oxygen is maintained and a potential is generated that is proportional to the logarithm of the ratio of concentrations:

~ 2 O2 + 4 e 2 0 -

E = 2.303 RT /4 Flog (P02 / Pref) (9.10) Note: It must be stressed that this reaction of oxygen only occurs in this type of cell at temperatures in excess of 800 QC; it could not happen in water.

Potentiometric enzyme substrate electrodes

An electrode may be made to respond to certain organic and biological molecules by coating an ISE membrane with an enzyme that is immobilised in a suitable matrix. As the enzyme works on the target molecule, the product of the reaction is measured by the ISE. For example, the enzyme urease causes urea to be broken down to ammonium ions and hydrogen carbonate ions. An ammonium ion-selective glass electrode can then de­ tect the ammonium ion released. Enzymes may be immobilised by cross-linking to serum albumin, PTFE or Nylon using glutaraldehyde, by occlusion in a polymer or by being trapped in an organic liquid. Porous polymer membranes may also be used to retain the large enzyme at an ISE while allowing passage of the smaller analyte molecule. A list of enzyme potentiometric sensors is given in Table 9.4. 204 Introduction to electrochemlstry

Table 9.4 Potentiometric sensors for immobilised enzymes Sensor Species detected Analyte pH glass H+ Penicillin, glucose, urea, acetylcholine NH: glass NH: Urea, amino acids NH: gas NH: Asparagine, creatinine, 5'·AMP, urea

CO2 gas CO2 Urea, uric acid, tyrosine 1- ISE 1- Glucose CN- ISE CW Amygdalin

9.2.4 Potentiometric trltratlons

Acid-base titrations

An indicator electrode that responds to pH may be used to follow the course of a pH titration. A plot of the voltage of a cell including a pH electrode and a reference electrode (which is directly proportional to pH) against titrant added has the familiar S-shape shown in Figure 9.12. The end point may be more easily located from a first or second difference curve. See Problem 9.4. For titrations of weak acids with strong bases (or weak bases with strong acids) the end point becomes less distinct as the pKa of the acid increases. This is illustrated in Figure 9.13.

16.------,

14

12

10 (a)

4

oL- --1..... --L -'--- --'- -:! o 0.5 1.5 2 2.5 Fraction of acid titrated Bec"oana/~icalchem~t~ 205

4

3

(b)

0'o O.S 1 I.S 2 2.S Fraction of acid titrated Sr------,

3

2 I-

(c)

-2

-3

-40'-----0-'-.S----....Jl'------IL..S----...L2----2-'.S

Fraction of acid titrated

Figure 9.12 (a) Potential (E) ofa pH electrode plotted against the volume of titrant (V) added during a strong acid-strong base titration; (b) first difference curve ~E / ~V; (c) second difference curve ~~E / ~~V

A pH titration may be used to determine the pKa of a weak acid. Up to the equivalence point the Henderson equation (or Henderson­ Hasselbach equation) may be used to calculate the pH of the solution, given the concentration of neutralised acid (i.e. the amount of salt formed) and the amount remaining: 206 Introduction to electrochemlstry

1S ,....------,

10

o ~------.------~

-S L.-- ---I.. ...L- l.-. ---1. .,..l o O.S 1 1.S 2 2.S Fraction of acid titrated

Figure 9.13 Titration curves of a strong base with acids of different pKa values

pH = pKa + log (Csalt / Cacid) (9.11) At the end point the pH of the solution is given by the extent of hydrolysis of the salt of the weak acid:

pH = 1/2 pKw + 1/2 pKa + 1/2 log (csalt) (9.12) After the end point the solution becomes increasingly alkaline as the strong base is added:

pH = pKw + log (Cbase) (9.13)

It is seen that from Equation (9.11) at half the equivalence point, when Csalt = Cacid' then pH = pKa• A rough value may be read directly from the titration curve. For more accurate work the activities of the ions must be allowed for and a plot against ionic strength performed. How this is done was given in Chapter 4.

Redox tltratlons

An archetypal titration is that between cerium(IV) and iron(II). I remem­ ber doing it as an undergraduate, I teach it in my lectures and now it will be enshrined in this textbook, as it has been in everyone that mentions electrochemistry. In the first draft of this chapter I wrote that 'I have never had to do a redox titration between cerium IV and iron 11 nor have I ever Electroanalytlcal chemistry 207 met anyone who has'. Would you believe that a reviewer of the draft promptly replied that he had found such titrations useful for measuring the redox potential of Fellilll complexes. So there you are. Anyway. it fits in nicely with my introduction to cells in Chapter 4 and it is no doubt good for you. The two parts of the redox titration - that is, before equivalence and after it - may be taken separately. When Ce4 + is being added to Fe2+, H 2 H 4 before the end point there is Ce , Fe +. Fe present (no Ce +, as it is all used up). The potential of a platinum wire that is immersed in the solution will be determined by the Fe~+/Fe.H couple. This in turn may be expressed in terms of the volume of titrant (Ce4 +) added (t) and the volume at the end point (T):

3 E = E'(Fe +/Fe2+) + R T I Fin (cpe3+ I cPe2+) (9.14) = E'(Fe3+/Fe2+) + R T I FIn (t I [T - t]) (9.15) After the end point, as excess Ce4 +is added, there is no more Fe2+ and the potential is determined by the Ce4 +ICe 3+ couple:

4 4 3 E = E'(Ce +/Ce3+) + R T I Fin (CCe + I CCe +) (9.16) = E'(Ce4+/Ce 3+) + R T I FIn ([t - TIT]) (9.17) The titration curve is shown in Figure 9.14. The formal electrode potential is found when t = T I 2 (for the iron system) and when t = 2 T (for ceriurn). See Problem 9.6.

1.8

1.8 -

1.4-

1.2 - > ~ 1 -

0.8 - V- 0.6 ~

0.4 I I I I 0 0.5 1 1.5 2 2.5 Fraction of Fe(lI) oxidised

Figure 9.14 The course of a cerium(IV)/iron(ll) redox titration 208 Introduction to electrochemistry

Systems that have been amenable to redox titrations are the deter­ mination of ascorbic acid by iodine and the determination of organic nitrogen compounds containing azo, nitro or nitroso groups by titration with chromium(II).

Precipitation titrations

It is possible to titrate a solution containing chloride, bromide and iodide with silver nitrate to give the concentration of each halide. A silver elec­ trode is used with a suitable reference electrode connected to the test solution via a salt bridge:

Hg, HgzClz I KCI (satd) I NH4 N03 salt bridge I halide soln I Ag As silver nitrate is added, silver iodide is precipitated. The concentration of silver ions is low and determined by the solubility product of silver iodide. The potential increases slightly as more silver is added and more iodide is removed from solution. At the end point the potential increases to that determined by the solubility product of bromide. When an the bro­ mide is titrated, another potential step is seen as chloride reacts. Finally, when there are no halides remaining, the potential shoots up as the concentration of silver ions is allowed to increase without hindrance as more silver nitrate is added. The titration curves are shown in Figure 9.15. See Problem 9.9.

Agel

v

AgBr

Agl

Volume AgNO,

Figure 9.15 Precipitation titration of halide ions by silver ions, followed by a silver electrode Electroanalytical chemistry 209

9.2.5 Flow analysis

Electrochemical methods of analysis are particularly useful in flow analy­ sis. Here I shall describe one method - flow injection analysis - and show how the concept of cells in series can be used to overcome some of the prob­ lems associated with the logarithmic response of potentiometric sensors. The basic layout of a flow injection experiment is shown in Figure 9.16 and multielectrode cells in Figure 9.17. A small volume (typically 100 1-11) of the analyte is injected into a carrier stream flowing through an electro­ chemical cell. The response of the electrode appears as a peak, the height

Electrolyte

Simple Mixing coil Cell Pump Injector

Figure 9.16 Block diagram of a flow injection apparatus of which is proportional to the amount of analyte injected. The cell is made from Perspex blocks and has a total volume much less than 1 ml. Metal wire electrodes or coated metal wire electrodes are used. The arrangement shown is a clever way of doing electrochemistry on small amounts of analyte. An added benefit is obtained when several indicator electrode­ reference electrode pairs are coupled in series as shown in Figure 9.17. If N cells, of which the potential of each varies as the Nernst equation (9.1), are connected in series, the total potential is a simple sum of N potentials and the slope of the E versus In (a) plot is NRT / F. Combining cells in series would reduce the error associated with such measurements and also improves the detection limit. However, the need for total isolation implies that the experiment must be done separately in N apparatuses. Any benefit gained would be lost in having to set up N titrations, N pH electrodes, etc. The arrangement in Figure 9.17 appears doomed, because the cells are all in the same electrolyte and common-sense tells us that they should short out, giving only a single potential (let alone the corrosion that should occur between crossed pairs of electrodes). However, whether or not additivity 210 Introduction to electrochemistry

Solution- out S2 53 54 S5 S6 in

Figure 9.17 Cross-section of a flow injection electrochemical cell with six cells in series occurs depends on the resistance between electrodes in any cell and the resistance between the cells. For two identical cells connected together in series the total voltage across the pair of cells (Vmeas) in terms of the single-cell voltage (Vcell) is

Vmeas = Vcell(Rn + 2 R12) / (RH + Rl2) (9.18) RH is the resistance between indicator and reference electrodes in one cell and R 12 is the resistance between the cells. As R12 goes to zero (complete short-circuit) Vmeas = Vce1b and as Rl2 goes to infinity (complete isolation) Vmeas = 2 Vcell with perfect additivity. As long as Rl2 > 10 Rn, a substantial measure of additivity (Vmeas = 1.8 Vcell) is achieved. This can easily be realised in the type of cell shown in Figure 9.17.

9.3 Conductiometric analysis

9.3. 7 Conductiometric titrations

The addition of one electrolyte to another will result in a change in the conductance of the solution. These will be more so if ionic reactions occur to remove species as precipitate or as a molecule. One obvious example is an acid-base titration in which H+ and OH- react to give water. In the titration of a strong acid with a strong base, initially the conductance of the solution is high, owing to the presence of highly mobile protons. As hydroxide is run in, protons are replaced by less mobile metal ions (e.g. Na+ or K+). The conductance of the solution falls until the end point, after which the hydroxide ions are in excess and continued addition serves to increase the conductance. This is illustrated in Figure 9.18 (a). The con­ ductance of the solution is also affected by volume changes, and so it is desirable to add small amounts of more concentrated titrant so the total volume of the solution does not change. The titration of a strong acid by a weak base gives a somewhat less distinct end point, as shown in Figure 9.18 (b). As before, as the base is added it reacts with the acid, removing protons and causing the conduc- Electroanalytlcal chemistry 211 I

Voluml (1) I

Voluml lb)

Voluml (c)

F1llure 9.18 Typical conductiometric titration curves: (a) strong acid-strong base. precipitation titration; (b) strong acid-weak base; (c) weak acid-weak base tance to fall. However, now after the end point, add'{ion of excess weak base that is only slightly dissociated does not increase the conductance and the curve levels off. See Problem 9.7. A weak acid-weak base titration (e.g. acetic acid and ammonium hydroxide) shows an initial dip (Figure 9.18c) as the small amount of free protons is consumed. Thereafter the conductance rises as undissociated acid is replaced by fully dissociated salt. At the end point the curve flattens off, as excess weak base again does nothing for the conductance. Conductiometric titrations are useful for turbid or coloured solutions, 212 Introduction to electrochemlstry for which indicators are not reliable. They are also applicable for a wide range of titrations: acid-base, precipitation, complexiometric. There is no reaction at the electrodes and there are virtually no interference problems. However, these titrations are not particularly sensitive and are not used for very small concentrations of analyte.

9.3.2 Conductiometric detection for ion chromatography

Ion chromatography separates ions by passing them through an ion­ exchange resin. By playing around with the resin and the eluent (the solution the ions are injected into) good separation of a range of anions or cations may be accomplished. Detection by measuring the conductance of the stream coming from the column is an obvious choice. The measure­ ment of conductance can be done quickly and easily and it is sensitive to all ions. One problem that arises is the high background of ions present in many eluents. For example, to analyse a mixture of anions containing halides, sulphate, nitrate, formate and acetate, a mixture of sodium car­ bonate and sodium hydrogen carbonate would be chosen as the eluent. The background conductance of sodium ions, carbonate ions and hydrogen carbonate ions would swamp the small changes as the different analyte ions eluted from the column. To overcome this problem a suppressor column is added after the separator column. The suppressor is an acid ion-exchange column of high capacity that exchanges a metal ion for protons. As car­ bonic acid is a weak acid, as sodium is replaced by protons these tie up carbonate as undissociated carbonic acid:

CO~- 2 Na+ + + 2 Catex-H+ ;= 2 Catex-Na+ + H2C03 (9.19) Catex is the name of a proprietary column. The background therefore is very low. When nitrate, for example, comes through, what is produced by the suppressor column is nitric acid, which has a very high conductivity. Figure 9.19 shows an ion chromatogram with conductivity detection for a number of ions.

• PROBLEMS

9.1 In the text I say that when using the Nemst equation the error caused by a 1 mV uncertainty in the measurement of voltage leads to a 4% error in determination of ion activity. Show that this is so for a pH electrode. What error is introduced by an uncertainty of 1 K in the temperature?

9.2 Calcium is present in sea-water to about 400 ppm and magnesium to 1500 ppm. What error does the magnesium introduce in measurements of a calcium electrode if the selectivity of the electrode to magnesium is 0.015? Electroanalvtlcal chemistry 213

Cl

Deteclor r..pon'lt

8r NO,

Figure 9.19 Ion chromatography using a conductivity detector. A range of anions are detected from a glucose-borate eluent on a ICPAK-A column. The concentration of each ion was 80 ppm

9.3 A 0.250 g sample of toothpaste was boiled in distilled water and made up J to 100 cm • A potential of -0.0887 V was measured by a fluoride ISE in a 25 cm J aliquot of the solution. After addition of 0.1 cm) of a 2.500 x 10-) mol dm-) standard solution of fluoride the potential was -0.1126 V. What was the percentage by weight of F- in the toothpaste?

9.4 Below are the data for a potentiometric titration. Determine the end point from plots of E, .1E and .1(.1 E) versus volume. 214 Introduction to electrochemistry

Volume added/cm3 VoltageN Volume added/cm3 VoltageN 21.540 0.3135 21.810 0.4395 21.630 0.3243 21.900 0.6375 21.720 0.3396 22.080 0.6591

9.5 The following are data from an experiment to determine the selectivity coefficient of a chloride electrode to bromide. The first column is the volume of 1.2 mol dm-3 KBr added serially to a 50 cm3 solution of 1.00 x 10-4 mol dm-3 KCI. The second column shows the potential re­ corded by the chloride electrode. Determine the selectivity coefficient of the chloride electrode to bromide.

E/V 0.00 -0.115 0.5 -0.122 1 -0.128 2 -0.1375 2 -0.1452

9.6 From the data below for the titration of 25 cm3 of a solution of acidified iron(I1) ammonium sulphate solution by 0.05 mol dm-3 CelV solution determine the molarity of the Fell solution. Estimate the formal electrode 2 3 3 4 potential of the Fe + , Fe + I Pt half-cell and the Ce +, Ce + I Pt half-cell.

Potential versus SHEN 0.02 0.450 6.93 0.608 18.48 0.666 21.48 0.697 22.88 0.750 23.12 1.39 25.41 1.51 27.72 1.53 32.34 1.55 41.60 1.56 46.22 1.57

9.7 In a titration of 50 cm3 of benzoic acid by 0.93 mol dm-3 sodium hydroxide the following conductances were recorded.

Volume NaOH / cm3 Conductance /S o 2.42 0.125 2.09 0.25 2.53 0.5 4.29 0.75 6.16 Electroanalytical chemistry 215

1 8.14 1.25 10.12 1.5 12.1 1.75 14.08 2 16.17 2.25 19.03 2.5 24.31 2.75 29.81 3 35.31 3.25 40.7 3.75 51.7 4.25 62.59

Calculate the molarity of the benzoic acid.

9.8 The standard potential of the half-cell Cuy2- + 2 e ;= Cu + y4- is + 0.13 V (where Y is the ligand EDTA) and that of the copper half-cell Cu2+ + 2 e ;= Cu is + 0.34 V. What is the formation constant of copper EDTA? 9.9 50 cm3 of a solution of 0.01 mol dm-3 lead nitrate was titrated with 0.04 mol dm-3 potassium iodate. The potential of a lead electrode in the solu­ tion during the course of the titration is given below.

Volume added fcm3 E f V versus SCE 5 0.402 12 0.416 21 0.437 24.5 0.463 24.8 0.475 25 0.499 25.1 0.528 26 0.587 30 0.627

Determine the stoichiometry of the compound formed between Pb2+ and 10; and the number of electrons involved in the electrode reaction.

• ANSWERS

9.1 We know (Equation 9.5) that Eeeu = Econst + RTf Fin (aH +). Differentiating, dEceu = RTf F d In(aH +). But d In(x) = dx f x. Therefore, daH + f aH + = dEcen F f R T. Integration gives .daH + f aH + = 0.001 f 0.0257 = 0.039, which is nearly 4%. It is only because of the In term that the relative errors is independent of the activity. In the case of temperature we need to know the pH and also the temperature dependence of the potential of the reference electrode. In the happy event of the temperature change

of E cons, being the same as E cell, then the only error lies in the uncertainty 216 Introduction to electrochemlstry

in determining the value of RT / F. An error of 1 K at 298 K is 0.34%. As typical potentials measured by pH meters are a few hundred millivolts, this leads to a 1 m V error, which in turn gives the 4% error in activity.

9,2 We use Equation (9.2) to see the effect of interfering magnesium. The kM~ relative error is k Mp aMp2+ / a c1I 2+ where is the selectivity to magnesium (0.015), aMp2+ is the activity of magnesium ions (1500/24.4) and a c1I 2+ is the activity of calcium ions (400 / 40.1). We ignore activity coefficients and use concentrations not because sea-water is dilute (which it is not) but because it is reasonable to expect the activity coefficients of Ca H and Mg H should be similar and thus cancel. Therefore, the relative error is 0.922 / 9.98 = 0.092 or 9.2%.

9.3 The response of a fluoride ISE is given by E ... Erer - RT / Fin (aF -). Therefore, writing a for the unknown activity and a' for the activity of the spike: -0.0887 ... Ere' - RT / F In (a) -0.1126 = Ere! - RT / F In (a + a') Therefore, adding and rearranging, 0.023 85 F / RT ... 0.8907 = In [(a + a')/a]

The concentration of the spike is 2.500 X 10-3 X 0.1 / 25 ... 1.000 X 1O~ 1 6 mol dm- • The equation solves to give a ... 6.974 X 10- mol dm-3, which is 1.325 X 10-4 g F-, which in 0.250 g of toothpaste is 5.300 X 10-4 g F- / g or 0.053 wt%. 9.4 Calculate differences in the voltage values and plot them at the half-way 3 3 3 point. I make the end points 21.83 cm , 21.855 cm and 21.88 cm from E,

700

600

500

400

0

-100

-200 21,4 21,,5 21,8 21,9 22 22,1 22,2

Volum••dd.dlcm3 Figure 9.20 Plots ofpotentiometric titrations Electroanalytical chemIstry 217

J1E and J1J1E, respectively. This shows that with discrete data there is an error associated with determination of quantities such as end points.

9.5 For the solution with no bromide the following holds (ignoring activities): E = E' + RT / Fin (CCI-)' When bromide is added Eb = E' + RT / Fin (CCI- + k cBr-), where k is the coefficient we need to determine. Subtract

the first equation from the second to give (Eb - E) = RT / Fin ({CCI- + k cBr-} / CCI-)' Raise both sides to the power of e:

(CCl- + k cBr-) / CCI- = exp ([Eb - El F / R T)

Rearrange to give f = exp ([E b - El F / R T) - 1 = k cBr-/ CCI-' Below are tabulated the total volume of bromide added, the left-hand side of the expression just derived (f) and the concentrations of chloride and bromide

corrected for the addition of the bromide. Iff is plotted against CBr- / Ccr (Figure 9.21), the slope is the selectivity coefficient k.

3 3 V / cm VIOl / cm E / V f CCl-/ CBr-/ mol dm-3 mol dm-3 0.5 0.5 -0.122 0.313 435 0.000 099 0.011 881 120 1 1.5 -0.128 0.659 212 0.000 097 0.034951 360 2 3.5 -0.1375 1.402 145 0.000 093 0.078505 840 2 5.5 -0.1452 2.171 08 0.000 09 0.118919 1320

3 The slope is 1.587 x 10- • 3 9.6 From the plot in Figure 9.22, the end point is estimated to be at 23.1 cm • 3 Therefore, the molarity of the Fell is 23.1/25 x 0.05 = 0.0462 mol dm- • 2 The potential at half the end point is 0.67 V (this is the value for Fe +, 3 3 4 Fe + I Pt) and at twice the end point 1.59 V (Ce +, Ce + I Pt).

9.7 The titration curve with the first derivative is given in Figure 9.23. The end 3 point is at 2.40 cm , which gives the molarity of the benzoic acid as 2.4 / 3 52.4 x 0.93 = 0.0426 mol dm- • Remember that the dip at the beginning is not the end point but just the using up of the small amount of free protons in the solution of the weak acid.

9.8 The formation constant of copper EDTA is the equilibrium constant of the 2 reaction Cu + + y4- ;=: Cuy2-, which is arrived at by summing the two reactions given: Cu + y4- ;=: Cuy2- + 2 e (E = -0.13 V, because we have reversed the reaction) 2 Cu + + 2 e ;=: Cu (E-e = +0.34 V)

7 As ~ = RT / n Fin (K), K = exp (n F E-e / R T) = 1.3 X 10 •

9.9 By plotting the titration curve or its differential, the end point of 25.0 cm3 3 3 2 3 may be deduced. As 50.0 cm of 0.01 mol dm- Pb + == 25 cm of 0.04 mol 3 dm- 10;, the compound must be Pb(103)2' Knowing the end point we can now plot a graph of E against In {(T - t) / t}, where T is the end point and t is the titre at some point before the end point. The slope of the line is RT / n F = 0.011 96, which gives a value of n = 2. (Figure 9.24.) 218 Introduction to electrochemlstry 2.6_------,

2

1.5 ....

0.5

oL------...... o 500 1000 1500

Figure 9.21 Calculation of the selectivity of an [SE

1.8...- ..;V..::;O;::lu::.:,m;::e..:l::.dd:.;e:,:::d:;:/c::.:,m:...3 ---...,

1.6

1.4

1.2

0.8

10 20 30 40 50 Volume Ce4 + Idded/cm3

4 Figure 9.22 Formal electrode potential of Ce +.J+ and Fe·1+.H , Electroanalytlcal chemistry 219

70 25

/------.... Titration 60 20

50 15 ~ "c: 40 ti.. > ~ 10 'C a c: 'C 0 30 u 1st derivative

5 20

0 10

0 -5 0 234 5 Volume NaOHlcm3 Figure 9.23 Conductance titrations of weak acid by strong base

0.49

0.45

0.46

0.47

0.48

> LLi 0.44

0.43

0.42

0.41

0.4

0.39 ~ -5 -4 -3 -2 -1 0 In [(T-t)/t] Figure 9.24 Precipitation titration. Plot of E against In [(T - t) I t], where T is the end point volume and t the volume giving potential E 220 Introduction to electrochemlstry

Volume added t / cm] E / V versus SCE In {(T - t) / t} 5 0.402 1.386 12 0.416 0.080 21 0.437 -1.658 24.5 0.463 -3.891 24.8 0.475 -4.820 25 0.499 25.1 0.528 26 0.587 30 0.627 70 Electroanalytical chemistry: voltammetry and coulometry

10.1 Introduction

Potentiometric methods of analysis are elegant in their simplicity. Just stick in a couple of electrodes and out comes the answer. However, if the analyst has more control over the method, it may be possible to obtain better answers. The extra handle in methods that I describe in this chapter, which is usually control of the applied potential, gives a greater scope for clever analysis. The quantity measured, usually current, is linearly proportional to the concentration of analyte and so these methods are often more sensitive than potentiometric methods that rely on the Nemst equation. The first voltammetric method described is polarography. For a review of what voltammetry is check out Chapter 7.

10.2 Polarography

Heyrovsky was one of the great electrochemists and was justly rewarded with the Nobel Prize in 1957. He was the first person to realise in practice the promise of electrochemistry and one of the few chemists to be recog­ nised for building a useful instrument. Polarography is deceptively simple. It is linear sweep voltammetry at a dropping mercury electrode (see Chapter 6) and is primarily used to determine metal ions in solution.

70.2.7 Instrumentation

A cell for polarographic analysis is shown in Figure 10.1. As the currents measured are small, it is possible to do away with the reference electrode and use a two-electrode cell of the DME and the mercury pool. The drop 1 rate is 10-60 drops min- • In pulse polarography the lifetime of the drop

221 222 Introduction to e/ectrochemlstry

Electrochemistry in the dentist's chair

A moment's reflection on the contents of an average mouth will lead you to the inevitable conclusion that there should be lots of electrochemistry going on in there. Saliva is a reasonable electrolyte, containing about 0.025 mol dm-3 chloride, nearly 0.01 mol dm-3 phosphate and 0.03 mol dm-3 potassium. Teeth may be filled with dental amalgam (a mixture of silver, tin and sometimes copper in mercury), gold alloy or nickel-ehromium alloy. Any two of these in contact can lead to corrosion. The cell that is produced may be sufficient to give an obvious shock when a new filling is brought down on top of an older one. The dentists call this galvanic pain. Even within a dental amalgam filling, there are different phases with different propensities for corrosion. The y2 phase of dental amalgam is thought to corrode by the reaction Sn,Hg + 56 CI- + 14 PO~ + 70 H+ -+

7 SnOCI2.2 POCl3 + Hg + 35 H20 + 28 e which must qualify as one of the more complex electrochemical reactions on record. Dental plaque next to a tooth may give rise to corrosion cells by virtue of a depleted concentration of dissolved oxygen. This is entirely analogous to the examples given in the text, and leads to the conclusion that corrosion will be enhanced under plaque. The pH in plaque can be more acidic, especially after a sticky bun, and the environment is reducing. The difference in potential so produced can be enough to convert nickel from a nickel­ chromium alloy to nickel sulphide. All in all, this is a panel I wish I had not written, but it does show that electrochemistry is all about, and within, us!

WE - RE - AE ~- E 0

B

A '/// cj//7T77--- Figure 10.1 Schematic of a polarography cell: A, electrolyte containing analyte, supporting electrolyte and buffer; B, dropping mercury electrode; C, mercury pool anode,' D, reference electrode; E, potentiostat with voltage ramp , Electroanalytlcal chemistry t 223 must be synchronised with the applied voltage and so a mechanical knocker-off bashes the drop at a moment controlled by the electronics of I the system. The voltage sweep rate is slow enough (50-200 mV min- ) to ensure equilibrium is maintained and the cell is not stirred, to allow the attainment of a diffusion-limited current. The voltage range of the sweep, which is in the cathodic direction, is typically 0 V to -1.2 V against SCE. The cathodic limit occurs when hydrogen is evolved, and at the anodic limit mercury oxidises (in chloride solution to mercury(I) chloride). A polaro­ gram, the graph of current against voltage, is the result of the experiment.

70.2.2 Theory of polarography

Form of a polarogram

As the voltage sweeps to more negative values, there comes a point at which a metal may be reduced at the mercury drop. As it does so, it amalgamates with the mercury:

Mz+ + Hg + z e -+ Hg(M) (l0.1) The current passed increases sharply, finally levelling off at the diffusion­ limited current. Superimposed on this current is the rise and fall from the growth and detachment of the mercury drop (Figure 10.2). The current is small and so there is negligible depletion of the metal ion in the solution.

El12 j -----

M2--....

o -0.5 -1.0 VVI SCE

Figure 10.2 Typical conventional polarogram of two metal ions. The lower curve is the residual current in the absence of analyte 224 Introduction to electrochemistry

Therefore, the current due to that ion remains constant for the rest of the sweep. If there is another ion that can be reduced, then, as a suitable potential is reached, it too will generate a current that will add to the first. The shape of the polarographic wave as a whole is determined by the Nemst equation. Take a general electrochemical reaction Ox + n e ~ Red, which follows, if it is reversible,

E = E' + RT / n F In (cox / CRed) (10.2) Notice we are working with concentrations, so the constant potential E' is the formal electrode potential and not the standard electrode potential. In polarography the only source of Red is by reaction of Ox, so the concentra­ tion of Red will be proportional to the current passing. The current is also proportional to the square root ofthe diffusion coefficient (DR ). Therefore,

12 CRed = const I / Di (10.3) The amount of Ox at the electrode surface will be a maximum when there is no current flowing and will fall to zero when the diffusion current is reached (this is part of the definition of diffusion current: see Chapter 5). cox is therefore proportional to the difference between the current (I) and the diffusion current (Id), and again its own diffusion coefficient (Do) appears:

COx = const (Id - 1) / D:!i (10.4) Equation (10.2) becomes

E = E' + RT / n Fin (DR / DoYl2 + RT / n F In ([Id - I] /1) (10.5) The term in the diffusion coefficients is incorporated into the constant to make the half-wave potential, E1/2:

E = E I12 + RT / n F In ([Id - I] / I) (10.6)

E1I2 = E' + RT / n Fin (DR / DO )112 (10.7)

A value of EI/2 may be obtained from a polarogram at the current at which I = Id / 2, i.e. when the log term [Id - I] / I equals 1. See Problem 10.1.

For once the parameter E I12 is logically named. Note too that this equation is similar to that of the potentiometric titration (Equation 9.15), in which the concentration of one species depends on how far along the titration you are, and of the other how far you have to go. The shape of the current against voltage curve is the characteristic S-shape shown in Figure 9.12. If the diffusion coefficients of Ox and Red are not too dissimilar (by the time you have taken the square root of the ratio and then its log the diffusion term does not change E very much at all), then E1/2 is a good approxima­ E~. tion to E'. See Problem 10.3 for the relationship between E I/2 and If both oxidised and reduced forms are initially present, the curve will extend from the anodic limiting current to the cathodic limiting current and follow Electroanalytlcal chemistry 225

_----/d •C Reduction

Oxidltion

Figure 10.3 Polarographic wave for system in which both oxidised and reduced species are present

E = EI/2 + R T/ n F 1n ([Id, c- I] / [I - Id. aD (10.8) where the subscripts a and c refer to the anodic and cathodic reactions. An example would be the polarogram of quinhydrone. The form of this wave is shown in Figure 10.3. For irreversible processes the kinetics of the reaction are slow, and so at any point (until the potential is so great as to force a diffusion-limited current) the current is smaller than it would be if the system were revers­ ible. This is seen in a smeared-out wave for which the potential at Id / 2 is not a good approximation to E'. Although thermodynamic parameters (e.g. E') cannot be obtained from irreversible waves, it is possible to estimate kinetic parameters (although polarography may not be the best way of doing this). If there are additional chemical reactions or if adsorp­ tion plays a part, then the polarographic wave becomes a right dog's breakfast, exhibiting odd kinks and steps.

Polarographic current

It was Ilkovic who solved the diffusion equations at a spherical mercury drop electrode whose size was changing with time:

1I2 2l3 116 I, =708 n D m t Cox (10.9) I, is the current in JJ.A flowing at the end of the lifetime (t) of the drop, 226 Introduction to electrochemistry which grows at m mg S-I. Cox is the concentration of the analyte in mmol dm-3 and D is its diffusion coefficient in cm2 S-I. If the fact that the drop is spherical is taken into account, an extra term must be added to the Ilkovic equation: (10.10) The new term adds about 5-10% to the Ilkovic equation, and therefore should be used for accurate work and when determining diffusion co­ efficients. Although it is better to measure the current late in the life of the drop, the use of chart recorders that have a slow response leads to measurement of the average current during the lifetime of the drop. This is t of the maximum, so in some texts you will see the Ilkovic equation written with a constant of 607 and with 34 in the extended term. Fear not: as long as you make it clear whether you are determining the maximum or the average current, all will be well. See Problem 10.2. In addition to the current produced by the process itself, there is also the current required to charge the double layer at the electrode. This has been treated in Chapter 7. Here, as well as the charging current due to the natural progression of the voltage, with each drop a new surface is formed that needs to have its double layer charged. In normal polarography (which is what I am describing here) this limits the ultimate detection limit of the method. For an analyte concentration above 10-3 mol dm-3 the charging current is minute compared with the faradaic current. By 10-5 mol dm-3 it is usually larger and leads to a sloping baseline that can mask a faradaic wave. We shall see later pulse methods that overcome this problem by sampling the current when the double layer is completely charged. A small improvement in sensitivity is gained by only measuring the current at the very end of the lifetime of the drop. This is TAST or current-sampled polarography. This smooths out the jagged form of the normal polarography.

Polarographic maxima

A practical problem that has no complete explanation but is easily over­ come is the appearance of polarographic maxima. These are seen as an overshoot as the diffusion current is reached (see Figure 10.4). They are not the sort of maxima associated with linear sweep voltammetry - the sweep rate in polarography is too slow for that - but they appear to be due to convection around the growing drop. The convection arises from differ­ ences in current density between the top and bottom of the drop, which in turn causes variation in surface tension, and from disturbances at the surface of the drop as mercury flows in. Addition of small amounts of surfactants eliminates these maxima, and a couple of drops of gelatin or Triton X-lOO are routinely added to solutions. Electroanalytlcal chemistry 227

-v

Fllure 10.4 Polarographic maximum

Effect of complexlng agents

In Chapter 4 we saw that the effect of the formation of a complex is to shift the equilibrium electrode potential. usually to more negative potentials. as free metal ion is removed from the electrolyte. The half-wave potential is similarly affected. By combining the expressions for half-wave potential

and formation constant for the complex [MLq]<" - q.) + (see Equation 4.37). we can derive (see Problem 10.7)

RT ( q ) E 1/2 (complex) ... E /2 -- In Kt cUlland (10.11) 1 nF If the formation constant is large. the term in In (Kt) drives the half-wave potential more negative. For example. Cu2+ which has a half-wave poten­ tial of +0.02 V against SCE, shifts to -0.22 V in 1 mol dm-J potassium chloride and to -0.15 V in 1 mol dm-J ammonia-ammonium chloride, and becomes too negative to measure (the supporting electrolyte evolves hyd­ rogen before copper is plated) in 1 mol dm-J potassium cyanide. Complex­

ing ions has two practical uses. First. where two ions have very similar E1/2 values, the addition of a complexing agent usually separates the waves, as different metals are likely to have different values of the formation con­

stant with the ligand. Second. measurement of E1/2 values with and without a complexing ligand allows determination of the formation constant.

I 228 Introduction to electrochemistry

70.2.3 Derivative and pulse polarography

Derivative polarography

If the polarographic wave is differentiated, a peak is produced. By careful filtering of the wave to eliminate the peaks and troughs due to the DME, smooth peaks of substances whose E I /2 values are separated by 0.09 / n V can be completely resolved (n is the number of electrons). The peak potential does not coincide with E1/2; it is about 0.028 / n V more negative. Although derivative polarography is more sensitive than normal polaro­ graphy, its use has been superseded by advances in pulse and differential pulse methods.

Pulse polarography

Pulse polarography uses the fact that following a sudden change in poten­ tial (a pulse, no less) the double-layer-charging current decays much faster than the faradaic current. So, if you wait for just the right amount of time, you should be able to measure a current free of charging currents. Measur­ ing the current at a single point will also have the advantage of removing the current zigzags as the drop grows and falls; more so if the measurement is made at the end of the lifetime of the drop, when it is not growing so quickly. In normal pulse polarography a voltage pulse is applied to coincide with near the end of the drop's life. So, if a drop lasts for 2 s, the pulse will occupy 40 ms, 1.5 s after the start of the growth of the drop. The pulse rises from zero and falls back to zero, each succeeding pulse being to a higher voltage (this is how the sweep comes in). Measurement of the current is made in the latter part of the pulse after the charging currents have decayed. The form of the pulses and resultant polarogram is shown in Figure 10.5. The detection limit is improved by a factor of about 100 over 7 3 classical polarography to about 10- mol dm- • The pulses may also be applied on a DC ramp (this is the waveform for differential pulse polar­ ography).

Differential pulse polarography

To do pulse polarography there has to be some nifty control of the elec­ tronics: when to put the voltage on and off, how to measure the current, and so forth. While this is happening, it is just as easy to make two current measurements and take their difference and so gain the advantage of a difference method. The form of the pulse, which is 0.05-0.1 V, applied on top of a voltage sweep is shown in Figure 10.6. As before, the pulse Electroonolytlcol chemistry 229

le)

..,,~ ...... 170roD life 246 Timetl Pulae ...... Current me.lured lb)

o 0.02 0.04 Tlmell

(c)

v

Fiaure 10.5 Normal pulse polarography: (a) the form of the applied voltage; (b) the current during a pulse,' (c) the recorded polarogram 230 Introduction to electrochemistry

Delay v time (a)

2 4 6 Timels

Measure current (b) curren~Measure I: Ili.~ L _

o 0.02 0.04 Timels

Ii./ (c)

v

Figure 10.6 Differential pulse polarography: (a) the form of the applied voltage; (b) the current during a pulse; (c) the recorded polarogram Electroanalytical chemistry 231 appears at the end of the lifetime of the drop. The two currents that are measured are just before the pulse and in the last 10 ms of the pulse. The polarogram now records the difference between the two currents. Before any faradaic current is passed, and when the diffusion-limited current has been reached, these two currents will be equal (after all, what is an extra 100 m V when nothing is happening anyway?) and the difference will be zero. In the middle, when the current is rising rapidly, the extra 100 m V from the pulse does make a difference and this is recorded. The current difference is proportional to the amount of reactant and so calibration graphs may be prepared. The sensitivity of differential pulse polarography is in theory not as good as that of normal pulse but it has better resolution (just as differential polarography is better than normal polarography), being able to discrimi­ nate between species with £1/2 0.05 / n V apart. The detection limit is also improved now down to 10-8 mol dm-3 with some species even lower (e.g. AsIlI has been reported down to 4 x 10- 10 mol dm-3 or 300 ppt, which is not very much at all).

Square-wave polarography

Square-wave polarography (or, in general, square-wave voltammetry) is similar to differential pulse polarography but with a staircase chain of square waves (see Figure 10.7) that is applied during the lifetime of a single

/

v

/ / / / /

Time

Figure 10.7 Form of the voltage applied during square-wave polarography 232 Introduction to electrochemlstry drop. The chain is characterised by the square-wave amplitude, E. w • the increment of potential during each pulse. Es • and the frequency of the pulse. v. The current is sampled at the end of the forward pulse (If) and at the end of the reverse pulse (I,).

The value of Esw is chosen to be sufficiently large (> 0.015 / n V) to reverse the reaction on the reverse pulse, leading to a current that is opposite in sign. (Of course. if the process is totally irreversible. then no reverse current will be measured.) The output is also similar to that of differential pulse polarography in that a peak results by taking the difference between forward and reverse pulses. This is greater in magnitude than that from differential pulse polarography. because the two currents are usually different in sign. The most useful aspect of this technique is that it may be swept at much faster speeds than other pulse methods (up to 100 V S-I compared with 10 mV S-1 for conventional techniques). The forward and reverse currents may also be plotted separately. These look like cyclic voltammograms and have some diagnostic use - for example, in determining reversibility of a reaction.

70.2.4 AC polarography

In AC polarography the square-wave pulses of the preceding example are replaced by a small-amplitude (0.01 V), low-frequency (10-60 Hz) sine wave. The AC current alone is measured and the resulting polarogram is similar to the peaks of differential pulse polarography. The peak current is

2 ll2 Ip = (n P A w DI/2 dE c) /4 RT (10.12) where w is the frequency and dE the peak-to-peak amplitude of the AC voltage, and A is the area of the drop at its maximum size. The relationship between the current and the DC sweep voltage is

E = E II2 + 2 RT / n FIn [(Ip / 1)112 - ({Jp - I} / 1)1/2] (10.13) In AC polarography the charging current is 900 out of phase of the faradaic current and therefore the faradaic current can be measured independently. Even better is the use of second harmonics. The response of AC polarography to irreversible systems is much reduced but this is of use in analysis when possible interfering compounds have irreversible reactions. For example, AC polarography may be carried out in the presence of oxygen. speeding up analysis time through removing the need to deaerate the solution. Electroanalytical chemistry 233

70.2.5 Applications

Polarography has been the most widely used voltammetric method of analysis. Tens of thousands of papers on applications of the method have been published since Heyrovsky kicked off in 1922.

Practical considerations

Polarography requires the sample to be in solution. Thus, gases must dissolve, and solids, such as mineral samples, must be digested, before analysis. The volume of solution must be great enough to cover the electrodes and to ensure that during the measurement the bulk concentra­ tion of the analyte does not change appreciably. The analyte must be in solution with an excess of supporting electro­ lyte (added acid, potassium or sodium chloride, or other salts, or buffered) to ensure that diffusion is the sole transport mechanism and to keep the resistance of the solution low. For most polarographic methods the solu­ tion must also be free of oxygen. Otherwise, dissolved oxygen in the solution puts a big irreversible wave right in the middle of the polarogram (see Figure 10.8). Addition of complexing agents shifts the value of £1/2 (see above) and

(b)

0.4 o -0.4 -0.8 -1.2

Figure 10.8 Normal polarogram of0.1 mol dm-3 Hel solution: (a) saturated with nitrogen; (b) saturated with oxygen 234 IntroductIon fo e/ectrochemlsfry ______'m•• -----1."

---_.... ----­

-v

Figure 10.9 Estimation of the diffusion·limited current by extrapolation of the baseline

this may be a way of removing unwanted interfering species or of separat­ ing species whose uncomplexed £1/2 values are too close together. Theoretically the measurement of the diffusion-limited current should be an easy matter. However, on a sloping baseline with waves that nearly overlap this may not be quite so obvious. The residual current slopes upwards and so, for species with £1/2 values near the negative limit, an estimation must be made of where the baseline would be at the diffusion­ limited current. This is usually done by simple extrapolation, as shown in Figure 10.9.

QuantItatIve polarography

The magnitude of the diffusion-limited current must be related to the concentration of the analyte by some form of calibration. A calibration graph may be drawn from measurements made on a number of solutions each containing a different known amount of the analyte. Measurement of the diffusion current of an unknown sample then allows the concentration of the analyte to be read from the graph. This procedure requires the standard curve to be determined under exactly the same conditions as the unknown. The matrix of any other compounds must be identical, and the height of mercury must be maintained throughout the calibration and analysis, as must the capillary and temperature. A method that gets around the matrix problem IS that of standard Electroanalytical chemistry 235 addition. In this a small volume of solution containing analyte of known concentration is added to the sample. If the diffusion currents are Id,l before addition and I d ,2 after addition, and the amount added causes a change in concentration of analyte of L1c, then Id,l = k c

Id ,2 = k (c +L1c) (10.14) where c is the unknown concentration of analyte in the original solution. Therefore, if the two equations are divided, the constant k cancels (this assumes that the volume of standard does not perturb the concentration of analyte) and the expression may be rearranged to give c = L1c Id,l / (Id,2 - Id,l) (10.15) A series of additions may be made and a graph plotted of Id against L1c. The intercept on the x-axis is -c A variation of the standard addition method, in which known amounts of a different species are added, is the pilot-ion method. This is the polarographic example of the internal standard method. The ratio between the diffusion currents of the analyte (Id,a) and pilot ion (Id,p) is given by the Ilkovic equation: (10.16) If similar ions are chosen, the square root of the ratio of the diffusion coefficients will be near unity and, hence, the concentration of the un­ known analyte may be determined, Both pilot ion and standard addition do not require rigorous temperature control, as changes in temperature would be expected to affect each current in the ratio equally. Calibration curves are held to be the most accurate if they can be constructed, because the use of them makes no assumptions about linearity of response. See Problem 10.8.

Inorganic polarography

Polarography was first demonstrated for metal ions and these probably still make up the majority of uses. Table 10.1 gives some metal ions and their half-wave potentials. In addition, the following metals have been deter­ mined in some of their oxidation states: thallium, iron, cobalt, bismuth, antimony, tin, europium, molybdenum, tungsten, vanadium, manganese, chromium, titanium and platinum. Anodic polarography is limited by the oxidation of mercury. However, if mercury forms a salt with a particular anion, then a wave will be seen. Therefore, it is possible to analyse the halides, sulphide, selenide and telluride oxyanions, Examples of these are sulphite, bromate, iodate, periodate, polythionate, dichromate and the oxyanions of metals (e,g. molybdate), See Problem 10.6. 236 Introduction to electrochemistry

Table 10.1 Polarographic half-wave potentials of metal ions

Ion £1/1 versus SCE / V Electrolyte

Cu1 + +0.04 0.1 mol dm'.' KCI 4 Sn + -0.25 4 mol dm '.' NH 4 C1 / 1 mol dm".' HCI 1 Sn + -0.52 4 mol dm' NH4 C1 /1 mol dm-.' HCl H Pb -0.40 0.1 mol dm-3 KCl Pb2 + -0.50 0.5 mol dm-3 Na tartrate (pH 9) Pb2 + -0.76 1 mol dm-3 NaOH (Pb(OH»)) Cd2+ -0.60 0.1 mol dm-3 KCl Zn2+ -1.00 0.1 mol dm-3 KCl Zn2+ -1.15 0.5 mol dm- 3 Na tartrate (pH 9) Zn2+ -1.53 1 mol dm-3 NaOH Nj2+ -1.10 0.01 mol dm -3 KCl Mn H -1.51 1 mol dm-3 KCl

Oxygen, although an interferent in polarography, can be determined quite accurately by this method. See Problem 10.4.

Organic polarography

Several functional groups can be oxidised or reduced at a OME, and so compounds containing these groups can be analysed by polarography. The available potential range means that carbon single bonds are not accessible unless highly activated, as with C-CI, conjugated and C-C and C-O next to carbonyl. Nitrogen-, oxygen- and sulphur-containing molecules and those with a high degree of unsaturation (lots of double bonds) can be reduced. Only strong reducing agents, such as aldehydes, and hydro­ quinones may be oxidised at a OME before mercury itself is oxidised. Non-aqueous solvents (e.g. acetonitrile, DMSO, DMF) may be employed to overcome problems of solubility in water. The support­ ing electrolyte is then usually an alkylammonium salt, such as tetra-t­ butylammonium tetrafluoroborate. Polarography h'as been used to determine naturally occurring and artificial substances in the environment. The insecticide DOT gives a good wave at -0.9 V in 96% ethanol containing lithium metal. Ascorbic acid (vitamin C) is reduced polarographically in an acetate buffer, and so may be analysed in fruit and vegetables. Electroanalytical chemistry 237 70.3 Voltammetry

70.3. 7 Linear sweep and cyclic voltammetry

Linear sweep voltammetry (LSV) and cyclic voltammetry (CV) are distin­ guished from polarography by the use of solid electrodes and much greater sweep rates. The state of the electrode is now much more intrusive and the form of the voltammetric wave more complex (see Chapter 7). For this reason polarography still holds sway when it comes to quantitative voltam­ metry. This may change for two reasons. First, the speed of LSV and the availability of microcomputers that can perform data analysis on the volt­ ammogram should remove the complexity from the method. Second, the possibilities for miniaturisation of electrodes will encourage the design of small, portable instruments that should supersede the more traditional methods. Speed is useful when dealing with inorganic complexes whose kinetics are fast. It is possible to obtain both thermodynamic (e.g. £1Iz) and kinetic information very quickly. Differentiation of the voltammogram has been used to give accurate formal electrode potentials. Figure 10.10 shows the

cyclic voltammogram of the complex Ru[bipylz[phenhqMezl (PF6 )z. The structure of the ligands is shown in the figure. The five peaks are split into a group of two, in which first ruthenium(II) is oxidised to ruthenium(III) and

20

10 0 ~ 'i -10 '"

-20

-30 Mea

-40

-2 -1 0 VN

Figure 10.10 Cyclic voltammogram of a ruthenium complex 238 Introduction to e/ectrochemlstry then the ligand [phenhqMe~] is oxidised. Returning in the negative direc­ tion, the three ligands are reduced, although we are not sure which are the two peaks as [bipy] + e - [bipy]-' and which is the peak due to the reduction of [phenhqMe~]. Cyclic voltammetry has been used when small electrodes are necess­ ary. Ascorbic acid has been monitored in the brain of a rat, using a carbon paste electrode. Ascorbic acid is oxidised at +0.4 V against silver-silver chloride.

70.3.2 Stripping voltammetry

Stripping voltammetry is one of the most sensitive analytical techniques, routinely determining metals at ppb or even ppt levels. Stripping voltam­ metry starts where polarography leaves off. Consider the analysis of a metal. In polarography we do not consider where the metal goes to in the mercury amalgam. Over some time, presumably quite a bit builds up in it. In fact, after a while, there must be a higher concentration in the mercury than outside in the solution. More so if, instead of knocking it off, we kept the same drop all the time (Le. used a hanging mercury drop HMDE). Suppose, then, having run the reduction of the metal for some time, we reversed the potential and swept it anodically. At some potential all the metal in the amalgam would be oxidised and a peak would result. The reduction step now is seen as a way of concentrating the metal prior to analysis. I have just described anodic stripping voltammetry. There is a catho­ dic version in which an initial oxidation concentrates the analyte at the electrode, to be followed by a cathodic sweep in which it is reduced. The apparatus is relatively simple and the method may be made portable. Stripping voltammetry has been shown to be particularly effective in the analysis of trace metals in water (in tap-water lead is a few ppb, and zinc and copper are tens to hundreds of ppb). Lead in blood (about 200 ppb) may be analysed after pretreatment with acid.

Anodlc stripping voltammetry

Anodic stripping voltammetry is usually carried out at a mercury electrode. This may be a hanging drop or, for better sensitivity, at a mercury film electrode (MFE). For the latter a carbon electrode is used in the analyte solution, to which 1O-~-1O-4 mol dm-3 Hgll nitrate is added. During the electrodeposition step mercury is codeposited with other metals and forms an amalgam film about 10 nm thick. Solid metal electrodes of platinum, silver or carbon have been used, particularly for metals that cannot be determined at mercury, such as silver, gold and mercury itself, but the Electroanalytical chemistry 239

I TimeJmin 10 10 TimeJs 100 0,..------+,-----1 I ------r---I II II Ed 1------I I I I I I I I I I I Anodic Rest I Pre-electrolysis period I I I

t Stirrer off

Figure 10.11 Progress of an anodic stripping voltammetry experiment, showing the imposed voltage (upper curve) and current response (lower curve) surface of a metal is not easily reproducible and results are not as good as with the MFE. Polymer-modified electrodes that can accumulate a metal ion have also been used. The form of the applied voltage and the resulting current with time are shown in Figure 10.11. It is not necessary to run the preliminary electrodeposition step until all the metals have been deposited at the electrode. As long as the calibra­ tion and analysis are done under the same conditions of stirring, time, temperature and voltage, then accurate results can be obtained. Having said this, the longer the deposition is continued the greater will be the stripping peak. Typical times used with normal sweep voltammetry are: 240 Introduction to electrochemistry

Cu

-0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 o VIV vs SCE

2 Figure 10.12 Stripping voltammogram of a solution containing Cu + (20 ppb), Pb2+ (30 ppb) and Bj2+ (100 ppb). Deposition time, 5 min at -1.0 V. Stripping scan rate, 20 mV S-l

7 3 8 3 5 min for solutions containing 10- mol dm- ; 20 min for 10- mol dm- ; 10 3 and 1 h for 10- mol dm- • The deposition potential is chosen to be at least 0.2 V more negative than the equilibrium potential for the metal. The solu­ tion is stirred during the deposition step. There follows a period of about 30 s without stirring, to give the electrode a rest. (In fact it is to allow the solution to settle down so that the background current during stripping is as low as possible.) The stripping step is done in a conventional polarographic way with a linear sweep going in the positive direction. Peaks are seen as the different metals are oxidised from the mercury film. As with polarography, at the DME the positive limit is when the mercury itself succumbs. Pulse and differential pulse voltammetry give added sensitivity during stripping, thus lowering the detection limit even further (Figure 10.12). It is seen that copper and bismuth overlap considerably and, to add to the problem, they do so on a rising baseline. However, chemometric methods of multivariate analysis can calibrate solutions even when the voltammo­ grams are as poor as the one shown. Voltammetry at a thin-layer electrode shows a linear dependence of the peak current on the sweep rate and not, as with bulk electrodes, on the Electroanalytical chemistry 241 square root of the sweep rate. The precision of stripping voltammetry is 9 typically a few per cent at concentrations above 10- mol dm -3, rising to a 10 few tens per cent at 10- mol dm -3.

Cathodic stripping voltammetry

Anodic stripping voltammetry at an MFE relies on the ability of a metal ion to be reduced to the metal and form an amalgam with mercury, thus limiting the techniques to elements such as copper, cadmium, zinc, lead, indium and bismuth. However, the idea of stripping voltammetry merely requires accumulation at the electrode of a species that can subsequently be removed. It is, therefore, possible to determine anions that are oxidis­ able, if a way of sticking them to an electrode can be found. This is done via insoluble salts of metals such as mercury and silver. Thus, halide ions form insoluble halides of mercury and silver by oxidation of the metal in a solution containing those ions. For example, Ag(s) + I-(aq) ~ AgI(s) + e. The reaction can be reversed in a subsequent negative sweep. Other anions that can be determined by CSV are sulphide, phosphate, arsenate and arsenite.

70.3.3 Gas sensors

Clark oxygen probe

The Clark oxygen electrode is a type of voltammetric device in which the oxygen reduction current is measured at a fixed voltage under conditions of diffusion control. The electrodes and electrolyte of the probe are separated from the outside world by a thin membrane. This is similar to the construc­ tion of potentiometric probes discussed above. Typically, the cathode is silver or platinum and the anode is silver or silver-silver chloride (Figure 10.13). The currents are small and so a two-electrode design suffices, although if a third reference electrode is used, there is an improvement in the accuracy. A voltage on the plateau of the voltammetric wave is chosen (about -0.6 V versus SCE), to minimise variation in the current due to voltage fluctuations and also to maximise the magnitude of the current. The probe is constructed to minimise the volume of the electrolyte and thus maximise the sensitivity of the determination. During operation all the oxygen is reduced in the electrolyte and a diffusion-limited current is established through the membrane. Voltammetric sensors for hydrogen, sulphur dioxide, chlorine and oxides of nitrogen have also been reported. 242 Introduction to electrochemistry

Port for refilling electrolyte Lead anode- Potassium hydroxide solution Silver anode Saturated potassium chloride

'0' ring Platinum cathode Silver tip (cathode) '0' ring Membrane

(a) (b)

Figure 10.13 Design of oxygen sensing probes: (a) Clark voltammetric sensor; (b) galvanic sensor

Galvanic oxygen sensors

Strictly speaking, what I am about to describe is not a voltammetric sensor, as no voltage is applied, but there is nowhere else convenient to stick this bit, so here it is. In the Hersch cell oxygen is reduced at a silver electrode and lead is oxidised to PbO;- in alkaline electrolyte.

Cathode: 1/2 O2 + H20 + 2 e _ 2 OH-

Anode: Pb + 4 OH- - PbO;- + 2 H20 + 2 e

Cell: Pb + 1/2 O2 + 2 OH- - PbO;- + 2 H20 (10.17) No voltage is needed, as the overall reaction is thermodynamically spon­ taneous and, indeed, is kinetically fast enough. As before, the current is a measure of oxygen concentration.

Enzyme sensors

If an enzyme produces or consumes a gas, particularly oxygen, then one of the above sensors could be used to detect changes in concentration of the gas and, hence, the enzyme substrate. Electroanalytical chemistry 243

70.3.4 Detectors for liquid chromatography

Voltammetric detection in high-performance liquid chromatography and ion chromatography depends on the possibility of oxidising or reducing the analyte in question. A thin-layer or tubular cell is used, with the reference and auxiliary electrodes downstream from the working electrode. The working electrode is usually carbon paste or glassy carbon, which may form the body of a flow-through tubular cell or be a microdisk in a thin-layer cell. The use of microelectrodes does not require the addition of support­ ing electrolyte or reference electrode, and, with the measurement of small (nA to pA) currents becoming routine, amperometric detection (as it is also called) is a powerful method for many organic compounds, such as alkaloids, antibiotics, vitamins and some proteins.

10.4 Amperometric titrations

70.4. 7 Titrations with one polarised electrode

Titrations in which the concentration of one or more of the products or reactants is monitored by the current passed at a given applied voltage are known as amperometric. It would be easier for you and the rest of us if they were called voltammetric (for this is what they really are), but ampero­ metric is what they are and I suppose what they will stay. Figure 1O.14(a) shows the progress of different amperometric titra­ tions. Ifsulphuric acid is added to lead nitrate in nitric acid, a precipitate of lead sulphate is formed. The concentration of lead is monitored at a HMDE set at a potential on the plateau of the lead polarogram. The current falls as sulphuric acid is added until the end point is reached, when it levels off at the low background current. Because mercury is a poor electrocatalyst for the evolution of hydrogen, there is no interference due to the discharge of protons. Figure 10. 14(b) shows the case of the addition of an electroactive titrant such as barium sulphate to an inactive solution such as sulphuric acid. Now at the end point a rise in current is seen from the reduction of barium ions. A titration may still be accomplished when both ions are reduced at the potential chosen. A V-shaped curve results, with a minimum at the end point when neither active ion is present. Thus, in Figure 1O.14(c) the titration of lead with dichromate ion shows the fall in diffusion current of lead ions before the end point and the rise in current due to dichromate after the end point. For accurate analysis the dilution of the solution due to the addition of the titrant must be allowed for. 244 Introduction to electrochemistry

Added reagent Solute C C ...l!! CD... ;:, :; u u 0 L (a) Applied voltage Volume of reagent

Solute C C ~ ...l!? ;:, ;:, u u 0 (b) Applied voltage Volume of reagent

I I I I I I II ------,-II--t---- (c) I I Applied voltage Volume of reagent

Figure 10.14 Amperometric titration curves (left) and polarograms of solute and added reagent (right) for: (a) titration of lead nitrate with sulphuric acid; (b) titration ofsodium sulphate with barium nitrate; (c) titration of lead nitrate with potassium dichromate

70.4.2 Titrations with two polarised electrodes

This technique was first reported before 1900, but it was 50 years before the theory caught up with this interesting but marginal practice. The apparatus is simplicity itself - just two similar electrodes with a small (50 mY) voltage difference between them, and an ammeter to measure the current flowing. The shape of the titration curve depends on the reversi­ bility of the titrant and titrate. Consider the case of a reversible titrate and irreversible titrant - for example, the titration of iodine, which is reversi­ ble, by thiosulphate, which is not. Before the start there is only iodine Electroanalytlcal chemistry 245

End point

Volume of titrant added

Figure 10.15 The course of a dead stop titration between a reversible titrate and irreversible titrant present in the solution, so, although there is plenty of material for the cathodic process (12 + 2 e ~ 2 1-), there is no iodide for the anode to work on. No current flows. As the titration takes its course, iodide is formed and now current flows, reaching a maximum at the half-way point of the titration when there are equal amounts of iodine and iodide (remember the sulphur species do not contribute to the current). By the end point, when all the iodine has been converted to iodide, the current has again reached zero for lack of a species for the anodic reaction. No matter how much extra thiosulphate is added, the current remains at zero. Figure 10.15 shows the current during the titration and why this type of analysis is known as a dead stop titration.

10.5 Coulometry and electrogravimetry

Analytical methods that rely on a measure of the quantity of electricity that is passed during electrolysis come under these headings. In coulometric analysis the charge passed is obtained from integration of the current with time, while in electrogravimetry the amount of material deposited is deter­ mined by direct weighing. The methods are characterised by high accuracy 246 Introduction to electrochemistry and relative simplicity of instrumentation. Coulometric analysis may be done under conditions of constant current (galvanostatic or amperostatic) or constant potential (potentiostatic).

70.5. 7 Potentiostatic coulometric analysis

The requirements to enable a substance to be analysed coulometrically are: the reaction must be of known stoichiometry; it must proceed with 100% current efficiency; and there must be no side-reactions that consume cur­ rent. The current passed following the application of a potential to a system is shown in Figure 10.16. The current decays exponentially as the electroactive substance is consumed:

Time

Figure 10.16 The current passed during a constant-current coulometric experiment

It = 10 exp(-p t) (10.18) The charge passed after time t (Qt) is

Qt = f: It dt = Q.,(l - exp[- pt]) (10.19)

= 10 / P - It / P (10.20) Electroanalytical chemistry 247 where p is a constant, and Q~ is the charge passed after t = 00, i.e. when all the material that is electroactive at the potential chosen has been con­ sumed. By Faraday's Law Q~ is equal to the number of electrons times the Faraday times the volume of the electrolyte times the concentration, i.e. n FV c. The advantage of this and all coulometric methods is that the amount of substance is directly related to the charge passed through constants that are known (n and F). No standardisation or calibration is needed. With a mercury cathode a block of elements in the periodic table may be deposited, ranging from chromium to selenium in period 4, molybde­ num to tellurium in period 5 and rhenium to polonium in period 6, the lanthanides and the actinides. Some are not quantitatively deposited but are quantitatively removed from solution. See Problem 10.5. There are many other reactions that have been used in coulometric analysis. For example, halides at a silver anode, the oxidation of hydrazine to nitrogen, the reduction of aromatic nitro compounds, the oxidation of ascorbic acid and the reduction of DDT.

Electrochemical separation

Careful choice of the potential may allow the deposition of one metal in the presence of another, thus separating two metals in a solution. For a two-electron process the equilibrium potential shifts by only 30 mV per tenfold change in concentration (at 25 cC, give or take) so in principle it should be possible to reduce the concentration of one metal in the presence of another. Suppose you have two metals: What is the minimum difference in their electrode potentials to achieve separation? If complete separation is taken as the removal of 99.9%, this represents three orders of magnitude change and so the deposition potential of the deposited metal El should be less than E; - 0.18/ n\> where E; is the formal electrode potential. If this is in the presence of another metal that you do not want to deposit, then E should be greater than E~ + 0.18/ nz. Therefore, E~ - E; = 0.18 (1 / n l + 1/ nz) (10.21) Addition of complexing agents may help to move apart two metals whose formal electrode potentials in a non-complexing solution are within the limits given by Equation (10.21).

70.5.2 Galvanostatic coulometric analysis

It is possible to conduct a coulometric analysis at constant current. Careful watch on the potential needs to be kept, to avoid it shooting off to some 248 Introduction to electrochemistry region where the wrong electrochemistry happens, in its desperate attempt to maintain the constant current. The main use for galvanostatic (also known as amperostatic) coulometry is in coulometric titrations.

Coulometric titrations

In a coulometric titration the reagent is electrochemically generated in situ from a suitable non-reacting precursor. The end point is detected in the usual way, after which the amount of reagent generated is obtained from the charge passed and Faraday's Law. For example, a base may be titrated by protons generated from water, or arsenic(III) may be titrated with bromine generated from bromide ion added to the analyte. The reaction is usually performed at constant current with the generator operated for small times near the end point. (This is the equivalent of adding titrant drop by drop.) The charge passed is determined from the cumulative current times time or by a silver coulometer in series with the titration cell. The method has many advantages over traditional titrations. There is no standardisation required. Unstable reagents may be generated and used immediately without fear of them going off. The amounts added near the end point may be made almost arbitrarily small by reducing the current or time of each addition. There is no dilution of the titrant as only electrons are added or removed from the system. Table 10.2 gives some examples of coulometric titrations.

Table 10.2 Examples of coulometric titrations. The analyte reacts with the reagent that is electrochemically generated from the precursor Analyte Reagent Precursor OH- As(III), SO;- As(III), Sb(III), U(IV), r, SCN-, NH20H, phenol, aniline, mustard gas Br2 Br­ 1­ As(III), S20;-, H2S 12 Fe(II), Ti(III), U(IV), hydroquinone Ce3+ Ce4+ Mercaptans, Cl-, Br-, 1- Ag+ Ag H+ OH­ H 20 MnOi, Cr(VI), Br2, Cl2 Fe2+ Fe3+ Cr(VI), Br2, V(V) Cu+ Cu2+

70.5.3 Electrogravimetry

Electrogravimetry is analysis by coulometry in which a deposit is weighed. This is primarily used for the analysis of metals that can be deposited on a platinum or other suitable electrode. An advantage is that the measure- Electroanalytlcal chemistry 249 ment is of the amount of charge passed in depositing the metal in question. Any current consumed in side-reactions is of no importance as long as it does not interfere with the deposition. This allows constant current deposi­ tion, and if the potential falls to give hydrogen evolution, then this is not disastrous, as it would be in normal coulometry, as long as the hydrogen evolution does not interfere with the metal deposition. Silver and copper are excellently determined by gravimetry. In fact the silver coulometer, a cell in which silver is plated from silver cyanide solution, placed in series with the electrochemical cell was a common method of measuring the charge passed. Determination of the value of the Faraday has been done by coulometry, by dissolution of silver and by coulometric titration.

• PROBLEMS

10.1 Current data from a polarography experiment at 25 °C are given below. Determine the half-wave potential and the number of electrons involved in the reaction.

Voltage against SCE /V Current /!-tA -0.2 0.00 -0.3 0.01 -0.33 0.07 -0.36 0.61 -0.39 2.38 -0.41 3.13 -0.42 3.27 -0.43 3.34 -0.45 3.39 -0.5 3.40 -0.6 3.40

10.2 If the smallest current that a particular polarograph can measure is 0.1 2 !-tA, estimate the lowest concentration of a metal ion M + that can be detected. Take D = 1 X 10-9 m2 S-I, the rate at which the mercury drops are formed as 2 mg S-1 and the lifetime of the drop as 5 s.

10.3 Derive the relation between the half-wave potential and the standard electrode potential.

10.4 If the limiting current for the first oxygen wave (-0.05 V) in a polarogram of aerated 0.1 mol dm-3 KCI solution was 3.30 !-tA, calculate the 5 concentration of oxygen in the solution in ppm. Take D = 2.1 X 10- 2 cm S-1 and the flow and drop time of the mercury from Problem 10.2.

10.5 The current readings shown below were taken in a coulometric experiment to determine the amount of copper in a solution of copper(II) 250 Introduction to electrochemistry

sulphate. Plot a suitable graph and determine the quantity of copper in the original solution.

Time Imin Current I A 1 3.1 4 2.6 7 1.25 10 0.31 13 0.08 15 0.03

10.6 In a neutral solution of 10-4 mol dm-3 bromide polarographic waves are seen at +0.11 V and +0.50 V versus SCE irrespective of the other ions present. Explain.

10.7 Derive Equation (10.11), clearly stating any assumptions you make. The data below give the half-wave potential for the discharge of a divalent metal ion at different concentrations of added ligand. Determine the stoichiometry of the complex and K f •

3 Cligand Imol dm- £1/2 N 0.0 -0.410 0.03 -0.448 0.08 -0.472 0.12 -0.488 0.32 -0.511 0.48 -0.52

10.8 Sketch the shape expected for a DC polarographic wave for a cadmium sample for which the half-wave potential is -0.6 V and the diffusion current is 2.4 !AA. What is the concentration of cadmium in the sample if it is known that a cadmium sample of 10.0 ppm concentration gives a diffusion current of 5.6 !AA?

• ANSWERS

10.1 First draw the polarogram and determine the half-wave potential and the diffusion-limited current. £1/2 = -0.38 V and Id = 3.4 !AA. Then, using Equation (10.6), we can construct the function In [(Id - 1) I I]:

Voltage against SCE I V Current I!AA In [(Id - 1) I I] -0.2 0.00 14.179 -0.3 0.01 6.270 -0.33 0.07 3.898 -0.36 0.61 1.524 -0.39 2.38 -0.850 -0.41 3.13 -2.443 Electroanalytlcal chemistry 251

4 r------..., 15

10 3

5 1 E ::::. ~ 2 I ::> ~ U 0 .E

-5

O~___4II__--_=~-...l----L----..1.----J-10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -VoltagelV

Figure 10.17 Polarogram and plot to determine E 1I2 and n for a reversible reaction

-0.42 3.27 -3.207 -0.43 3.34 -4.068 -0.45 3.39 -5.511 -0.5 3.40 -0.6 3.40

Plotting In [(Id - I) / I] against the voltage gives a straight line of slope n F / R T. The graph in Figure 10.17 has a slope of 79.1 V-I. F / RT = 38.95 at 298 K, which leads to n = 2 (2.03, I make it, but of course you cannot have 0.03 of an electron!).

10.2 Using the I1kovich equation (10.9) without correction (this is only an 116 estimate anyway), 0.1 = 708 x 2 x (1 X 10-5)112 x 22/3 X 5 X co, which 5 3 gives Co = 0.0108 mmol dm-3or about 1 x 10- mol dm- , which is indeed the limit of conventional polarography.

10.3 Equation (10.7) defines £112' so it is just a matter of going from the formal electrode potential to the standard electrode potential by Equation (4.58):

£112 = ee + RT / n Fin (YR / 1'0) + RT / n Fin (DR / DO )ll2 10.4 This is another I1kovich equation. The two waves in the polarogram of oxygen are each of two-electron processes, so n = 2. From the I1kovich 252 Introduction to electrochemistry

3 equation we calculate Co = 0.244 mmol dm- • The molecular weight of oxygen is 32 so the concentration in ppm is 7.8.

10.5 The current decays exponentially, so plot In (1) against t:

Time Imin Current I A In (1 I A) 1 3.1 1.131 4 2.6 0.955 7 1.25 0.223 10 0.31 -1.17 13 0.08 -2.52 15 0.03 -3.50 4...------,

3

2

<~ 0 E

-1

-2

-3

-4 0 5 10 15 20 Timelmin

Figure 10.18 Determination of Q~ from coulometric deposition of copper

The line is straight only once the reaction has got into its stride. One problem early on is that high currents should flow but cannot. By Q~, Equation (10.20) the charge passed after an infinite time, is 10 I p. The intercept of the line In (10) = 3.476 and the slope -p = -0.464 min-I. Thus, Q~ = 4178 C (don't forget to multiply by 601), which at 96500 C mol-I leads to an answer of 2.75 g.

10.6 Bromide reacts with the mercury at 0.11 V; thus,

2 Hg + 2 Br- - HgzBrz + 2 e Bec"oQnQ/~/cQlchem~t~ 253

The wave at +0.5 V is the anodic limit at which mercury is oxidised: 2 Hg-+ H~+ + 2 e 10.7 Starting with the definition of £112 (Equation 10.7), we need to consider the change in formal electrode potential going from free metal ion to complex. This is given in Equations (4.38) and (4.39) in terms of activities. Assuming the activity coefficients will cancel leads to Equation (10.11). From the equation we need to plot £1Iz(complex) - £112 against In (Cligand) (Figure 10.19):

3 Cligand Imol dm- £112 IV £1/2(complex) - £1/2 IV 0.00 -0.410 -0.000 0.03 -1.523 -0.448 -0.038 0.08 -1.097 -0.472 -0.062 0.12 -0.921 -0.488 -0.078 0.32 -0.495 -0.511 -0.101 0.48 -0.319 -0.520 -0.110

The slope is -0.0606 V and the intercept -0.1305 V. Multiplying -0.0606 by -2 FIR T gives q = 2.049, i.e. the complex has the formula MLz; while multiplying the intercept by 2 FIR T gives In (Kf) and Kf = 2.59 x Hr.

10.8 As the diffusion current is directly proportional to the concentration, the concentration of the unknown is simply 10.0 x 2.4 I 5.6 = 4.29 ppm.

-0.03

-0.04

-0.05 > :::.. -0.06

JQ. E ~ -0.07

l:! Iii -0.08

l:! -0.09 Iii

-0.1

-0.11

-0.12 -2 -1.5 -1 -0.5 o log (Ctlgond)

Figure 10.19 Ligand stoichiometry from the shift in E 1/2 on complexation 77 Electrochemical synthesis

11. 7 Introduction

All electrochemical reactions synthesise something, but up to now this has not been a facet of the process that we have been interested in. We have looked in detail at the minutiae of electrochemical cells and the electron transfer that occurs and we have seen how the different techniques of electrochemistry are used to discover what and how much of different chemical stuff is present. Now we turn our attention to how to make something of practical use. The subject started with the earliest researches of Faraday, Daniell and cohorts. The big industrial processes of the chlor-alkali process and aluminium extraction soon appeared and these will be reviewed in the next chapter. However, the use of electrochemistry to effect transformation went largely uncared for until recent years when some of the obvious benefits (a high level of control, no contaminating reagents, etc.) have forced their way into the addled consciousnesses of organic and inorganic chemists. Now one of the growth areas in electrochemical synthesis is the creation of weird and wonderful oxidation states in inorganic compounds, and highly specific (stereo-, regio-, chemo-) organic compounds. The scope of electrochemical synthesis divides into large- and small­ scale syntheses, and into inorganic and organic syntheses. Recently (in the latter half of the twentieth century) there has been a shift of emphasis away from large-scale industrial electrochemical processes to the search for high-added-value speciality chemicals. This does not mean that the world's aluminium, chlorine and caustic will not continue to be produced electro­ chemically, but the economics of electrochemical synthesis on a commercial scale mean that there has to be a reasonable profit in what is being produced. Therefore, new processes that are coming on-stream are likely to be giving from 1 to 10 000 tonnes of the product. At the very small end, laboratory electrochemical syntheses are being investigated to provide unique routes to compounds.

254 Electrochemical synthesis 255

Victor Frankenstein: An early bioelectrochemist

When Mary Shelley wrote the novel Frankenstein, or, the Modern Prometheus, she was drawing on much of the current (1817) thinking on what made living things live. There had been many experiments on 'galvanism' following the observation that wires from an electric pile (battery) could cause the leg of a frog to twitch when applied to the nerve. Giovanni Aldini, the nephew of Galvani, had experimented on corpses in 1803 and 1804. In 1803 he obtained the body of the hanged English murderer Forster about an hour after his death. He subjected the corpse to the 'precise effects of galvanism with a voltaic column of one hundred and twenty copper and zinc couples'. It was then almost common practice for scientists to try electrifying dead animals and people. Earlier in France, at the height of the Terror, when guillotined aristocracy were readily available, the physician F. X. Bichat experimented with bodies in an attempt to revitalise them. Mary Shelley was quite well versed in the science of the day, and starts the preface to Frankenstein with 'The event on which this fiction is founded has been supposed by Dr Darwin, ... , as not of impossible occurrence.' It was some time later that the relationship between electrochemistry and biological systems was fully researched, but the imagination of Shelley's readership was stirred by the vision of the monster being brought to life by a bolt of lightning. It also firmly anchored the idea of the mad scientist.

71.2 Experimental methods

77.2. 7 General considerations

In electroanalytical chemistry and mechanistic electrochemistry in general, it is usually desirable to change as little of the electrolyte or electrodes as possible. Micro- or ultramicroelectrodes are used to accomplish this. In order to most efficiently use the reactants and produce reasonable amounts of products in a short time, in electrochemical synthesis it is desirable to react as much of the available material as possible. This is done by having large electrodes that take up a great fraction of the volume of the cell. The nature of each electrode reaction must be assessed and, if necessary, a separator is planned. If a supporting electrolyte is required, it must not interfere with the reaction but must dissolve in the solvent used. This is particularly at issue in organic synthesis. The product must be able to be recovered. Gases evolve easily but products that dissolve in the electrolyte may then be available for further, unwanted electrochemistry. 256 IntroductIon to electrochemlstry

77.2.2 Electrodes

I have remarked that the electrodes must occupy a large part of the volume of the cell. If reasonable amounts of material are to be synthesised, the current distribution about the electrode is important. There is no point in having ten square metres of electrode area if, practically, only one square metre is used. Electrodes may be sheets of metal arranged in a mono- or bipolar fashion (see Chapter 12), or may be compacted porous powders, or even loose particles, as in a fluidised bed electrode. If the electrode does not actually take part in the reaction or even act in a catalytic manner, then the choice of electrode will focus on its conductivity and its resistance to corrosion in the proposed electrolyte. For a commercial synthesis the cost of the electrode will also be a consideration. The most generally used electrode materials are lead, platinum and carbon. Lead dioxide is suitable for oxidations, as it is stable in acid and alkaline solutions and has a reasonable conductivity (2 x 106 S m-I). Lead dioxide is electroplated from an aqueous solution of lead nitrate on to an iron, steel or graphite anode:

2 Pb + + 2 H 20 -+ Pb02 + 4 H+ + 2 e (11.1) To avoid the accumulation of acid, lead(II) oxide or copper carbonate is added to control the pH, and a suitable temperature for this process is 50 QC. Reference electrodes are used in laboratory-scale syntheses when careful control of potential is desirable. The saturated calomel electrode is popular for many applications, even in non-aqueous media, when the liquid junction potential that is set up between the liquid phases is con­ veniently ignored. Ifabsolute dryness is required, a non-aqueous reference electrode is used, such as silver wire in 0.1 mol dm-3 silver nitrate dissolved in acetonitrile. A calomel electrode may also be used with a non-aqueous salt bridge employing a tetraalkylammonium salt as electrolyte.

77.2.3 Cells

There are many designs of cells for electrochemical synthesis. Laboratory­ scale apparatus is usually of glass and is constructed to accommodate the particular requirements of the given synthesis (whether a separator is required, or a flow cell, or whatever). A cheap and cheerful batch reactor is shown in Figure 11.1. The anode and cathode compartments are sepa­ rated by a glass frit and the electrolyte is stirred and thermostatted. The extent of the electrolysis may be followed by monitoring the current passed (as long as there is some confidence about the current efficiency), by withdrawing small aliquots for analysis, or by having a set of microelec­ trodes in the cell at which voltammetry or other electroanalytical tech­ niques may be performed. For reasonable yield a flow-through cell is Electrochemical synthesis 257

Counter electrode

Reference electrode -+--+-... Diaphragm

Thermostatted water jacket

Working Luggin electrode capillary

Figure 11.1 A two-compartment glass cell for small-scale batch electrosynthesis

employed. These may also be made from glass, or a more sophisticated 'filter press' design may be made from more durable materials. These consist of a series of electrodes, gaskets and separators that are screwed together. The electrodes are connected in series to give a number of cells through which electrolyte flows. The design has the advantage of optimis­ ing the useful electrode area, current and voltage, and its modular design allows the stack to be expanded or contracted as required. These are used in industrial-scale electrolysers and are described in the next chapter (see Figure 12.4). In contrast to two-dimensional electrodes, a much greater conversion per amount of electrode material is possible if the electrodes may be made three-dimensional. This is done by the use of porous electrodes for gaseous reactions, by packed bed electrodes or by fluidised bed electrodes. The electrode material is in the form of beads or coarse powder, and is packed if the flow of electrolyte is down and is fluidised if the flow is upwards. A I 258 Introduction to electrochemistry

,----=~.~==~Electrolyte .,..~"...-n' Reference in electrode

Diaphragm

Luggin capillary Mesh contact

Packed bed electrode Cylindrical counter electrode

Electrolyte Iout

Figure 11.2 A packed bed cell for electrosynthesis packed bed cell is shown in Figure 11.2. The design should be compared with fluidised bed cells shown in the next chapter (Figure 12.2).

77.2.4 Electrolytes and solvents

ElectfOchemistry has traditionally been done in water and this has also been the case with electrochemical synthesis. However, water has its limitations. Aqueous solutions are thermodynamically stable only between 0.0 V and 1.23 V (against SHE) although practically this limit may be widened by the use of electrodes at which the kinetics of oxygen or Electrochemical synthesis 259

Table 11.1 Useful potential ranges for solvents and electrolytes used in organic electTOchemistry Solvent Electrolyte Cathodic limit Anodic limit against SCE /V against SCE /V

CH3COOH CH3COONa -1.0 +2.0 CH3CN LiClO4 -3.0 +2.5

CH3CN (CZH5)4N BF4 -1.8 +3.2

(CH3)zSO LiClO4 -3.4 +1.3

Dimethylformamide LiClO4 -2.8 +1.6

Tetrahydrofuran LiClO4 -3.2 +1.6 hydrogen evolution is unfavourable (e.g. mercury will not evolve much hydrogen above -0.9 V). Many organic compounds do not dissolve in or are not miscible with water. Water is also a nucleophile and will be a willing reactant with radicals and ions generated in the course of a reaction. While this may be desirable for some reactions, for many it will not. A variety of organic solvents have been assayed for electrochemical syn­ thesis, but non-aqueous solvents also have their drawbacks. Because of their tendency to be of low polarity and low relative permittivity, their ability to dissolve electrolytes as ions is somewhat limited. This leads to high-resistance electrolytes, which is a highly undesirable condition. The available solvent and electrolyte systems are considerably more expensive than aqueous systems, a factor to be considered at all scales. Table 11.1 gives some solvents and suitable electrolytes and the potential range in which they are stable.

77.2.5 Potential or current control

When setting up a cell, the chemist has the choice of passing a known current through the cell, applying a known voltage to the cell or applying a known voltage to the working electrode. The first two do not need the paraphernalia of reference electrode and potentiostat but lose some con­ trol in the process. Especially with galvanostatic control, the cell potential may shift in an attempt to satisfy the current, thus causing unwanted reactions of the reactants, products or electrolyte. Constant current does, however, set the amount of product formed in a given time and is ex­ perimentally easy to arrange. Therefore, the tendency is only to use a potentiostat and reference electrode if there is a real danger of unwanted side-reactions. 260 Introduction to electrochemlstry

11.3 Mechanistic aspects

Chemical reactions may be considered to be driven by differences in the polarity of the reaction sites. In organic chemistry we talk of nucleophilic and electrophilic reactions. However, in target syntheses the required reaction may be between reactants of similar polarity. Electrochemistry may come to the rescue by changing the polarity of a reactant by oxidation or reduction. A neutral molecule may have electrons pumped in or out: (11.2)

77.3. 7 Adsorption and catalysis

Whether or not a reactant or intermediate adsorbs at an electrode may dictate the course of an electrochemical synthesis. The potential range used may introduce adsorbed species. For example, hydrogen atoms will be formed at an electrode as the potential becomes more cathodic in an aqueous electrolyte. These may be a hindrance or may be turned to advantage in synthesis (see subsection 11.4.2). The ability of an electrode to catalyse the required reaction selectively is also important. We shall see in the next chapter that ruthenium dioxide on titanium is an excellent anode for the evolution of chlorine from brine. It is corrosion-resistant, an important point, but one of its main claims to fame is that it catalyses the evolution of chlorine (C12 / Cl- EB- = 1.35 V) in preference to the evolution of oxygen (02 / H+ EB- = 1.23 V), even though the latter has a lower reduction potential. If a simple metal does not show the desired activity, composite elec­ trodes may be used that have thin coatings of an active catalyst on a substrate metal.

77.3.2 Stereochemistry

An electrode certainly is sterically oriented. One direction points out into the solution and the other is a brick wall (as far as reacting molecules go). Ifa molecule is adsorbed through certain combinations of atoms, it is likely

o

C02CH 3 Figure 11.3 Oxidative acetoylation of a cyclic dienol ethanoate Electrochemical synthesis 261 to have a fixed conformation and the reaction, if it occurs on the electrode surface, stands a good chance of being stereoselective. For example, the oxidation of some cyclic dienol ethanoates in etha­ noic acid and potassium ethanoate gives 14 times more of the Bisomer than of the a isomer. That is the good news, but it must be said that often the expected stereoselectivity is not observed. Although the reason for this is not totally clear, presumably the adsorbed species has more room for movement than we think and it is also fair game for a variety of other reactions.

11.4 Types of electrosynthetic reaction

77.4. 7 Direct electron transfer at the electrode

If the electrode merely suffices to be the vehicle for the passage of elec­ trons, it is possible to classify the possible reactions that can take place in terms of whether oxidation or reduction is the first step and what subse­ quent steps, chemical or electrochemical, may follow. This does not mean to say the electrode has no part to play. Remember the role of the electrode in the evolution of hydrogen (Chapter 8) and that the reaction is a thousand billion times more efficient on platinum than on mercury. Organic compounds offer the greatest diversity and it may be useful to take an overall look at the possible reactions. Figure 11.4 shows the different paths followed after oxidation and Figure 11.5 those after reduction of a generic species R. The existence of nucleophiles or electrophiles in the solution leads to many reactions that are determined by the nature of the solvent. Another way of looking at the process is to view, for example, the cation radical produced by oxidation as

RN: (nucleophilic addition) ~RR(dimer)

2 ~ 1/2 R + + 1/2 R (disproportionation)

R- e -> R~ ?=: R'+ (carbonium or carbenium ion) ~ R'R' (dimer) R2+ (dication)

Note: R' is R with a little bit added on or taken off (e.g. HI

Figure 11.4 Reactions involving electrochemical oxidation of species R 262 Introduction to electrochemistry

~ RE~(electrophilic addition)

~ RR'(dimer)

2 ____ 1/2 R - + 1/2 R (disproportionation)

?=:: R'- (carbanion) ~ R'R' (dimer)

2 R - (dianion)

Note: R' is R with a little bit added on or taken off (e.g. H)

Figure 11.5 Reactions involving electrochemical reduction of species R

--.-e

+

Figure 11.6 Reaction scheme for the oxidation of bicyclo[4.1.0]heptane in methanol an electrophile and a radical that will react with suitable species in the solution. For example, the oxidation of bicyclo[4.1.0]heptane in methanol gives a seven-membered ring cation which loses a second electron and a proton while reacting with the solvent. If the electrode just acts as a metallic conductor to produce a reactive species in solution, the rates of reactions will not be expected to change as the electrode material is changed. Most of the reaction goes on in solution once the electrochemistry is over. Therefore, factors such as the type of Electrochemicol synthesis 263 solvent and the pH will be of greater importance. The fact that so many reactions are influenced by the electrode suggests the mechanisms of electrosynthetic reactions could be more complex than appears at first sight.

77.4.2 Redox reactions of electrochemically generated mediators

This section describes electrosyntheses that do not proceed directly by electron transfer at the electrode but by reaction with an electrochemically generated species, either attached to the electrode or in the solution. Ifthe potential at the electrode is not appropriate for a reactant to be oxidised or reduced, there is still hope if an electrochemically generated species may react in some beneficial way. Figure 11.7 shows the general principle of mediated electron transfers. The essence of mediation is that some intermedi­ ate is formed at the electrode, and this species does the electrochemical bizzo

SR E I e c t r 0 d e So (a)

E I e c t r ne o d e

Surface layer (b)

Figure 11.7 Schematic of a redox reaction mediated by an electrochemically generated species 264 Introduction to electrochemistry

(this is an Australianism for business). Traditionally this mediator per­ forms its task in the solution, but reactions at surface layers on the elec­ trode also come under this heading. See Problem 11.1. The reaction between a mediator (M) and reactant (R) in an oxidation may be written (11.3) M+· + R ~ M + R+· (11.4)

R+. ~ ~ products (11.5) Depending on the relative reduction potentials of the mediator and the reactant, the equilibrium of Equation (11.4) will lie to the right or left. Often a mediator is used that will be oxidised at a lower (more negative) potential than the reactant itself. The advantage of using a mediator may be that the degree of oxidation is controlled, or that oxidation of the solvent may be avoided. In this case the equilibrium is to the left and the reaction proceeds at all by virtue of the irreversible removal of the radical cation of the reactant (Equation 11.5). Good old Le Chatelier does the rest. The mediator is involved in the reaction scheme catalytically, so in theory, if the reactions are fast enough, only small amounts of M need be generated.

Redox reactions of mediators at the electrode

I shall give examples of reactions of electrochemically generated hydrogen, of oxide layers and of other oxidations that go via species at the electrode surface. Whatever the mechanism of the hydrogen evolution reaction, during the evolution of hydrogen from any solvent containing an available proton the surface of the electrode becomes covered with hydrogen atoms. These atoms are both good reducing agents and sources of hydrogen. Electrocatalytic hydrogenations are usually highly selective and stereo­ specific. Electrode materials are chosen that maintain a high coverage of hydrogen atoms, such as platinum group metals and nickel. Examples of useful hydrogenations are the reduction of sugars, the hydrogenation of steroids, the conversion of benzene to cyclohexane and the reduction of naphthalene to 1,4-dihydronaphthalene. Anodised metals give oxides that may mediate electrochemical reac­ tions. We have already seen the role that oxides of platinum have in the evolution of oxygen. Just as the evolution of oxygen occurs at potentials that may be associated with the formation of higher oxidation states of the electrode, so too with some organic oxidations. The surface of nickel, copper or silver when anodised acts as a source of hydroxyl radicals (OH·) that can abstract hydrogen from a molecule. In the case of nickel, nickel Electrochemical synthesis 265

(Ill) peroxide (NiO(OH» has been identified as the source of OH·. For example, the oxidation of n-butanol is as follows: NiO + OH- - NiO(OH) + e (11.6)

C3H7 -CH2-OH + NiO(OH) - C3H7 -CH·-OH + NiO + H20 (11.7)

C3H 7 -CH'-OH - - C3H7 -COOH (11.8) Oxygen itself is transferred from lead dioxide to species. Thus, chromium (Ill) salts are converted directly to chromic acid and aromatic systems yield quinones. Hydrocarbons may be fluorinated at nickel, copper or iron anodes in liquid hydrogen fluoride. Metal fluorides (e.g. NiIIlF3) are thought to participate in the reactions.

Redox reactions of mediators in solution

A distinction may be made between systems that are so-called homo­ mediatory (or redox catalysis) and those that are heteromediatory (or chemical catalysis with electrochemical regeneration). In the former the reaction between the mediator and the reactant is one of direct electron transfer. You can think of the mediator as being an offshoot of the electrode. In a heteromediatory (or chemomediatory) system the mediator reacts chemically with the reactant. If the redox catalyst is a metal com­ plex, then a homomediatory system will involve an outer-sphere electron transfer, while a heteromediatory system proceeds via an inner sphere reaction. An example of a homomediatory system is the oxidation of carboxyl­ ate anions via tris-(4-bromophenyl)amine: (Br-C6H4)3N - (Br-C6H4)3N+' + e (11.9) (Br-C6H4)3N+' + RCOO- - (Br-C6H4)3N + RCOO' (11.10) RCOO' _ R' + CO2 (11.11) Halide ions that are oxidised to the halogen are frequently used as mediators. The intermediate (the halogen) chemically reacts with the substrate regenerating the halide ion. It is this chemical reaction that classes it as a heteromediator. In non-aqueous media the positive halide ion may be formed-for example, 1- _ 1+ + 2 e (11.12) An example of the use of potassium iodide in water as a mediator is the oxidative coupling of a secondary amine and formaldehyde (methanal). The overall reaction is HCHO + (CH3)2NH _ (CH3)2NCHO + 2 H+ + 2 e (11.13) Inorganic couples are more often used for mediated reactions: Ce3+ / 266 Introduction to electrochemistry

4 3 z 3 3 Ce +, Cr + / CrzO~-, Mn + / MnOz, Mn2+ / Mn +, V2+ /V +, RuOz / RuO;, Hal- / Halzand Hal- / HaIO- for oxidation, and Sn4 + / Sn2+, Cr3+ / 4 Crz+ and Ti + / TP+ for reduction. See Problem 11.2. However, organic species can also act as mediators-for example, organic sulphides via a radical cation. Secondary alcohols may be oxidised to ketones using methylphenyl sulphide (C6Hs)SCH3 : ~ (C6Hs)SCH3 (C6Hs)SCH;' + e (11.14) ~ (C6Hs)SCH;' + RzCHOH (C6Hs)S(CH3)-O-CHR; + H+ + e (11.15) ~ (C6Hs)S(CH3)-O-CHR; (C6Hs)SCH3 + OCRz + H+ (11.16)

77.4.3 Redox reactions of the electrode

In some cases the electrode material itself may be a reactant. The electro­ chemical preparation of Grignard reagents in the preparation of tetraethyl lead is an example. This will be discussed in the next chapter. Metal alkyls generated by dissolution of the metal in a solution containing an alkyl halide have been made using electrodes of Hg, Zn, Cd, AI, Mg, Mn, Au, In, Sb, Sn, Ca and Be. Some organometallics may also be prepared by oxidation of the metal electrode in a solution containing ligands. Ferrocene may be made by reaction of the cyclopentadiene dimer with an iron anode in dimethyl sulphoxide as solvent. In inorganic synthesis solid copper(I) oxide is made by the anodic dissolution of a copper electrode in sodium chloride electrolyte. See Problem 11.4.

17.5 Examples of organic electrochemical synthesis

When Kolbe discovered his eponymous reaction in 1849 no one would have guessed that the next useful electro-organic synthesis would not appear until 1952 with the oxidation of furans. Somehow organic electro­ chemistry has never quite taken off as a major synthetic route. However, it does have its uses, and with better understanding and education of syn­ thetic chemists (chemists doing synthesis, not plastic ones!), electrochemis­ try may yet take its rightful place in the organic and inorganic chemist's armoury. See Problems 11.3 and 11.5.

77.5. 7 Kolbe reaction

The Kolbe reaction, one of the earliest reactions applied in organic synthesis, is the oxidation of a salt of a carboxylic acid to yield a hydrocarbon: Electrochemical synthesis 267

2 RCOO- - R-R + 2 COz + 2 e (11.17) Depending on the conditions used (electrode material, electrolyte, concen­ tration of reactants and temperature), the Kolbe reaction affords products that stem from radical intermediates (e.g. RCOO· and R·, giving Rz by dimerisation or unsaturated compounds by disproportionation) or carbon­ ium ions (e.g. RCOO+ and R+ giving RSolv by reaction with a solvent nucleophile SolvH or Solv-). These are summarised in Table 11.2.

Table 11.2 Conditions used in the Kolbe reaction Products from radicals Products from carbonium ions Electrode Platinum Carbon Electrolyte Aqueous or non-aqueous Aqueous, nucleophile Concentration High Low-medium Current density High Low-medium

77.5.2 Oxidation of organic compounds

The Kolbe reaction is, of course, an oxidation but I have taken it separ­ ately because of its historical value and also because it is one of the most researched electrochemical synthetic reactions. However, there is a whole world of different oxidations. Ultimately organic compounds are oxidised to carbon dioxide and water, and while this is synthesis of a sort, these two products are not exactly what you would want to spend much time making by electrochemical means. On the way there are many useful compounds to be made and I shall choose a few at random to show you. As we have seen with the Kolbe reaction, the solvent, temperature and concentration of reactants can affect the outcome of the synthesis. A good example of this is the set of reactions of 1,4-dimethoxybenzene shown in Figure 11.8. The reactions can all be seen in terms of the schemes presented above (Figure 11.4). The radical cation formed initially can react with a nucleophile at position 1 or 2 on the ring and the resulting radical may react further in a second oxidation, usually with the loss of a proton, to give the products. The oxidation of 1,2,4-trimethoxybenzene (Figure 11.9) at a lead dioxide electrode in aqueous acid gives a dimer. Astute readers will realise that this could be the beginning of polymerisation, which is covered below. Oxidative halogenation results when the nucleophile that attacks the newly formed radical cation allows the subsequent addition of halide, or is itself a positive halide ion or halogen molecule. Thus, benzene becomes chlorobenzene during electrolysis of a solution of benzene in acetonitrile and lithium chloride. Iodoform and chloroform can also be prepared by oxidation of ethanol in an aqueous solution of the appropriate sodium halide. These reactions are examples of heteromediated reactions.

~ J 268 Introduction to electrochemistry

CH,O OCH, CHJOH KOH, Pt CH,O0OCH, CN

CHJCN (C,H.I.NCN @ Pt OCH, OCH, OCHJ CHJCOOH .. cQr~' @ CHJCOO Pt OCH, OCH J 0

H,SO./H,O PbO, 00

~@C0 ,::0. CHJCN LiCIO. 3,5-lutidene Pt OCHJ

Figure 11.8 Electrochemical oxidations of 1,4-dimethoxybenzene

Figure 11.9 Oxidation of 1,2,4-trimethoxybenzene

71.5.3 Reduction of organic compounds

Some of the earliest examples of electrosynthetic reductions came from polarographic studies of organic compounds. Elimination of halide (X- in the reaction below) is usually quite facile in the reaction Electrochem/cal synthesIs 269

RX + H+ + 2 e ~ RH + X- (11.18) with the ease of carbon-halogen bond fission being in the order of decreas­ ing electronegativity, F < Cl < Br < I. Carbanions may be generated electrochemically. Tetrachloromethane in a non-aqueous solvent (e.g. dimethyl formamide) is reduced in a two-electron process to CCl; and Cl-. The trichloromethyl carbanion adds rapidly to aldehydes or ketones to give the alcohol:

~ CCl4 + 2 e CCl; + Cl­ (11.19) RCHO + CCl; ~ RC(O-)HCCI3 (11.20) In the presence of trichloromethane the reaction continues in a chain reaction: RC(O-)CCI3 + HCCl3~ RC(OH)HCCI3 + CCI; (11.21) SN2 substitution may occur in the presence of alkyl halides. For example, azobenzene (remember its cyclic voltammogram in Chapter 8) is reduced in the presence of iodomethane with the addition of methyl groups across the double bond:

C6Hs-N=N-C6Hs + 2 CH3I + 2 e ~ C6Hs-N(CH3)-N(CH3)-C6Hs + 21- (11.22) Ketones may be reduced to secondary alcohols and thence to hydro­ carbons in aqueous electrolyte. The radical intermediate RzC'OH may also couple to give a pinacol, RzC(OH)(OH)CRz. This is dependent on the

...... +2e ...... 0 -C-'H--C-N-....•• 2 3 CH 2(COOC 2H.),

OH

(a)

oH 0 0 R +2e ©fVOH R CH 0H .. cgfY' 3 H20 (b) Figure 11.10 Reductive coupling ofaldehydes and ketones to give pinacols: (a) the reaction of retinal in diethyl malonate; (b) the formation of a cyclopropane diol 270 Introduction to electrochemistry electrode material. For example, at a lead electrode, acetone is reduced to pinacol (R = CH,) and 2-propanol, but at mercury to 2-propanol and propane. In synthesis, coupling of species to give a pinacol is used to generate reactive or relatively unstable products. For example, long con­ jugated molecules may be linked without danger to the double bonds, and strained cyclopropane diols may be prepared (see Figure 11.10).

77.5.4 Initiation of polymerisation

The possibility of polymer formation is always present when radicals are about. If you are trying to make a nice pure product, then the black stuff at the bottom of the reaction flask is usually a polymer of something. On the other hand, some polymers are quite useful and the majority of pOlymer­ isations are produced by a free radical chain mechanism. What better to kick the whole thing off than an electrochemical oxidation or reduction? No extraneous species must be added, the potential may be controlled to give the radical selectively and the current may be controlled to fix the rate at which radicals are being produced. This in turn could affect the degree of cross-linking. The electrochemistry may be performed at a low tem­ perature, which makes life easier for all concerned. Polymerisation may be initiated in a number of ways. Discharge of an ion at an electrode may produce an atom, radical or radical ion. A stable polymerisation initiator may be produced electrochemically, or an inhibi­ tor be removed. 1,3-Butadiene is polymerised by reduction and the process terminated by oxidation:

2 CH2 -CH=CH-CH2 + 2 e - [CH2 =CH-CH'-CHJ - (11.23)

[CH2 =CH-CH'-CH2]2- + CH2 -CH=CH-CH2 -

[CH2 =CH-CH'-CH2 -CH2 -CH=CH-CH2]2- (11.24) The current is pulsed through the cell. The number of pulses determines the amount of polymer and the molecular weight is governed by the duration of the initiating and terminating pulses.

17.6 Examples of inorganic electrochemical synthesis

77.6. 7 Industrially important syntheses

Electrochemistry in industrialised countries is responsible for the synthesis of key inorganic chemicals; aluminium, chlorine and sodium hydroxide. Added to this, the electrolysis of water is responsible for much of the Electrochemical synthesis 271 production of hydrogen. These processes are of sufficient importance to rate a chapter of their own (Chapter 12).

77.6.2 Synthesis of organometallic compounds

Inorganic chemists have taken to electrochemistry as a useful tool for identifying and quantifying redox states in compounds. With bigger elec­ trodes the processes may be turned to preparation of compounds of interest. The complex [hs-CsHsFeCO]4 may be both oxidised and reduced in acetonitrile or dichloromethane with [n-Bu4N]+[PF6]- as electrolyte: [(hs- CsHsFeCO)4]2+ i J, +1.08 V

[(hs - CsHsFeCO)4] + i J, +0.32 V (hs-CsHsFeCO)4 i J, -1.30 V

[(hs-CsHsFeCO)4]- The monocation, which is only slightly soluble, may be prepared at +0.8 V (against SCE) at a platinum electrode. A green precipitate of [(hs­

CsHsFeCO)4] [PF6 ] is produced. The anion may also be prepared as a yellow, air-sensitive solution. In acetonitrile the dication reacts with the solvent to give complexes induding NCCH3 • A test of the success or otherwise of an electrolysis is the measurement of the number of electrons passed per mole of product. Often this may be different from the value of n determined by voltammetry. The time that products have to linger in a preparative electrolysis is such that side­ reactions may occur. The number of electrons is usually greater (because less product is formed) unless a mediator is formed in catalytic amounts, in which case the apparent number of electrons may be very small.

• PROBLEMS

11.1 One of the earliest mediated electro-organic syntheses was the oxidation of glucose to calcium gluconate: ~ 2 C6H 120 6 + CaC03 + H20 Ca(C6Hu 0 7)2 + 2 H2 The reaction occurs in the presence of bromide ion. Suggest a mechanism for the reaction. 272 Introduction to electrochemistry

11.2 With a suitable transition metal ion to act as a reducing agent, hydroxylamine reacts with maleic acid, (HOOqCH=CH(COOH), to give aspartic acid, H2NCH(COOH)CH2COOH. Suggest an electrochemical scheme in which the ion is generated at the cathode and offer candidate transition metal ions.

11.3 Write balanced equations for reactions at the anode and cathode and for the overall cell for the following electrochemical syntheses:

Reactant(s) Products Conditions Nitrobenzene 4-Aminophenol Cu cathode with highly acidic electrolyte Butene Methylethylketone Lead anode in sulphuric acid Acetone Pinacol Lead cathode

11.4 Nickel may be used as an anode in alkaline electrolyte for the oxidation of organic compounds by the removal of hydrogen (RCH2X ---+ RCHX, etc., where X is an activating group). Suggest a mechanism for the reaction.

11.5 Benzyl iodide is easily reduced to toluene at mercury, cadmium and lead cathodes. Why is this?

• ANSWERS

11.1 The cathodic reaction will be the evolution of hydrogen. At the anode bromide ion will be oxidised to bromine, which in turn will react with calcium carbonate to give calcium hypobromite, Ca(OBr)2' It is this species that effects the oxidation of glucose. .

11.2 In organic chemistry Ti3+, y3+, Sn2+ and Cr+ are often used as reducing agents, Ti3+, y3+ are conveniently generated electrochemically. Therefore the scheme is

3 4 Ti + + NH20H -+ Ti + + 'NH2 + OH- 'NHz + CHz(COOH)z -+ HzNCH(COOH)C'H(COOH) 3 4 H2NCH(COOH)C'H(COOH) + Ti + + W -+ H2NCH(COOH)CH2 (COOH) + Ti +

11.3 (a) Cathode:

C6HsNOz + 4 H+ + 4 e ---+ C6HsNHOH + H20

C6HsNHOH ---+ (HO)C6H4NHz

Anode: 2 H 20---+0Z + 4 H+ + 4 e

Overall: C6HsN02 + HzO---+ (HO)C6H4NH2 + O2 Electrochemical synthesis 273

(b) The first step is the chemical hydration of butene followed by the oxidation of the alcohol that is formed:

~ CzHsCH=CHz + HzO CzHsCH(OH)CH3 ~ Anode: CzHsCH(OH)CH3 CzHsCOCH3 + 2 H+ + 2 e Cathode: 2 H+ + 2 e ~ Hz ~ Overall: CzHsCH=CHz + HzO CzHsCOCH3 + Hz

(c) Cathode:

~ CH3COCH3 + H+ + e CH3C"(OH)CH3 ~ 2 CH3C"(OH)CH3 (CH3)zC(OH)C(OH)(CH3)z Anode: 2 HzO ~ Oz + 4 H+ + 4 e

~ Overall: CH3COCH3 + HzO (CH3)zC(OH)C(OH)(CH3)z + 1/20z

11.4 Nickel oxidises to Ni(OH)z, NiO(OH) and possibly higher states. Therefore, a typical oxidation will proceed as follows Ni(OH)z + OH- ~ NiO(OH) + HzO + e NiO(OH) + RCHzX ~ RC"HX + Ni(OH)z

11.5 An intermediate organometallic compound is formed. Metals that can make bonds to carbon will be preferred:

~ C6HsCHzI + Hg C6HsCHzHgI ~ C6HsCHzHgI + e C6HsCHzHg + r ~ C6HsCHzHg + e + SolvH C6HsCH3 + Hg + Solv- 72 Industrial electrochemistry

12.1 Introduction

Ultimately electrochemistry must be of use to someone. Understanding how electrons footle about in lumps of platinum immersed in bizarre solutions may be a way of spending one's wet Saturday afternoons, but there should be some aim in mind. In the introductory chapter I argued how electrochemistry is in some ways the science of the modern age. In this chapter I survey the major industrial uses of electrochemistry. Together with energy-producing devices (Chapter 13), electroanalytical chemistry (Chapters 9 and 10) and corrosion (Chapter 14), I shall have covered most of the consumers of the $30 billion per year that was spent on electrochem­ istry in the USA by the end of the 1980s. Industrial uses of electricity in the USA are greater than either residential or commercial. I shall start with a quick look at how chemical engineers approach the problem of electrochemistry and then concentrate on the major inorganic and organic uses of electrochemistry.

12.2 Electrochemical engineering

Electrochemical engineering is not just scaled up electrochemistry. To produce 1000 t of a chemical by electrolysis introduces new problems that ultimately revolve around the cost of producing the chemical safely and with due regard to environmental, legal and social issues. The cost that needs to be optimised is made up from the capital costs of the proposed plant, the running costs, including electricity, labour, raw materials, waste disposal, etc., and other factors such as depreciation. In the final analysis it will be the percentage return on investment that will be the figure that informs a board of directors whether to go ahead with a particular process. The contributions of the specifically electrochemical parameters are deter­ mined in terms of figures of merit. 274 Industrial electrochemistry 275

The story of electrolysis

How do you publish a new and important phenomenon when someone else has just discovered it? Answer: print your own journal. In these days of near-cut-throat science, when you would rather sell your old granny than tell anyone else your Nobel Prize-winning idea, the leisurely pace of early nineteenth century natural philosophy may seem a little tame. Not so, as you will see. On 20 March 1800 Alessandro Volta (no prizes for guessing what electrical unit is named after him), of the University of Pavia, sent to Joseph Banks, President of the Royal Society of London, a letter describing the 'Voltaic piles' that he had just constructed. These were disks of different metals separated by paper soaked in brine, which produced a voltage. As was the custom, Banks (I write this in Australia, where Banks is well known as a companion of Captain Cook on his voyages of discovery) presented this work to the Royal Society and later in the year it was published in the Society's Philosophical Transactions. These things get around and Banks showed Volta's letter to Anthony Carlisle, a famous surgeon, who in turn passed it on to his friend William Nicholson. Nicholson was an amateur scientist and publisher of Nicholson's Journal, said to be the world's first independent scientific journal. Nicholson and Carlisle promptly made their own pile, using silver half-crowns and copper disks. When wires from a pile were put into water, hydrogen was evolved at one wire and oxygen at the other. It was duly reported in Nicholson's Journal coming out in July 1800, before the report of Volta's own work (although credit is actually given to Volta). The great problem that this discovery produced was why the gases came off at different wires almost independently of how far apart they were? Ions were not known then (Faraday coined the words 'anion' and 'cation' some 40 years later), so if water were to be split up by electrolysis, both gases would be expected to be evolved, presumably at the same electrode. From this beginning, over the next 100 years came all the theory of electrolysis and of electrolytes.

72.2. 7 Figures of merit

Percentage yield

The yield is defined as the fraction of the starting reactants that are converted to product expressed as a percentage. Another figure that is related to the yield is the selectivity, which is the fraction of the number of 276 Introduction to electrochemlstry moles of all products that is the desired product. Obviously each of these numbers needs to be as near to 100% as possible.

Percentage conversion per pass

Some processes may allow the mixture of products and unreacted starting material to be recycled through the cells (see subsection 12.2.2). In this case the yield per cycle is a figure to be optimised. In the case where there is no chance to have a second go, as in the treatment of effluent, or if the product is unstable, then the yield is whatever it is in one cycle. The factors that influence this figure of merit are the flow rate (a high flow rate tends to lower the conversion per pass) and the ratio between the electrode surface area and the cell volume.

Space-time yield

The space-time yield is the amount of product obtained per unit volume of reactor per unit time. It depends on the current density, current efficiency and the arrangement of electrodes. The fact that electrochem­ istry is a heterogeneous process and that the electrodes must be in electri­ cal contact with the outside world places a great constraint on the engineer's ability to achieve a good ratio of surface area to cell volume and thus a good space-time yield. Comparison with typical chemical reactors which have space-time yields up to I kg h - I dm -3 shows values ten times worse for electrochemical cells.

Energy considerations

There are two factors that are computed-the current efficiency and the energy consumption. The current efficiency (E) is a measure of the useful yield in terms of the electricity consumed and is defined as the fraction of the total current used to form the product expressed as a percentage. It is not quite the same as the yield as lCX)o.~ of the starting material may well cnd up as product. but the current efficiency may not be 100% if the solvent is broken down. An example would be the evolution of hydrogen in cathodic processes and oxygen in anodic processes. In this respect it is more akin to a measure of the selectivity. The rate of energy consumption in a process is the power, which is the voltage times current. The weight of the product produced per second is E I MW /!l F. where MW is the molecular weight and E is the current efficiency defined above. The rate of energy consumption in W kg I is therefore Industrial electrochemistry 277

rate of energy consumption = n FV / (E MW) (12.1)

Energy consumption is more often quoted in kW h kg I, which is

6 energy consumed = n FV /3.6 X 10 E MW ( 12.2) Note that although the units are the same as for energy density of a battery (see Chapter 13), the concept is different. Equation (12.1) shows that the energy consumed depends only on the voltage and current efficiency, not the current itself. It is important therefore to keep the voltage as low as possible. In Chapters 4 and 6 we have discussed what contributes to the voltage across a cell. Absolutely unavoidable is the energy to do the reaction (-L1G / n F). Added to this are the overpotentials at each electrode and the IR drop through the electrolyte. Each of these factors is the subject of intense research. Energy efficiency may be defined as energy efficiency = -EL1G / (n F V) (12.3) where V is the actual cell voltage and -L1G / n F is the 'ideal' voltage.

72.2.2 Cell designs

Constraints and problems

In laboratory-scale electrochemistry mass transfer in a cell is something that can be controlled easily and used to the advantage of the exper­ imenter. At an industrial scale the need to get large quantities of reactants to electrodes and products away from them presents major problems. This is exacerbated by the desire to work at high current densities. Added to this problem is that of the current distribution in a cell. As soon as the geometry of the electrodes is not symmetrical, there may be 'dead spots' on one electrode where the current just does not reach. This is of course wasteful of both electrode and the volume of the cell. Usually, therefore, the most simple arrangement of electrodes is best, as parallel plates or in a cylindrical arrangement. In electroplating the object to be plated has the shape that it has, so careful design of the anode is needed to give smooth plating on the cathode.

Arrangement of electrodes

There are two alternatives to the obvious solid anode-eathode-anode­ cathode arrangement in which each electrode is connected to the voltage supply (a so-called monopolar cell). The first is the bipolar electrode, a way of introducing an electrode without making external contact. The second is the fluidised bed electrode. 278 Introduction to electrochemistry

+ + +

+ + ~ I Bipoler ,-- , electrodes + + + .>

e $ e '------Iv..., .------' '------Iv..., ------' (e) (b)

Hgure 12.1 Electrical connections in (a) a series of monopolar electrodes; (b) a cell with bipolar electrodes

Bipolar electrodes are not connected to the external supply but are simply placed between the anode and cathode as shown in Figure 12.1. In a bipolar cell the side of the bipolar electrode facing the cathode becomes an anode. the electrons pass through the electrode and the other side operates as a cathode. and so on until the cathode at the end of the cell is reached. The advantages of bipolar cells comes from the savings in connections. the lack of contact resistances and the use of high voltages and low currents. The voltage required will be the single-cell voltage times the number of cells created by the bipolar electrodes. In comparison. the assembly of many monopolar cells uses low voltage (just the single-cell voltage to drive all the cells in parallel) but requires a high current. The bipolar arrangement must have good insulation between the cells to avoid leakage currents (also called shunt or bypass currents) when the current passes between the end electrodes. ignoring the bipolar electrodes in the middle. As in catalysis. the use of fluidised beds has been shown to be effective in electrochemistry. Figure 12.2 shows two arrangements of a fluidised bed electrode. one with a separator and one in which the electrolyte is common to cathode and anode. A fluidised bed electrode has a large surface area-ta-volume ratio coupled with a high flow rate of the electrolyte. This leads to a high space-time yield even for low current densities. such as are found. for example. in effluent control of low concentration solutions. The current distribution in a fluidised bed is not easily controlled and if the product is deposited. such as in metal winning. the bed may agglomerate under the weight of the deposit. Industrial electrochemistry 279

Calholyle AnOIYlt' ~ufrOducts ~ -, aul

Feeder electrode

Plait­ an()(h'

(al

Ml'll,IH

Electrode parllcles --~~"'''''

Catholyle Anolylt>

Electrolyte oul

<.idl';!' cOlJf11erf'If'(IroO,.

Ib) Ei\,clrrHle pdrloC1f'S

Pr:"()\I'> rI, ...

Figure 12.2 Cells containing fluidised bed electrodes: laj with a separator: (b) with a common electrolyte 280 Introduction to electrochemistry

Cell construction

Cells may be divided into two broad classes - batch reactors (tank cells) and flow reactors (flow cells). In the first the reactants are fed into the cell, electrolysis occurs and then the products are recovered. In a flow cell reactants flow through the cell and the products are removed from the outlet stream. A typical batch cell is shown in Figure 12.3. The separators between each electrode may be asbestos, glass, porous pot or ion-selective membranes.

Anode

..--J" I'~ Cathode

I i : : : 1 I I I I Electrolyte I II I I I II I I I II II I I I I I Tank I II I I cell I II I I I I ~ II I ~ I / \ Electrode Diaphragm

Figure 12.3 A tank cell with monopolar electrodes

Separators are only used if there is a need to keep the anolyte from the catholyte, or the products from each other (e.g. hydrogen from oxygen in water electrolysis). They introduce resistance and cost, and so are intrinsi­ cally undesirable. In a flow cell the requirements are to allow the flowing electrolyte to make as much contact with the electrodes as possible. This is done by minimising the gap between the anodes and cathodes (including separator if necessary). In a filter press arrangement up to 100 cells are screwed together with gaskets insulating and separating each cell. The electrode area is up to 1 m2 and bipolar cells are often used (Figure 12.4). The output from one cell may be fed into the next to produce a cascade of cells. Industrial electrochemistry 281

------Spacers /

Figure 12.4 A filter press arrangement

72.2.3 Aspects of engineering

A reasonably sized electrochemical plant may consume up to one million amperes of current. The conversion of mains alternating current to direct current at a few hundred volts must be done as efficiently as possible, and then it must be distributed around the cells of the plant in a proper manner. Considerations would include chemical and electrochemical safety, minimisation of magnetic fields generated by the high current, minimisation of the distribution path of high-current electricity (to avoid the use of excess quantities of metals in busbars), and allowing individual cells to be isolated and shut down for maintenance. 282 Introduction to electrochemistry

72.3 The chlor-alkali industry

The chlor-alkali process refers to the electrolysis of brine (aqueous sodium chloride), to give chlorine, sodium hydroxide and hydrogen. It is the largest, in terms of product and electricity consumed, of the electrochemi­ cal industries. Chlorine is used as a chemical feed stock for the manufac­ ture of solvents (e.g. tetrachloromethane) and plastics (polyvinylchloride, PVC), for bleaching wood pulp and paper, and for the treatment of water. Sodium hydroxide is used as an alkali in many organic syntheses, in the preparation of soaps and detergents, in oil refining and for the preparation of other sodium salts. The numbers associated with the production are staggering. Thirteen million tonnes of chlorine are produced annually (1989) in the USA, consuming fifty million megawatt-hours of power. The size of this industry means that the processes have to be completely optimised. Ifone-tenth of a volt could be shaved off the operating voltage of a cell, millions of dollars would be saved. See Problems 12.1, 12.3 and 12.5.

72.3. 7 Cell designs

There are three types of cell used in the chior-alkali industry - the diaphragm cell, the membrane cell and the mercury cell.

Diaphragm cell

The diaphragm cell is named after the use of an asbestos coating, treated with polymers, to separate the anode and cathode reactions. The asbestos is deposited on a steel cathode at which hydrogen is evolved: E-G = -0.84 V (12.4) The electrolyte is 30% brine. The anodes are made of titanium covered with a layer of ruthenium dioxide promoted with other transition metal oxides such as C030 4 • These are known as dimensionally stable anodes (DSA) and show excellent activity towards chlorine evolution while having the corrosion resistance and mechanical stability required for long use in this severe environment. The reaction at the anode is, therefore,

Cl- ~ 1/2 Clz + e E-G = 1.36 V (12.5) The equilibrium potential of the cell is -2.2 V, and although the over­ potentials for each reaction are not great, there is a large resistance IR drop associated with the asbestos diaphragm. The operating voltage is Industrial electrochemistry 283

Steel gauze cathode

Asbestos pad --t7t-/

,.

I NaOH Brine NaOHlNaCI NaCI Figure 12.5 Schematic of a diaphragm cell for the production of chlorine and sodium hydroxide about -3.5 V. The brine must be very pure as calcium and magnesium may find their way into the diaphragm, blocking the pores and resulting in an even greater resistance. The product hydroxide must be kept away from the anode because of its reaction with chlorine to give unwanted hypochlorite, and also because the increase in pH favours the evolution of oxygen at the anode. This is the job of the asbestos coating. The asbestos is only a physical barrier and not too efficient, so the hydroxide ion concentration must be kept to 10%. The required strength is 50%, which adds another evaporation step to the overall process. At this stage most of the unreacted sodium chloride crystallises out and is recycled.

Membrane cell

A membrane cell is a modern diaphragm cell with the asbestos coating on the cathode replaced by a cation-selective membrane, such as Nation or 284 Introduction to electrochemistry

Flemion (see Section 2.7). The construction of the cell uses a filter press design, with anode and cathode compartments separated by a membrane. The membranes are not perfect, in that they cannot totally exclude hydrox­ ide when it is present on one side at high concentration, but it can tolerate around 30% hydroxide, which is a considerable improvement on the asbes­ tos diaphragm and thus reduces the cost of evaporation. The hydroxide produced is also free of chloride. The membrane limits the size of the cell and therefore membrane cells are often preferred for smaller-scale, local generation of chlorine - for example, in water treatment plants or pulp mills. A typical cell would produce 100 t of sodium hydroxide per year, which is one-tenth of the production of a diaphragm cell. The operating voltage of a membrane cell is the same as or slightly higher than that of a diaphragm cell, but it operates at twice the current Z density (500 mA cm- ). See Problem 12.1.

Mercury cell

A schematic of a mercury cell is shown in Figure 12.6. At a slowly flowing mercury cathode sodium is discharged as an amalgam: Na+ + Hg + e ~ Hg(Na) EB- = -1.89 V (12.6) The equilibrium cell voltage is about -3 V under the operating conditions

Carbon anodes

Concentrated 1==::t:===t:===~==:I===-~ brine 1-__- Diluted brine

H20

Hg(Na)

Cathode

Hg 1-__-H 2

NaOH

Figure 12.6 Diagram of a mercury cell for the production of chlorine and sodium hydroxide IndustrIal electrochemlstry 285 of the cell. With small overpotentials and resistance losses the operating voltage is about -4.5 V. The electrolyte in the cell is typically 35% sodium chloride solution, which is depleted to 17% after traversing the cell. The operating temperature is 60 qc. The mercury cell dominated the large­ scale production of chlorine for many years. The product quality is excel­ lent. The sodium hydroxide does not need to be concentrated, and the chlorine is 99.2% pure. However, the possible environmental hazards of mercury, and the greater consumption of electricity (in the case of the membrane cell even after allowing for concentration to 50% sodium hydrox­ ide), has meant that this technology has lost out to the membrane cell.

72.3.2 Production of hypochlorite

Sodium hypochlorite is produced by the reaction between chlorine and sodium hydroxide. This may be done directly in a cell with graphite electrodes, or by mixing the products from a conventional chlor-alkali cell. When sea-water is available, electrolysis provides a convenient method of sewage treatment. The hypochlorite that is formed sterilises the sewage, which then sediments out. Magnesium hydroxide that is also formed helps this process.

72.3.3 Production of chlorate

Chlorate is formed by the reaction of chlorine with water at a temperature of 50°C and pH of 6.

Cl2 + H20 -+ ClO- + CI- + 2 H+ (12.7)

2 HCIO + ClO- -+ CIa; + 2 Cl- + 2 H+ (12.8) The chlorine is produced from an electrolyte of 3 mol dm-3 sodium chlor­ ide and 3 mol dm-3 sodium chlorate, at a DSA and a steel cathode.

12.4 Metal winning, refining and finishing

Metal winning is the process of extracting metals from solutions of their ions. This is the basic process by which many metals are recovered from their ores. Refining is a similar process but the anode is now a block of the impure metal. As this dissolves, pure metal is deposited on the cathode. In metal plating a conducting object is coated with a metal for protective or decorative purposes. 286 Introduction to electrochemistry

72.4. 7 Electrowinning

Aluminium

The extraction of aluminium from alumina (AI20 3) is second only to the chlor-alkali industry in production tonnage and exceeds it greatly in the value of the product. The process is called the Bayer Hall-Heroult process and takes place in a melt of cryolite (Na3AIF6) with small amounts of aluminium fluoride and calcium fluoride at a temperature of 970°C. The alumina is refined from the ore bauxite and is present at a concentration of 2-6%. At the carbon cathode aluminium(III), which is present as a series of complex oxygen- and fluorine-containing species, is reduced to the metal, which collects as a molten pool at the bottom of the cell: AllII + 3 e ~ Al (12.9) The anode is a graphite bar, which is consumed, giving carbon dioxide and carbon monoxide. The overall reaction is (12.10) or (12.11) The reversible cell voltage is only -1.2 V because the energy of the oxidation of the carbon goes towards the reduction of the alumina. Addi­ tion of overpotentials and, in particular, the IR drop in the electrolyte push the cell voltage up to a still acceptable level -4.3 V. The heat that is 2 generated by the high current density (1 A cm- ) passing through the resistive electrolyte helps to keep the electrolyte molten. The current efficiency is only 85-90% because of the oxidation of aluminium by carbon dioxide. A more recent development uses a lower-temperature (750°C) chlor­ ide cell that uses an electrolyte of the chlorides of aluminium, lithium and sodium. A bipolar arrangement of electrodes is used, giving an improved use of cell volume and current efficiency.

Alkali and alkaline earth metals

Sodium is produced as an amalgam in the chlor-alkali process but it is not feasible to extract the pure metal. Instead sodium is extracted from a melt of sodium (42%) and calcium chlorides in a Down's cell. At a central cylindrical graphite anode chlorine is discharged (Equation 12.5), while at the steel cathode sodium is formed: Na+ + e ~ Na (12.12) Industrial e/ectrochemistry 287

Sodium is less dense than the melt and it rises up a tube, to be collected in a reservoir. A steel gauze diaphragm separates the anode and cathode and allows each product to be collected separately. Calcium that is formed precipitates and is kept at a low concentration by an equilibrium with sodium chloride:

Ca + 2 NaCI ;::::: CaClz + 2 Na (12.13) Other alkali and alkaline earth metals are produced in similar ways.

Hydrometollurgicol processes

Metals that may be reduced in aqueous solution are extracted by so-called hydrometallurgy. This is done when electricity is relatively cheap, as more traditional methods of reduction of ores (e.g. the use of carbon) are generally more cost-effective. Copper and zinc are extracted electrochemi­ cally, and cobalt, nickel, gold, silver, indium, gallium, thallium, manga­ nese, chromium and cadmium have been reported. The metal in question is made the cathode and oxygen is evolved at the anode, which is a lead-silver alloy. The electrolyte is a solution of a suitable salt of the metal. This is often sulphate from the sulphuric acid used to take up an oxide into solution. See Problem 12.2.

72.4.2 Electrorefining

Iftwo electrodes of a metal, such as copper, are immersed in an electrolyte of a salt of the metal, and a small voltage is applied between them, metal will dissolve from the anode and be deposited on the cathode. As there is no overall chemical reaction, the energy requirements arise from a very small overpotential and IR drop in the electrolyte. Electrorefining is car­ ried on at a greater scale than e1ectrowinning, and the majority of proces­ ses are conducted in aqueous solution. The impurities that are present in the metal will either remain solid, if their electrode potential is more anodic than that of the refined metal, and eventually fall to the bottom of the cell as anode sludge, or go into solution but remain there or precipitate out as an insoluble salt. These impurities build up with time and must be removed chemically. Organic compounds are added to the electrolyte to improve the quality of the electrodeposit. The current density is low and current efficiencies usually high. 288 IntroductIon to electrochemlstry

72.4.3 Metal finishing

To complete a product, the surface may be plated with a decorative or protective metal, may be anodised to give corrosion resistance or may be painted by an electrophoretic method (see subsection 3.7.2).

Electroplating

Electroplating is similar to electrorefining, except that the anode is of pure metal, and the cathode is the article that requires the metal coat. A variety of metals are plated: tin, nickel, copper, zinc, chromium, cadmium, lead, silver, gold, platinum and palladium. In addition, alloys of tin, copper, lead and nickel may be plated, and composites in which inert material such as Teflon are incorporated into a metal coat. The plated layer is usually as thin (less than 0.1 mm) as is compatible with the use of the article. Drastic cleaning of the article is necessary to ensure a good adherence of the plate. Sometimes a very thin layer of a third metal which forms a solid solution with the substrate metal and the plated metal is deposited first. The electrolyte composition and electrode geometry are chosen to give the finest possible deposit. As well as a salt or complex of the plating metal, the electrolyte may contain a buffer, surfactant or brighteners (organic compounds such as thiourea). These improve the smoothness and evenness of the deposit. The throwing power of a plating cell (or bath, as it is known) is a measure of the uniformity of the deposit. It is good if the plate can follow the contours of an object, plating both the valleys and the hills. Hydrogen may be evolved in parallel with metal plating. This may not be a bad thing. Although hydrogen evolution leads to a loss of current efficiency, it also tends to improve the throwing power. The anode is important, because the dissolution of the anode must match the plating at the cathode, to avoid changes in the composition of the electrolyte. Passivation of the anode, due to the formation of an oxide layer (see Chapter 14), is very much frowned upon. Nickel is a problem here and necessitates the addition of complexing agents. Chromium passi­ vates so badly that an inert anode at which oxygen evolves is used. Even with a pure anode, some impurities eventually build up as an anode sludge. These must be kept away from the cathodes and so the anodes are sur­ rounded by porous cloth bags that collect any droppings from the elec­ trodes (a sort of electrochemical guano). Industrial electrochemistry 289

Anodising

Anodising is the electrochemical formation of an oxide or chloride film on certain metals in order to impart corrosion resistance, hardness, improved appearance or reflection or radiation properties. It is principally used for aluminium, but also for steel, copper and titanium. For aluminium the object is made the cathode in a cell in which the cathode is of steel and the electrolyte dilute sulphuric acid, oxalic acid or chromic acid. The oxidation Z is done at constant current density (1D-20 mA cm- ) and a layer of ID-lOO !!m is formed. If the current density is increased to over 100 mA cm-z and phosphoric acid is used, the surface is electropolished and achieves a high mirror finish. The surface must already be smooth, and it is thought that a combination of oxide formation with dissolution leads to the desired finish.

Electrophoretic deposition of polymers and paints

The paint is a mixture of pigments (inorganic - e.g. titania, copper chrom­ ate - and organic) in a polymer that contains either acidic or basic groups that can form micelles in a solution of proper pH. Depending on the charge on the polymer micelles, they will be deposited at a metal acting as an anode or cathode. Most commercial processes use polymers with carb­ oxylic acid groups that are deposited at the anode at a cell voltage of 100 to 400 V. The advantage of electrophoretic deposition is that the paints are water-based and have low solids content, the throwing power is excellent and it is well suited for an automated production line (for example, the automotive industry). The range of colours is restricted and only one coat may be deposited on a conducting substrate. The deposit is baked, to produce the final stable coat.

12.5 Electrolysis of water

Hydrogen and oxygen can be prepared by a variety of methods, but where electricity is cheap the electrolysis of water produces gases of high purity. The electrolysis of water is the main route to deuterium gas and heavy water (DzO). You will recall from Chapter 8 that the large H-to-D isotope separation factor has been used to determine the mechanism of the reac­ tion. In the production of deuterium, electrolysis of water gives a gas richer in protium, leaving behind an electrolyte enriched with deuterium. 290 Introduction to electrochemlstry

12.6 Electrochemlcal preparation of organic compounds

We have considered the trillion and one chemicals that can be prepared electrochemically in the previous chapter. Here I shall describe the large­ scale production of some of the more important ones. There are about 30 commercial processes in production, with another 100 that have been demonstrated to be industrially feasible. A list of reactions that are in production now (1992) is given in Table 12.1.

Table 12.1 Commercial electroorganic processes Reactant Product Acrylonitrile Adiponitrile Glucose Sorbitol/mannitol Maleic acid Succinic acid Nitrobenzene Aniline sulphate Naphthalene Naphthaquinone 2-Methylindole 2-Methylindolene Oxalic acid Glyoxalic acid flexafluoropropene flexafluoropropene oxide Dimethyl sulphide Dimethyl sulphoxide Alkyl / Grignard, Pb Tetraalkyllead

72,6.7 Synthesis of adiponitrile

The importance of adiponitrile is that it is a precursor of adipic acid, which is condensed with hexamethylenediamine to give Nylon 66. The possible mechanisms have been discussed in Chapter 11. The reaction at the cathode is 2 CH2CHCN + 2 H20 + 2 e ~ CN(CH2)4CN + 20H- (12.14) The anode reaction is the evolution of oxygen. In the new Monsanto process an emulsion of acrylonitrile and 15% of disodium hydrogen phosphate in water containing 0.4% of hexamethylene­ bis(ethyldibutylammonium) phosphate is electrolysed in a bipolar stack of carbon steel electrodes. The electrodes are plated with cadmium and 2% borax and t or 1% EDTA are added to slow down corrosion at the anode. The electrodes are spaced 2 mm apart and the electrolyte flows through the cell to a reservoir where the product is extracted and fresh acrylonitrile added. The cell voltage is -3.85 V, which represents a saving of two-thirds on an earlier process which employed a cation-permeable membrane. See Problem 12.4. Industrial electrochemistry 291

72.6.2 Production of tetraalkyl lead

With the advent of lead-free petrol this success story of the electrochemical industry is winding down. However, it is an interesting reaction in which a Grignard reagent is formed electrochemically. To prepare tetraethyllead, for example, the lead is provided directly by the anode in the form of lead pellets: 4 CzHs + Pb - (CzHs)4Pb + 4 e (12.15) while at the cathode magnesium is the product:

4 MgCI+ + 4 e - 2 Mg + 2 MgClz (12.16) In the presence of excess chloroethane magnesium reacts to regenerate the Grignard reagent.

72.6.3 Indirect electron transfer via mediators

These reactions employ redox couples that effect the reaction homogeneously in solution, but are regenerated by an electrochemical reaction. For general examples and mechanisms see the previous chapter. For example, oxidising agents used are bromine (Brz / Br~), dichromate H (CrzO;- / Cr ) and periodate (10; / IO~). The advantages of these methods are that they can be carried out in aqueous solution, which ensures high conductances of electrolyte, the products are generally easily extracted and they employ simple cells with cheap electrode materials. However, the overall process is somewhat complicated by the introduction of an electrochemical step.

• PROBLEMS

12.1 A membrane cell to produce potassium hydroxide contains 4 mol dm-3 each of potassium hydroxide and potassium chloride. The resistance of the cell is 3 x 1(J' n m-z of membrane and the temperature of operation is z 50°C. The evolution of chlorine has E ~ = -1.36 V, io = 1000 A m- and z a = 2. The evolution of hydrogen from alkali has io = 5 A m- and a = 0.5. For a cell current of 2000 A m-z calculate (a) the cell potential (ignore activity coefficients), (b) the rate of production of potassium hyd­ roxide and chlorine in kg h- 1 m-z, (c) the power density of the cell and (d) the efficiency of the cell calculated as the thermodynamic voltage / cell voltage.

12.2 Electrochemical data for plating copper from two different baths are given below. Comment on the composition of each bath and suggest reactions that may occur at the anode. 292 Introduction to electrochemistry

Electrolyte T / QC i / A m-2 Current efficiency

CuS04 , H2S04 , dextrin, 20-40 200-500 0.98 gelatin, thiourea

CuCN, KCN, K2C03, 40--70 100-400 0.75

Na2S03

12.3 Derive an equation in terms of E ~ values, pH and pCl (-loglo [Cl-]) to calculate the possible saving in energy by using an oxygen cathode in the production of chlorine and potassium hydroxide instead of the usual evolution of hydrogen. Why are oxygen cathodes not used more often? (E~ = 1.36 V, E-: = 0.0 V, E~ = 1.23 V).

12.4 In the synthesis of adiponitrile from acrylonitrile the major side products are 1,3,6-tricyanohexane, hydroxypropionitrile and biscyanoethylether. Write reaction schemes for these reactions and suggest a mechanism.

12.5 The largest plant in the world producing chlorine by membrane cell 8 1 technology is in Holland, with a capacity of 2.7 x 10 kg yr- • If 2 the current density is 2500 A m- , how many cell stacks with 100 membranes 1 x 0.21 m are needed?

• ANSWERS

12.1 This is a straightforward calculation in an industrial context. First write the cell reactions, then calculate the thermodynamic voltages, remembering the temperature is 323 K, not 298 K.

Anode: Cl2 + 2 e :;:= 2 Cl-. Ethenn (anode) = 1.36 - RT / F In(ccd = 1.32 V

Cathode: 2 H20 + 2 e :;:= H2 + 2 OH-. Etherm (cathode) 15 = 0 + RT / F In(2.5 x 10- ) = -0.936 V Therefore, the thermodynamic cell voltage is 2.256 V. Now calculate the overpotentials from the Tafel equation 1/ = RT / a F In(i / io)' Anode: 1/ = 0.0278 / 2 In(2000 / 1000) = 0.009 64 V Cathode: 1/ = 0.0278 / 0.5 In(2000 / 5) = -0.3335 V

The voltage due to resistance is I x R = 2000 x 3 X 10-4 = 0.6 V. (a) The total voltage is therefore = 1.32 + 0.936 + 0.00964 + 0.3335 + 0.6 = 3.2 V (b) The rate of production of potassium hydroxide is 2000 / 96 500 x 3600 3 1 2 x 56 x 10- = 4.18 kg h- m-- • The production of chlorine is 2000 / (2 3 1 2 x 96 5(0) x 3600 x 71 x 10- = 2.65 kg h- m-- • 2 (c) The power density is 2000 x 3.199 = 6.40 kW m- • (d) The voltage efficiency is 2.256 / 3.199 = 0.705.

12.2 Copper plates at high current on simple substrates from the aqua copper(II) ion. Cyanide complexes copper, which aids in preventing side Industrial electrochemistry 293

chemical reactions with the substrate (e.g. on iron cathodes) and also helps dissolve the anode without the formation of oxide films. Organic additives are used to level and brighten the deposits. Sulphur-containing organics are often used as brighteners.

12.3 Chlorine is evolved by 2 Cl- ---+ Clz + 2 e (Ec!) and the choice of cathode reaction is between 2 HzO + 2 e ---+ Hz + 2 OH- (E~) and Oz + 2 HzO + 4 e ---+ 4 OW (E ~). Therefore,

ECl = 1.36 - RT / F In(ccd = 1.36 + -0.059 pCI; EH = 0.059 pH; Eo = 1.23 - 0.059 pH

ECell•1 = 1.36 + 0.059 (pCI + pH); Ecell•2 = 0.13 + 0.059 (pCI + pH). Thus, whatever the pCI or pH, the use of an oxygen cathode is better by 1.23 V. Unfortunately, the kinetics of the evolution of hydrogen is superior to the reduction of oxygen by more than this difference in E ~ values.

12.4 3 CHzCHCN + 2 HzO + 2 e ---+ CN(CHz)zCH(CN)(CHz)CN + 2 OH­ CHzCHCN + HzO -+ HOCHzCHzCN HOCHzCHzCN + CHzCHCN -+ CN(CHz)P(CHz)zCN The most likely explanation is the formation of an anion radical which may react further with acrylonitrile to give the dimer and trimer.

12.5 The rate of production of chlorine = 2500 / (2 x 96 5(0) x 71 X 3 4 z l 10- x 3600 x 24 x 365 = 2.90 x 10- kg m- yr- • Therefore, the number of cells = 2.7 X 108 /9.20 X 10-4/0.21 = 44 330. So 45 cell stacks are needed. 73 Batteries and fuel cells

13.1 Introduction

In the previous two chapters we have seen what can be made with electrical energy, reviewing electrochemical synthesis in Chapter 11 and larger-scale industrial processes in Chapter 12. Now the scene is reversed. We are to look at how to make electrical energy from the free energy of an electrochemical reaction. Consider our old friend, the reaction ~ H2 + t O2 H 20 (13.1) which has a standard electrode potential of 1.23 V and so a free energy change of -1.23 x 2 x 96 487 = -237.4 kJ mol-I. (There are two electrons involved in the reaction. Ifyou do not know why, see Chapters 4 and 8.) If you combine 1 mol of hydrogen and t mol of oxygen, the reaction releases 237.4 kJ. If you have 237.4 kJ, then you can stick it into water and make 1 mol of hydrogen and t mol of oxygen. This is what is at the heart of energy-producing and energy-storing devices (batteries and fuel cells to you and me). In theory any chemical reaction that is exoenergetic (has a negative L1 G) that can be expressed as the sum of two redox reactions may be the basis for a battery. Some are better than others, and that is what this chapter is all about.

13.2 Definitions

A battery is a cell that contains the reactants of an energy-producing reaction within it. Once the reactants have been used up in a primary battery, the battery is dead. In a secondary or rechargeable battery (or, archaically, an accumulator) the reactions are reversible and so, by putting back energy into the lifeless cell, it may be charged up again. These cells may be seen as energy-storage devices. A fuel cell is an energy-producing cell in which the reactants for an

294 Batteries and fuel cells 295 exoenergetic reaction are kept outside the cell and fed to the electrodes as needed. Any products are removed continuously. The reactant that is reduced at the cathode is known as the fuel and the reactant oxidised at the anode is the oxidant. Fuel cell reactants are nearly always gases. Half-way between rechargeable batteries and fuel cells come redox batteries, in which solutions containing transition metal ions are fed to each electrode and a redox reaction generates the working potential. When exhausted, the solutions can be recharged, as in a secondary battery, or disposed of and replaced by new solutions, as in a fuel cell.

13.3 Energetics of batteries

The three major characteristics of an energy-storage device are: (1) the operating voltage; (2) the current that can be drawn at a usable voltage; and (3) how long it will last.

73.3. 7 Cell voltage

The energetics of batteries does not start and end with the value of !i.G. The actual voltage obtained depends on a number of factors, including the overpotentials associated with the reaction, resistance losses in the cell, the concentrations of the electroactive species in the electrolyte and the way that the cell is discharged. !i.G gives the maximum possible potential and it is downhill from there. Figure 13.1 shows the voltage delivered by a Daniell cell as the current is increased. It is seen that the voltage starts at the equilibrium value (about 1 V if the activity of each ion is 1), then falls, eventually reaching zero at some maximum current. The form of Figure 13.1 is typical of all batteries. A consideration of the voltage-eurrent curve for the reactions at each electrode is very instructive, especially if that for the reverse (electrolysis) process is also plotted. This is done for the Daniell cell in Figure 13.2. The cell voltage is the difference between the potentials for each electrode minus the IR drop in the cell. The reactions of the Daniell cell are given below (subsection 13.6.1). Essentially, the cell is a copper half-cell plus a zinc half-cell. Ifthe battery is charged up, as shown on the right-hand current axis of Figure 13.2, the voltage required to

accomplish this (V1N in the figure) increases as the current increases. Using the Daniell cell as a battery is shown on the left-hand side of Figure 13.2. Now, as the current drawn from the cell increases, the available voltage (VOUT) falls until at some point, where the lines cross, no voltage may be measured at all. This is Murphy's Law writ large in electrochemistry. Ifyou want energy out of the system, you get less energy than you might thermo­ dynamically hope for, but if you put energy into the battery to recharge, it costs you more than you thought. Only if the battery were charged and 296 Introduction to electrochemistry

1.0

VIV

OL.- ~:--__.J_ IIAm- 2

Figure 13.1 The voltage of a Daniell cell as a function ofcurrent

v

+0.34

2 cu + + 2e ---4 Cu Cathode

BATIERY ELECTROLYSIS Spontaneous reaction Reaction caused Cu]' + Zn _ Cu + 2n]' by energy in Energy out Cu + 2n 2 ._ Cu 2t + Zn

Figure 13.2 The voltage ofeach electrode of a Daniell cell Batteries and fuel cells 297

Battery research in the 1830s: J. F. Daniell (1791-1845)

Daniell was the essence of the modern Victorian scientist. He was well connected, had a wide interest in all matters of natural philosophy and invented a number of scientific devices that ensure his fame to the present day. As an electrochemist Daniell is known for his cell comprising a zinc half-cell and a copper half-cell, but he also invented a dew-point hygrometer and a pyrometer, investigated ways of defending British ships against lightning and worked on the corrosion of the copper cladding of naval vessels. When Daniell was appointed to the foundation chair of Chemistry at King's College in London, he had never given a lecture in his life and was more interested in meteorology. However, his sister had persuaded the poet Samuel Taylor Coleridge to ask the professor of surgery to ask the members of the selection panel to support Daniell. In spite of the blatant nepotism this represented, Daniell was a success, carrying on a variety of projects. The great Michael Faraday was working at the time at the Royal Institution, and the two exchanged visits and collaborated on the electrolysis of salts. The original Daniell cell is on display at King's College London, and consists of five copper cylinders about +- m tall by 15 cm diameter. Inner tubes of porous pot separated the two half-cells and zinc rods comprised the anodes. These would deliver about 5 V and were used as a source of electrical power for the new electrical telegraph. discharged at equilibrium (Le. with zero current) could the energy in and out be the same. Although Daniell was a good thing for electrochemistry (see Panel), no one would dream of using a Daniell cell for any useful purpose today. Why? The Daniell cell cannot deliver enough current at a reasonable voltage for long enough. The amount of copper sulphate limits the process. The presence of reactants in solution also makes the battery quite un­ wieldy, and the evolution of hydrogen would cause inefficiencies when the cell was recharged. See Problem 13.1. The battery-maker's art is to make the available voltage as near as possible to the theoretical (thermodynamic) one at useful currents. How near he or she succeeds is bound up with the concept of efficiency.

Intrinsic efficiency

There are no Carnot cycle inefficiencies in the operation of a battery or fuel cell. That is because the reaction operates isothermally. However, there 298 Introduction to electrochemistry

may be an entropy change in the reaction, which must be accounted for if the cell is to run isothermally. For example, in fuel cell reactions, where the reactants are often gases and the products liquids, !1S for the reaction is negative and so !1G / !1H is less than 1. This means that to maintain a constant temperature if a cell is operated at -!1G / n F, excess heat is evolved. In terms of the energy that is produced as a fraction of the total enthalpy change of the reaction, the intrinsic efficiency is defined as (!1G / ~ !1H) x 100. Typical values range from about 80% (H2 + 1/2 O2 H20 is 83%) to over 100% if the entropy of the products is greater than the ~ entropy of the reactants (e.g. the hypothetical C + 1/2 O2 CO, E = 124%). In this case running the cell at -!1G/ n F would result in the cell cooling down and heat would need to be supplied from outside. The potential that corresponds to the isothermal reaction is -!1H / n F, and it is known as the thermoneutral potential.

Voltage efficiency (units per cent)

A real battery operates at somewhat less than the theoretical potential because of overpotential and resistance losses. The voltage efficiency is therefore the intrinsic efficiency multiplied by the ratio between the actual

voltage of the cell (Vcell) and the equilibrium voltage. Thus, it is n F Vcell / !1H.

73.3.2 Capacity (units C)

The capacity is the amount of charge that may be delivered by a battery. The theoretical capacity may be calculated if the weight (W) of active electrode material is known: C = n F(W/MW) (13.2) where MW is the molecular weight of the material. The capacity of the battery is determined by the electrode of smallest capacity. In practical devices the capacities of the electrodes are matched. If you have learned nothing while reading this book, at least you will have gained the impres­ sion that the world is an imperfect place. So is it here. The actual capacity of a battery can be much less than the theoretical value. The build-up of reaction products, or physical changes in the electrodes, as the reaction proceeds can mean that not all the available reactive material is utilised. For example, the cathode of a lead-acid battery (see below) makes lead sulphate, which forms an insulating layer around the active lead dioxide, thus curtailing the life of the battery. Batteries and fuel cells 299

13.3.3 Weight factors

Almost every use of batteries would benefit from a reduction in weight, or more energy or power for the same weight. The use of batteries is often in response to the need for portability. A battery car in which the energy generated must move the battery as well as the car must be as light as possible. Size and weight go together. Imagine trying to fit a lead-acid battery into someone's chest to run a heart pacemaker.

Storage density (units C kg-I)

The storage density is the capacity per unit weight of battery.

3 Energy density (units W h kg-I, or W h dm- )

The energy obtained from the battery per mole is n P times the voltage. The amount converted per unit weight is the storage density divided by n P, and so the energy density is the voltage times the storage density. It may be expressed per weight or per volume of battery, depending on what is important in any given application. Energy densities vary from low values of a few tens of W h kg-1 for the lead-acid battery to hundreds of W h kg- 1 for batteries such as metal-air batteries and the sodium-sulphur battery. Table 13.1 gives values of energy densities of some common cells.

Table 13.1 Values of the energy densities of some common cells Cell Energy density I W h kg-1 Energy density I W h dm-3 Lead-acid 22-33 49-83 Nickel-zinc 37-77 67-134 Nickel-cadmium 24-55 61-90 Silver-zinc 55-220 8~1O Cadmium-air 8~9O 14-24 Zinc-air 155-175 Lec1anche 55-77 12~152 Sodium-sulphur 750 (theoretical)

1 Power density (units W kg- )

The power density of a battery is important if a certain rate of energy delivery is needed. For example, to turn a motor car engine over, the starter motor needs to be able to provide about 100 W kg- 1 for 20 s. This is in contrast to the heart pacemaker, which needs only 1 mW kg- 1 but must keep going for years. 300 Introduction to electrochemistry

73.3.4 Energetics of rechargeable batteries

Energy efficiency (units per cent)

The energy efficiency measures the difference between the energy required to charge a secondary battery and the energy delivered by the battery in use. The problem is the same as the one I outlined above with cell voltage. You have to put more in to get less out. This figure depends on the rate of charge and discharge: the faster you want to do anything the more you have to pay. The energy efficiency of a lead-acid car battery is about 60-80%.

Current efficiency (units per cent)

The current efficiency is the ratio between the quantity of electricity obtained from a battery and that used to charge it. These figures are often higher than the energy density because they do not have the voltage term discussed above. The lead-acid battery is, for example, about 90% current-efficient.

Cycle life

A rechargeable battery should, ideally, be able to be discharged partially or completely, then be recharged, and this should be feasible an infinite number of times. In practice this is never so. In designing rechargeable batteries cells are chosen that can be practically reversed. The state of the electrodes, electrolyte, separator must be the same after a charge-dis­ charge cycle as at the beginning. There should be no irreversibility in the electrochemical reactions, the electrodes should not physically change as the electrode material is converted between the oxidised and reduced forms, and there should be no chemical change in any of the components of the cell. In practice there is some deterioration of performance. The lead-acid cell can survive more than 600 deep discharge cycles, but if the battery is kept topped up with charge and never allowed to completely run flat, its lifetime is considerably longer. On the other hand, it is recom­ mended that nickel-eadmium batteries be completely discharged before recharging.

13.4 Economics of batteries

The economics of battery production is based on a trade-off between the requirements of the market and the cost and performance of the battery. Batteries and fuel cells 301

The energy factors discussed above are of major importance. There are some other factors that relate directly to whether a battery is marketable. See Problem 13.4.

13.4. 1 Shelf life

Most batteries must be stored, whether on the shelves of a store or connected but not used in a device. Self-discharge is the term used to describe the loss of charge during storage. Corrosion may be a problem. Most electrolytes are corrosive, and if the electrodes are attacked at all, then deterioration will occur if left on the shelf for several months or years. Direct reaction between the anode and cathode materials may also occur.

13.4.2 Reliability

The reliability of a battery is quoted as the average time between failures. The need for the pacemaker battery to be reliable is somewhat greater than that of the battery in a Walkman.

13.4.3 Overcharge

Once batteries fall into the hands of the consumer, it is not possible to expect that the good burghers of New York or Paris will bother recharging their batteries with the care and precision with which the tests have been done in the laboratory. A battery left on charge may have to suffer the indignity of being accidentally allowed to have a recharging current poked at it for much longer than is really needed to accomplish the job. What happens then may seal the fate of the battery as a useful part of modern society. For many batteries with aqueous electrolytes water will be electrolysed and hydrogen and oxygen given off. This may damage the electrodes or the battery case (if the gases cannot escape) or represent a safety hazard. Lead-acid batteries either are made with vents to allow the escape of gases or are sealed with a catalyst to promote the reverse reaction between the mixed gases.

13.4.4 Economic and environmental factors

The initial cost of a battery is only one economic factor that must be considered. Even this may not be of prime importance if the use is urgent enough (e.g. heart pacemaker). The ease and cost of servicing over a lifetime of a secondary battery is a factor that the buyer must determine, 302 Introduction to electrochemistry while for the producer the availability of raw materials has to be con­ sidered. In recent years the environmental impact of the disposal of primary batteries has been highlighted. With ten batteries per head per year used in the developed world, there are an awful lot of dead batteries containing toxic heavy metals out there. It is proposed that part of the cost of a battery should reflect the environmental damage done by disposal of it.

13.5 Battery design

To be of any use as a suitable vehicle for energy storage and production, an electrochemical reaction must have a theoretical potential of at least 1 V. Thereafter considerations of reasonably fast kinetics come in, followed by the possibility of fabrication, the feasibility of making the reaction work in the confines of a battery case, and, finally, the cost, lifetime and reliability of the design. It is always better to make the cell as compact as possible, to cut down resistance losses between the electrodes. Against this is the need to avoid mixing and premature chemical reaction of the active compo­ nents. As with industrial processes, separators are used only when neces­ sary. They can be simple physical barriers or more sophisticated selective membranes. The active chemicals whose reaction energy is going to pro­ vide the battery voltage are often a paste surrounding a current collector which is an inert metal or carbon electrode.

13.6 Types of battery

Some of the points discussed above will be brought out in the following description of a range of batteries.

73.6. 7 Primary batteries

Daniell cell

Daniell gets in out of my sense of history. The cell is quite straightforward, being a zinc rod dipping into zinc sulphate separated from a copper cylinder containing copper sulphate. The cell reactions are thus

2 Anode: Zn ~ Zn + + 2 e E~ = 0.761 V

2 Cathode: Cu + + 2 e ~ Cu E~ = 0.339 V

2 Cell: Cu + + Zn ~ Cu + Zn2 + E~ = 1.100 V Batteries and fuel cells 303

Notice that the zinc electrode is the anode, because oxidation occurs, even though it is the negative terminal of the battery. because that is where the electrons come out into the outside world.

LecJanche cell

The Leclanche cell was developed in 1880 and has survived ever since, being the cheap 'dry battery' used for torches, radios and the like. Only in recent years is it losing its market share to more modern cells such as mercury or nickel-cadmium batteries. The production of Leclanche cells remains at about 10 billion per year. The cathode is a carbon rod packed about with powdered manganese dioxide, ammonium chloride and carbon made into a paste with the electrolyte, which is concentrated ammonium chloride and zinc chloride. A starch thickener is added, so the battery is quite dry, as its name suggests. The anode is the zinc case of the battery itself, which is separated from the cathode compartment by a cardboard cylinder next to the anode. A small amount of mercury(II) is added, which is reduced on the zinc anode. This protects against corrosion and inhibits the evolution of hydrogen.

Positive ,.._..J;::;:t:=:;--- terminal

Zinc can anode Carbon --h-~~-+­ rod

Paste of

...... -F?-t---Mn02• NH.CI, C.ZnCI2

Negative terminal

Figure 13.3 The Leclanche dry battery 304 Introduction to electrochemlstry

The cell reactions are as follows Anode: Zn -+ Zn2+ + 2 e

Cathode: 2 Mn02 + 2 H20 + 2 e -+ MnO(OH) + OH-

2 Cell: 2 Mn02 + 2 H20 + Zn -+ Zn + + MnO(OH) + OH- In the presence of ammonia a sparingly soluble zinc ammine salt crystal­ lises out: 2 Zn(NH3)~+ Zn + + 2 OH- + 2 NH: -+ + 2 H20 The mechanism of the cell reaction is poorly understood. The cell characteristics are crucially dependent on the manganese dioxide, what crystal structure it has, the crystallite size and the oxidation state of the manganese. The cell yields about 1.6 V and is typically constructed with a capacity of 1-10 A h. It has a good energy density (55-77 W h kg-\ 12(}"152 W h dm-3) and is very cheap to make. However, it has a poor discharge performance, in that the voltage falls continuously during its life, especially if high currents are drawn. See Problem 13.3.

73.6.2 Rechargeable batteries

Lead-acid battery

A family of car batteries have been developed from the pioneering work of Plante in 1860 for starting, lighting and ignition. The lead-acid battery depends on the reaction of lead(O) and lead(IV) to le~d(II) in the following reactions:

Anode: Pb + HSO';- -+ PbS04 + H+ + 2 e E =0.28 V

Cathode: Pb02 + 3 H+ + HSO';- + 2 e -+ PbS04 + 2 H20 E = 1.74 V

Cell: Pb02 + Pb + 2 H+ + 2 HSO';- -+ 2 PbS04 + 2 H20 E = 2.02 V The reactions are reversible. The charge and discharge curves are shown in Figure 13.4. The current collectors are grids of expanded lead plus 5% antimony. The active material is spongy lead and porous lead dioxide, and the plates are separated by glass fibre or microporous plastic. The electro­ lyte is 35% by weight sulphuric acid, with a specific gravity of 1.26. This falls during discharge to 1.1 and provides an easy check on the state of charge of the battery. Lead sulphate, which is produced by both electrode reactions, is insoluble and non-conducting, and it is the build-up of this that limits the available energy that can be extracted from the battery. For example, the Batteries and fuel cells 305

2.6

2.4

> it; 2.2

2.0

DiScharge 1.8

Timelh

Figure 13.4 Charge and discharge curves for a lead-acid battery theoretical energy density is 161 W h kg- 1 but in practice only about 30 W h kg- 1 is achieved. The battery does perform when required, though. Starting a car requires currents of 400 A for 20 s with a voltage of not less than 7.5 V (from six lead-acid cells). When running, the requirements are less intense - about 25 A for 3 h at a voltage not less than 10.5 V. Everyone's considered opinion is that the lead-acid battery must eventually give way to lighter, cheaper batteries with better characteristics. Ultimately the goal is to run the car completely using batteries. However, that day has not dawned and PIante's invention still holds sway.

Nickel-cadmium battery

The nickel-eadmium battery or NiCad is the rechargeable battery of choice for medium- to high-power, long-life applications. The notional cell reac­ tions are Anode: Cd + 2 H20 - Cd(OH)2 + 2 H+ + 2 e Cathode: 2 NiO(OH) + 2 H+ + 2 e - 2 Ni(OH)2 Cell: Cd + 2 NiO(OH) + 2 H20 - Cd(OH)2 + 2 Ni(OH)2

When excess cadmium hydroxide is added, the cells may be sealed so that, if the battery is overcharged, no hydrogen is evolved at the cathode and only oxygen is evolved at the nickel hydroxide electrode. The oxygen is scavenged by cadmium: 306 Introduction to electrochemlstry

r ,",- l ~

CUTAWAY VIEWS OF STANDARD RATE BUTTON CEll

Negative plates Contact spring Cover

Insulator ring Can Separator Positive plates

CROSS-SECTION VIEW-DOUBLE PLATE MOULDED ELECTRODE HIGH RATE BunON CELL

Figure 13.5 Ever Ready sealed nickel cadmium button cell. From T. R. Crompton, Small Batteries, Vo/. 1: Secondary Cells, Macmillan, London, p. 53 (1982)

Cd + 1/2 O2 + H20 -+ Cd(OH)2 An advantage of the nickel-cadmium cell is that it maintains its operating voltage to a high degree of discharge. It is not advisable, how­ ever, to trickle-charge these batteries. They must be allowed to completely discharge before recharging. NiCad batteries can be fabricated in a variety of forms and can be purchased in the full range at present covered by the primary Leclanche cells. One application that has found popular use is the button cell (Figure 13.5). These have low power densities, 0.01-2 A h, and are quite inefficient, but their size and weight have found niche markets in powering electronic devices. Batteries and fuel cells 307

Sodium-sulphur battery

This battery is included as an example of a high-temperature battery involving modern technology. It can in theory achieve an energy density of 750 W h kg-I and, practically, has maintained 150 W h kg-I. If the safety problems of having molten sodium and sulphur in close proximity can be overcome, this battery is seen as the system that will power the electric car. The cell reactions are Anode: 2 Na ~ 2 Na+ + 2 e Cathode: n S + 2 e ~ S~-

~ Cell: 2 Na + n S Na2Sn S~- is the polysulphide ion, where n is about 3. The electrolyte is a solid sodium ion conductor, sodium B-alumina operating at 300-400 QC. The cell develops a voltage of 2.08 V. The design problem is to maintain a discrete distance between the reactants and is usually solved as in Figure 13.6. Molten sulphur containing different amounts of sodium polysulphide

Positive terminal

Negative terminal

H- Fi1m of Carbon --Ho"H---+ sodium rod

I--__ Steel case

Sulphur -++++--

I-'H ~-alumina tube

.,..q.-H---- Carbon felt

Sodium reservoir-...... -::... PHI---- Wick for sodium

Figure 13.6 A sodium-sulphur battery 308 Introduction to electrochemistry

(depending on the state of charge) is contained in a B-alumina tube with graphite felt and central graphite rod acting as current collector. A small gap separates the tube from an outer steel cylinder, which is coated on the inside with a film of sodium. The sodium is maintained by a wick dipping into a lower reservoir of molten sodium.

73.6.3 Redox batteries

In a redox battery the thermodynamically spontaneous reaction of two redox couples is used to generate electricity. The redox couples are held in solutions that are pumped into and through the electrode compartments. When the reactions are complete, energy input into the cells can reverse the couple and recharge the batteries. The iron-ehromium battery relies on the couples Crll / CrIII and Fell / FeIII, with a cell voltage of about 1.1 V and theoretical energy density of 103 W h kg-I. A much better prospect is the vanadium battery. This uses the couples VII / VIII and V 1V / YV, and has a cell voltage of 1.4 V and energy density 135 W h kg-I. Anode: VII ~ VIII + e E = 0.26 V Cathode: VV + e ~ V 1V E = 1.00 V Cell: VII + VV ~ VIII + V 1V E = 1.26 V Carbon felt is used as the electrode material and the reactants are (V02)2S04 and VS04. The cell may be rapidly charged and discharged without damage, and the electrolyte contains a common ion, so there is no problem with cross-contamination between anolyte and catholyte. Because the electrolyte with all the electroactive materials is held separate from the cell, discharged electrolyte can always be removed and bottles of new electrolyte replaced, to give an almost immediate recharging. The energy efficiency of the battery is nearly 90%.

13.7 Fuel cells

The essential attraction of a fuel cell is that its capacity is only limited by the amount of fuel and oxidant available for reaction. If the oxidant is oxygen from the air, then the fuel cell is limited by the available fuel. Most fuel cells use hydrogen as fuel, either directly or by reforming natural or petroleum gas. Possible reactions that could be used in fuel cells, with their ef­ ficiencies, are given in Table 13.2. The history of fuel cells started with William Grove, who, in 1834 (he published in the Philosophical Magazine in 1839), showed that for a series Batteries and fuel cells 309

Table 13.2 Theoretical voltage and efficiency values of some possible fuel cell reactions Reaction e~/v

H2 + 1/2 O 2 -> H20 1.229 83 CH4 + 2 O 2 -> CO2 + 2 H20 1.060 92

CH30H + 1.5 O2 -> O 2 + 2 H2 0 1.206 97

N2H 4 + O2 -> N2 + 2 H 20 1.559 99

CO + 1/2 O 2 -> CO2 1.332 91 of platinum foil electrodes in upturned test-tubes alternately filled with oxygen and hydrogen, a potential was developed that was sufficient to split water into hydrogen and oxygen. A moment's thought may lead you to the conclusion that the experiment was an unusually complicated way to go round in circles. It did, however, demonstrate how electricity interacted with water. He almost had it right but not quite, and when any current was drawn from the cell the voltage dropped nearly to zero. It was recognised, however, that this arrangement had an intrinsically high efficiency compared with the equally new combustion engines. It is interesting to reflect what the world would have been like if the amount of research and effort that has since gone into petrol engines had been put into batteries and fuel cells. That it did not, despite a call to switch from heat engines to electrical engines by the great Ostwald in 1894, is probably due to the imperfect knowledge of the mechanisms of electrochemical processes that persisted until the second half of the twentieth century. The modern interest in fuel cells arose in the 1960s with concerns, not about pollution or the environment or the impending oil shortage, but the desire of President Kennedy to put an American man on the Moon. The Gemini and Apollo craft were powered by liquid hydrogen and oxygen, and so a device that produced electrical energy from these two chemicals was earnestly sought. An Englishman by the name of Bacon (yes, he was a relative of the Elizabethan natural scientist Francis Bacon, and lived in the family home outside London. I met him once) solved the problem, opening the door to the research and cells that were to follow.

13.7. 1 Hydrogen-air cells

Most work has been done on hydrogen-air or oxygen cells, and these will be described in some detail. They may be divided up into four different classes, depending on the temperature of operation. The higher the temperature the better the efficiency, but of course the need to maintain a high temperature has its price. It is still not clear which type of cell, if any, will eventually be mass produced. The reactions of hydrogen and oxygen in alkaline solution are 310 Introduction to electrochemistry

Anode: 2 H2 + 4 OH- ---+ 4 H20 + 4 e E = -0.84 V

Cathode: O2 + 2 H20 + 4 e ---+ 4 OH- E = 0.39 V

Cell: 2 H2 + O2 ---+ 2 H20 E = 1.23 V and in acid

Anode: 2 H2 ---+ 4 H+ + 4 e E = 0.00 V

Cathode: O2 + 4 H+ + 4 e ---+ 2 H20 E = 1.23 V

Cell: 2 H2 + O2 ---+ 2 H20 E = 1.23 V The mechanisms of these reactions are well known (see Chapter 8) and it is clear that the rogue reaction is that of the reduction of oxygen. This is seen in the polarisation curves of hydrogen and oxygen (Figure 13.7). The voltage that might be delivered by a fuel cell is shown.

1.23

1.0

O2 + 4H+ + 4e -+ 2H20

VIV

0.5 1

01-=::::::::....- ---' o

Figure 13.7 Polarisation curve of the hydrogen and oxygen electrodes of a typical low- or medium-temperature fuel cell

The different types of cell attempt to solve the problem in different ways. The low-temperature cells rely on electrocatalysis, the higher­ temperature acid cell on the elevated temperature, and the high-temperature molten carbonate cell and zirconia cell on different reactions. One of the problems common to all fuel cells employing gaseous reactants is how to produce that all-important three-phase interface between gas molecule, Batteries and fuel cells 311 electrolyte ion and electron. We have seen how to do this in Chapter 7. The use of biporous and Teflon-bonded electrodes is de rigeur in fuel cell technology.

Low-temperature alkaline cell

This cell operates at, or just above, ambient temperature, which is a factor in its favour, as is its low cost of construction, but the search still goes on for an anode material that is stable in the electrolyte (5 mol dm-3potas­ sium hydroxide) and has the required activity. Much interest has been shown in conducting metal oxides such as perovskites (e.g. Lao.sSrO.SCo03) and the technology has almost been realised. Although potassium hydrox­ ide is less corrosive than the phosphoric acid used in acid cells, the disadvantages have so far outweighed this advantage. One of these dis­ advantages is that the gases must be free ofcarbon dioxide, which dissolves in potassium hydroxide, forming the less conducting potassium carbonate. This precludes the use of air directly. The low cost of the cell allows for the removal of carbon dioxide within an overall price per kilowatt that is still competitive. Bacon developed two low-temperature cells for the Gemini and Apollo programme - an acid cell with platinum-coated titanium elec-

Anode Cathode

Polystyrene ~H*--+-- sulphonic acid membrane

Pt-coated Water titanium reservoir screen

Figure 13.8 A single hydrogen-oxygen fuel cell designed by Bacon for the Gemini space programme 312 Introduction to electrochemistry trodes sandwiching a solid polymer electrolyte (e.g. Nafion; see Chapter 3), and an alkaline cell with nickel electrodes and potassium hydroxide electrolyte. The present (1990) generation of space shuttles relies on three alkaline fuel cells each delivering up to 436 A at 27.5 V. Power densities of better than 20 kW kg~1 have been achieved for space shuttle alkaline fuel cells. One advantage of a fuel cell for the space programmes was the production of drinkable water (about half a litre per kW h).

Medium-temperature acid cell

The few commercial cells available for small- to medium-power electricity production (about 5 MW) are of this type. The electrolyte is phosphoric acid and the cell operates at 200°C. At 200 mA cm,-2 the cell voltage is 0.67 V. Platinum dispersed on carbon is the catalyst. Nickel has also been used.

High-temperature cells

At a higher temperature still a cell has been constructed based on a eutectic of lithium aluminate, lithium carbonate and potassium carbonate, which is adsorbed into a porous inorganic matrix such as alumina. The cell operates at 650°C and can accept either hydrogen or carbon monoxide as fuel. For hydrogen the cell reactions are Anode: H2 + CO;- ~ CO2 + H20 + 2 e

Asbestos gasket Metal powder electrodes

..+---$ Terminals e

Wire gauze Electrolyte disk Steel container current collectors

Figure 13.9 A molten carbonate fuel cell Batteries and fuel cells 313

CO~- Cathode: 1/2 O2 + CO2 + 2 e _

Cell: H2 + 1/2 O2 - H20 Overall this is the same as the other fuel cells we have seen, but carbon dioxide mediates the reaction. The anode reaction with carbon monoxide as fuel is

CO + CO~- - 2 CO2 + 2 e The advantage of being able to use both hydrogen and carbon monox­ ide is that this is the mixture obtained by steam reforming hydrocarbons. For example, methane reacts over a nickel catalyst:

CH4 + H2 0 - CO + 3 H2 Methane is really quite stable and we despair of ever finding an electro­ catalyst to effect its oxidation directly, so in the meantime reforming the hydrocarbon is the best we can do.

Very-high-temperature cells

A very-high-temperature fuel cell is based on the ability of zirconia to 2 conduct 0 - at temperatures around 1000 °C. Silver electrodes are de­ posited on disks of zirconia/copper oxide and the reaction of the cell is

2 Anode: H2 + 0 - - H20 + 2 e

2 - Cathode: 1/2 O2 + 2 e _ 0

Cell: H2 + 1/2 O2 - H20 We have seen this cell operating as an oxygen sensor in Chapter 10.

73.7.2 Other fuel cells

Although both hydrocarbon and alcohol fuel cells have been demon­ strated, usually with platinum anodes, the exchange currents of the reac­ tions are much lower than those that may be achieved for a hydrogen­ oxygen fuel cell. The oxidation of the fuel tends to be incomplete, leading to a build-up of carbon on the electrode. Also, organic fuels have a deleterious effect on the oxygen electrode, requiring separation of the anode and cathode compartments. Consequently, they have yet to find favour. See Problem 13.2. 314 Introduction to electrochemistry

• PROBLEMS

13.1 Calculate the amount of zinc anode that is required in a Daniell cell containing 2 I of 1 mol dm-3 copper sulphate.

13.2 If the free energy of combustion of propane is -2108 kJ mol-I, calculate the reversible potential of a propane fuel cell and the potential of the propane half-cell.

13.3 If the standard electrode potentials of a zinc-zinc(II) ion half-cell and a chlorine--ehloride ion half-cell are -0.763 V and +1.360 V, respectively, what is the maximum voltage of a cell whose overall reaction is

Zn + Cl2 - ZnCI2 ? How many cells would be required to generate 250 V? If the use of the cells were limited by the storage of chlorine as 1 kg

chlorine hydrate (CI2 .8 H20), what electrical capacity, in kW h, would the stack of cells have?

13.4 It is often required to balance the conflicting requirements of a process in an optimisation of the various factors. Here is a simple example. Suppose a vanadium battery operates with porous carbon electrodes. The effective electrochemical area is given by the volume of the carbon which we write as L (the thickness) x A (the cross-sectional area). The operating voltage is given by V = VO - i R, where i is the current density (= 1/ A) and R is the resistance of the cell = RO + a L / A. (a) Derive an expression for the current at the maximum power in terms of VO and R. (b) If it is desired to minimise the cost of the cell, which is given by cost = A (c + c' L), where c and c' are constants, derive an expression for the optimum thickness of the electrode when operated at the optimum current.

• ANSWERS

13.1 In 2 I of 1 mol dm-3 copper sulphate there are 2 mol Cu. This requires 2 mol Zn, which weighs 2 x 65.4 = 130.8 g.

B B 13.2 We need to determine the number of electrons to use E = -L1G / n F.

The cathodic reaction is the reduction of oxygen O2 + 4 H+ + 4 e _ 2 H20 and the overall oxidation is

C3H g + 5 O2 - 3 CO2 + 4 H 20 We can say immediately that there are 20 electrons from the fact that 5 mol of oxygen are consumed and these come at 4 electrons a throw. Just to reassure you, the equation of the anodic reaction is

C3Hg + 6 H20 - 3 CO2 + 20 H+ + 20 e

6 ~ = - (- 2.108 X 10 ) /20 x 96 500 = 1.092 V. As the oxygen electrode Batteries and fuel cells 315

has ee = 1.229 V, the standard electrode potential of the propane electrode must be 1.229 - 1.092 = 0.137 V.

13.3 The cell voltage is 2.123 V. (If you took the difference of the numbers and forgot the minus sign, go back to Chapter 4. Do not pass go. Do not collect $200.) Therefore, 250 I 2.123 = 118 cells are required. The molecular weight of chlorine hydrate is 71 + 8 x 18 = 215 g. Therefore, 1 kg contains 4.651 mol. The reaction requires 2 electrons and so the charge passed is 4.651 x 2 x 96500 C. At 2.123 V the energy is 2.123 x 4.651 x 2 x 96500 V C. 1 V C is 1 V A s or 1 W s. Therefore, in kW h the energy is 2.123 x 4.651 x 2 x 96 500 I 1000 I 3600 = 0.529 kW h.

13.4 (a) This is easy if you know that P = VI = (VO - i R) I =(VO - IR A) I. At the maximum dP I dI = 0; thus, VO - 2 I RA = 0 or I = VO I 2 R A. (b) We need to obtain A in terms of L and I. From the result in part (a) we have R = VO I 2 I A, which is also = RO + a LI A. Therefore, A = VO /2 I RO - a L / RO. In the expression for the cost = (VO / 2 I RO - a L / R~ (c + c' L). Differentiate with respect to L, to get VO c'l 2 I RO - a eLl RO - 2 c' a L I RO = 0 at the optimum. Cancel RO to give Lopt = VO c'l 2 I a (c + 2 c'). 74 Corrosion

14.1 Introduction

Corrosbn is the process of the spontaneous oxidation of a metal in which the cathodic reaction also takes place on the metal or on a surface in electronic contact with it. It is ubiquitous in the world. The fact that all metals, with the exception of gold, are thermodynamically unstable with respect to oxygen in acid solution means that the writing is on the wall for all our metallic artefacts. The fact that we have to put so much energy into extracting metals from their ores would suggest that at the first opportunity they head back to the stable warmth and comfort of an oxide. The cost of this thermodynamical inevitability is great for modern society. Cars rust away; oil rigs fall over; metals, wherever they are exposed to the atmos­ phere and moisture, suffer eventual degradation. This chapter will explore the world of corrosion and show how a knowledge of the processes involved gives us a chance to delay, if not totally stop, these reactions.

14.2 Electrochemistry of corrosion

I shall develop the idea of corrosion from the familiar Daniell cell that we saw in Chapter 13. Imagine what would happen if a wire was connected between the electrodes. Current would flow as zinc was consumed (cor­ roded) and copper plated (Figure 14.1a). Imagine now making the wire shorter and shorter until the copper and zinc electrodes were connected together in the electrolyte, which now contains only copper sulphate (Fig­ ure 14.1b). The reaction would still proceed. Let us continue our flight of fancy and reduce the coppery bits to minute inclusions in the surface of the zinc (Figure 14.1c), and, finally, let us realise that the copperplating was just a convenient reaction to use up the electrons from the zinc and any other reduction would do - for example, the reduction of oxygen (Figure

316 Corrosion 317

Clean up your silver

A visit to a large Sydney market sees a man offering to the crowd that had gathered a magic metal plate that would clean small articles of silver. 'Ladies and gentlemen, do you hate cleaning silver? Do you fear that rubbing away at your precious jewellery will eventually destroy a treasured heirloom? I have the answer. Take a bowl of water. Clean water, ladies and gentlemen. No nasty chemicals. Add a spoonful of bicarbonate of soda. Now does anyone have a silver ring? Thank you, madam. As you can see, all I do is put this magic metal plate in the water and rub your ring gently against the plate and .. .'. Man takes out of solution a bright and shiny ring. Gohs and aahs from crowd and rush to pay $30 for magic plate. Enter Dr Roy Tasker (chemist and friend of mine). RT: 'What is the plate made of?' Man (in response to several iterations of the question): 'It's magic.' 'It's an alloy.' 'It's an alloy with aluminium.' 'Well, quite a lot of aluminium.' 'Mostly aluminium.' 'Aluminium.' Another friend of mine is a Professor of Marketing, and he saw nothing wrong with a man selling a 50 cent piece of aluminium for $30. For the moment, let us leave the morals of modern business practice and turn to the electrochemistry. Tarnish on silver is largely silver sulphide caused by sulphur from acid rain, sulphurous coals, eggs, and so on. Aluminium, as we know, is well down the electrochemical series. It is only a protective film of aluminium oxide that passivates the metal and allows any aluminium to survive in the world. Remember that aluminium cooking pots should not be used in alkaline solution, because of the formation of soluble aluminates. The bicarbonate is sufficiently alkaline to remove the protective oxide from the surface of the aluminium. Form an electrical contact between silver and aluminium in a suitable electrolyte and the following corrosion cell is set up: Anode: 2 Al ~ 2 AP+(aq) + 6 e Cathode: 3 Ag2S + 6 e ~ 6 Ag + 3 S2-(aq) Cell: 3 Ag2S + 2 Al ~ 2 AP+(aq) + 6 Ag + 3 S2-(aq) Notice that the method is better than rubbing off the tarnish with a cloth and silver polish. This way the silver is restored. Wrapping silver articles in aluminium foil and immersing them in sodium bicarbonate solution for an hour or so works well too, and is much cheaper! 318 Introduction to electrochemistry

e e

e

__Cu + 2 Cu __Cu2+ Cu

Zn2+-- Zn Zn2+-- Zn

e

Zn2+- Zn

(c) (d)

Figure 14.1 The transformation ofa Daniell cell to a corrosion cell: (a) the Daniell cell; (b) the Daniell cell with short wires; (c) zinc with copper impurities in copper sulphate solution; (d) zinc in aerated water

14.1d). What we have arrived at is a credible picture of how zinc might corrode in an aerated solution. At suitable sites on the surface dissolved oxygen is reduced by electrons liberated by the oxidation of zinc. These sites at which oxygen is reduced need not be impurities (although they help). Corrosion can take place on a homogeneous surface if the thermo­ dynamics is right. In practice, however, there are always some sites that are more conducive to reduction.

14.2. 1 Thermodynamics of corrosion

Corrosion is a spontaneous process (that is, it has a negative free energy change). However, unlike the battery, from which useful free energy is produced, the energy released in corrosion is wasted. It is this aspect of corrosion that will allow us to determine under which circumstances a metal would corrode. Corrosion 319

Stability of metals

To determine whether a metal will corrode we need to look for a half-cell that could occur, the electrode potential of which is more positive than that of the metal. Then, using the rules of making electrochemical cells in Chapter 4, this half-cell would become the cathode and the metal would be oxidised at the anode. The only two candidates for the job are water, which is reduced to hydrogen:

2H20+2e-H2 +20H- (14.1) or oxygen, which is reduced to water:

O2 + 2 H2 0 + 4 e _ 4 OH- (14.2) The copper half-cell that I started with is not a possibility. People do not come round and throw buckets of copper sulphate solution over my car. It can rust quite happily in the wet aerated conditions that it sits in every day. Notice that in comparing the electrode potentials we need to know the concentration of metal ions if they are released into solution, the concen­ tration of oxygen if that gas is being reduced and the pH, as the potentials of both reductions depend on the concentration of H+ or OH-. In addi­ tion, if the metal finds itself in a solution containing ions with which it can complex (most often this is chloride from brine), then corrosion will be enhanced. It was a Frenchman called Marcel Pourbaix who embarked on a mammoth project to determine the limits of stability of all metals. The resulting text (Atlas ofElectrochemical Equilibria in Aqueous Solutions) is the starting point for many considerations of the most stable form of an element.

Pourbaix diagrams

A Pourbaix diagram is a graph of potential against pH and shows on it the limits of stability of different compounds of an element containing the element, hydrogen and oxygen. (When chloride and other ions are con­ sidered, the stability of complexes of these ions is also included.) Super­ imposed on every Pourbaix diagram are the lines depicting the equilibrium potential of the half-cells given in Equations (14.1) and (14.2). Figure 14.2 shows the Pourbaix diagram of nickel. The oxygen and hydrogen lines represent the Nernst equation applied to Equations (14.1) and (14.2), Le. E = -0.059 pH (14.3) E = 1.23 - 0.059 pH (14.4) To see how these equations are derived, see Problem 4.4. 320 Introduction to electrochemlstry

2.0

O2 + 4H+ ---- +4e~2H 1.0 --__ 20---

> i:iJ 0 2H+ -- -.:!: 2e~H2 Ni(OHb 1------_-_-~'_"~~~NiO HNiO; --- Ni --- -1.0

o 2 4 6 8 10 12 14 pH

Figure 14.2 The Pourbaix diagram ofnickel

The limit of stability of a species in solution (e.g. NF+) is arbitrarily 6 3 defined as 10- mol dm- • Thus, the horizontal line in Figure 14.2 separating Ni from NF+ is obtained from the Nernst equation, for NF+ + 2 e ;= Ni (14.5)

E~ 2 that is, E = + 2.303 RT / 2 F 10glO(CNi +) (I am afraid activities have been ignored yet again) = -0.25 - 0.03 x 6 = -0.43 V. The line is horizontal because pH has no effect on the stability. In the case of the divide between NF+ and NiO, the vertical line at around pH 9 indicates that the equilibrium does not involve a net electrochemical reaction and so potential has no effect on the stability:

NiO + 2 H+ ;= NF+ + H20 (14.6) A Pourbaix diagram is used to determine the limits of stability of a metal by observing the relationship of the region on the diagram inhabited by the metal to the lines for oxygen and hydrogen. In the presence of oxygen there is no pH at which nickel is stable. If oxygen is excluded, nickel metal could just hold out at pH > 9, where there is a tiny region in which nickel exists above the equilibrium line for hydrogen. 'Hang on', I hear you say. 'Why, then, is there any nickel remaining in the world?' There is, because the thermodynamically spontaneous reaction indicated by the Pourbaix diagram is held up by the kinetics of the process. As it happens, nickel passivates, with the layer of oxide on the surface protecting the rest of the metal from further attack. So before you ask what is the value of Pourbaix diagrams at all, let me tell you that thermodynamic spontaneity is a necessary condition for corrosion (it does not happen without a healthily negative L1G), but to know whether a thing corrodes at

------~------Corrosion 321

a reasonable rate we must understand the kinetics of corrosion too. See Problem 14.1.

74.2.2 Kinetics of corrosion

In discussing the kinetics of corrosion, we bring to bear all the electro­ chemistry we have learnt so far about mechanisms, electrocatalysis, electrolytes, and so on. We need to identify the limiting step in the corrosion process, as it is there that we may make most headway in protecting materials from corrosion. Remember that the rate of corrosion is simply given by the current, and so our attention must be directed to this quantity. First a note about how corrosion rates are expressed.

Corrosion units

Real people who worry about corrosion have developed a number of practical ways of defining corrosion rate. Some of the more popular are: thousandths of an inch per year (mpy); milligrams per dm2 per day (mdd); and millimetres penetration per year (mmpy). To give you an idea, a corrosion current of 8 ~A cm-2 on steel is 20 mdd. It is possible to interconvert from one system to another if the density of the material is known.

Corrosion potential and current

In defining the corrosion potential, we must realise that the potential between the cathodic and anodic sites on a corroding metal can be virtually zero. When we shorted the Daniell cell with a wire, we were tying the potential of the cathode to that of the anode. The cell voltage is zero (the case when there is a substantial resistance between anode and cathode is treated later), but the metal can still have a potential that may be measured with respect to an external reference electrode. It is this potential that is known as the corrosion potential. In more general terms, when more than one electrochemical reaction occurs at an electrode the potential is known as a mixed potential. This is illustrated in Figure 14.3. The corrosion current will be limited and so defined by the slowest step in the cycle of electrode reactions. The candidates for this are:

(1) The electron transfer reaction at the anode. (2) Migration or diffusion of ions and neutral species through the electrolyte. (3) The electron transfer reaction at the cathode. 322 Introduction to electrochemlstry

Reference electrode

Figure 14.3 Illustration of the corrosion current and corrosion potential

Because we are not dealing with nice 1 cm2 electrodes, the area available to the reactions may be vital to rate of corrosion, as we shall see in some of the practical examples later on. Forgetting for a moment what is happening in the electrolyte, consider what happens when the electrodes of our Daniell cell are shorted together. Just before this happens, the copper electrode is sitting at a potential of around +0.34 V (versus SHE) and the zinc is at -0.76 V. When they are connected together and current flows at an ever-increasing rate, the copper 2 potential falls as Cu + is reduced to Cu, and the zinc potential rises as Zn is 2 oxidised to Zn +. The steady state situation is when enough current is flowing to make the potentials at each electrode equal. This potential is the corrosion potential.

Evans diagrams

A neat way of showing the corrosion potential and current and how they are affected by changing the conditions was suggested by Evans. If the curves of voltage against current for the anode and cathode reactions are displayed on the same graph and in the same quadrant (Le. take no notice of whether the current is anodic or cathodic), where they cross gives the corrosion current and voltage. The logarithm of the current may also be used, giving a Tafel plot (see Chapter 6) of the electrode reactions. The curves in Figure 14.4 may lead you to suppose that the corrosion voltage is about half-way between the equilibrium potentials of anode and cathode. This is only the case if the current versus voltage curves for each are symmetrical. The effect of different electrochemical parameters on corrosion is best seen in relation to the cathodic reaction. Let us fix the Corrosion 323

'CO" log 'con log (I)

Figure 14.4 Evans diagrams for a simple corrosion process plotted with (a) current and (b) log (current) abscissae anodic reaction as the oxidation of zinc. There are three parameters that could change: the equilibrium potential (i.e. if there is a different cathodic process); the exchange current (different electrocatalysis, surface area, concentration of reactant); and the transfer coefficient, a (the mechanism of reduction). Figures 14.5-14.7 show each of these in turn. Having avail­ able a cathodic reaction with a much more positive equilibrium potential (for example, the reduction of oxygen instead of the reduction of water to give hydrogen), should lead to an enhanced corrosion current and higher corrosion potential (Figure 14.5). Note that this is not always the case. If the kinetics of the reduction of oxygen is very slow, hydrogen may still win out, even though it starts from behind the thermodynamic eight ball. A higher exchange current (Io) brought on by better kinetics (for example, in the unlikely event of platinum impurities in a surface the evolution of hydrogen would be considerably enhanced), a greater avail­ able surface area for reduction or a greater concentration of reactant (e.g. oxygen) pushes out the intersection of the lines and, hence, gives a greater rate of corrosion. If the Tafel slope increases, the point of intersection again moves to higher corrosion currents. Often the currents are not governed by the electron transfer but are diffusion-limited. This is indicated by a vertical line on the Evans diagram. The effect ofdifferent limiting currents is shown in Figure 14.8. Another observation that may be made from looking at the Evans diagrams is that the corrosion potential winds up nearest the equilibrium potential of the most active electrode. Finally, if there is an appreciable resistance between the anodic and cathodic sites, then the potential required to drive current through that 324 Introduction to electrochemlstry

1.23

v

o~-..----_--...... ",c....--....4--

-0.7

Figure 14.5 Evans diagrams for the corrosion of zinc in the presence ofair (cathode reaction is the reduction of oxygen) and the absence ofair (cathode reaction is the evolution of hydrogen)

1.23 r--_.--__

v 0 1------4---r--~,....,...c:...... ---__ log (I)

-O.7L----

Figure 14.6 Evans diagrams for the corrosion of zinc, showing the effect of

increasing the exchange current of the cathodic reaction. 10 ([,) > lo(a) Corrosion 325

1.23 r--__.....

v

ol------.--J~--_+----- log (I)

-0.7

Figure 14.7 Evans diagrams for the corrosion of zinc, showing the effect of increasing the transfer coefficient of the cathodic reaction. a(a) > a(b) resistance must be allowed for in constructing the Evans diagram. This situation may arise if the anodic and cathodic sites are widely separated and there are no handy ions to act as electrolyte. The Galvani potential difference between metal and solution is now different at anode and cathode because the solution potential has changed by an amount of [ R, where [ is the corrosion current and R is the resistance of the solution. This is shown in Figure 14.9.

Calculation of corrosion potential and current

The most simple case is when one reaction is diffusion-limited (see Figure 14.8). The corrosion current is the diffusion-limited current of that reaction and the corrosion potential is given by the potential of the other (non­ limiting) reaction at that current. In the example of Figure 14.8, if the corrosion of zinc is in the Tafel region and the limiting current of oxygen reduction is [lirn, 02'

O )- 11 = L1epcorr - L1epe = RT / a Fin (llirn, 2 RT / a Fin (10) (14.7) 326 Introduction to electrochemistry

v

o~---+---+------,,,L------

-0.71----....,..-

Figure 14.8 Evans diagrams for the corrosion of zinc when the cathodic reaction is diffusion-limited at different values of IUm - I'im(a) > llim(b)

1.231--_~

v

log (I)

-0.7

Figure 14.9 Evans diagrams for the corrosion of zinc when there is a resistance (R) in the electrolyte Corrosion 327

or the corrosion voltage measured against a suitable reference electrode is Vcorr = t14>corr - t14>ref = t14>e + RT / a Fin (Ilim, 0) -RT / a Fin (Io) - t14>ref (14.8) If both electrochemical reactions (designated a for anodic and c for cath­ odic) are given by the Tafel equation, we obtain two equations in two unknowns: "a = t14>corr - t14>e,a = RT / aa Fin (Icorr) - RT / aa Fin (Io,a) (14.9) "C = t14>corr - t14>e,c = -R T / ac Fin (Icorr) + RT / ac Fin (Io,c)(14.10) Note that the cathodic Tafel equation has a minus sign in it. Expressions for I corr and t14>corr are thus

_ Ta T ( [aa + acl F [t14>e,a + t14>e,cl ) C (14.11) Icorr - 10,a 10.c exp RT

aat1 4>e,a + act14>e,c RT (/o,c) (14.12) t14>corr = + In aa + ac (aa + ac)F lo.a These rather formidable equations are easier to cope with in the case in which aa = ac = 0.5, In this case the corrosion voltage is the mean of the equilibrium voltages of anodic and cathodic reactions plus RT / F In (Io.c / I o.a). Ifthe exchange current of the cathodic reaction is greater than that of the anodic reaction, the logarithm is positive and the corrosion potential moves in the direction of the cathodic equilibrium potential. If lo.c < lo.a, then the corrosion potential moves in a negative direction, Le. towards the anodic equilibrium potential. See Problems 14,2 and 14.3.

Corrosion rate meters

It is possible to buy so-called corrosion rate meters that estimate the corrosion from a measurement of the corrosion voltage and the low-field approximation to the Butler-Volmer equation, which gives

d I = I (;c + ;a ) (14.13) d corr 1: 1: " \Oc\Oa in which ;c is the Tafel slope for the cathodic reaction (R T / acF) and ;a is the Tafel slope of the anodic reaction. 328 Introduction to electrochemistry

74.2.3 Passivation

I have already alluded to the fact that metals do not always vanish in a puff of rust at the first opportunity because of a thin layer of oxide that initially forms on the surface and then protects the underlying metal from further reaction. This is called passivation. The phenomenon was observed in the last century when, to everyone's surprise, iron was observed not to corrode in concentrated nitric acid when it fair fizzed away in dilute acid. Concen­ trated nitric acid is such a good oxidising agent that it forms a protective passive film. The current against voltage curve for a metal that passivates is shown in Figure 14.10. When a metal such as iron is moved away from its equilibrium poten­ tial in an anodic direction, it begins to corrode, giving different species of iron(II) (e.g. Feu, Fe(OHt, Fe(OH)z)' The current increases to a maxi­ mum quite in accordance with what we would expect, having read Chapter 6. Suddenly, however, the current, instead of increasing with voltage, falls to a very small value. The passivation potential is the potential at which this collapse occurs and the Flade potential is the potential when the low current is finally established. Not all metals passivate, even if oxides are formed. The oxide film, which is a few hundreds of nanometres thick and

Passivation potential l

O2 evolution + breakdown of film

v Figure 14.10 Graph of the steady state current against potential ofa passivating metal Corrosion 329

Table 14.1 Passivation potentials of some metals at 25°C and pH = 0 Metal Passivation potential vs SHE Titanium -0.24 Chromium -0.22 Nickel +0.36 Silver +0.40 Iron +0.58 Platinum +0.91 Gold +1.36 which grows with increasing potential, must not allow electrolyte to pene­ trate to the metal underneath. Table 14.1 gives some passivation potentials of metals in acid solution. At high anodic potentials the current increases once again.

14.3 Examples of corrosion

Corrosion is a practical sort of phenomenon and it is often the practical realisations of it that give interesting electrochemistry. It is unlikely that every single bit of a metal object will corrode equally as quickly. The study of practical examples is thus not so much whether an object is going to corrode (the answer is invariably yes) but where this might happen. The following examples of local corrosion also show that Murphy's Law is alive and well and at work in the world.

74.3. 7 Corrosion at cracks

It has long been known that flaws in metals, be they impurities or physical blemishes, seem to enhance the rate of corrosion. Consider a crack in a piece of metal (Figure 14.11). By capillary rise, if nothing else, the crack will accumulate moisture at its tip. If oxygen reduction is the favoured cathodic reaction, the concentration of oxygen will be lowered as dissolved gas is reduced and the slowness of diffusion down into the confined space of the crack tip does not allow its replenishment. This is no great problem, because oxygen can be reduced anywhere on the available surface - at the mouth of the crack, for example. The anodic reaction, the dissolution of metal, therefore takes place at the apex of the crack and so causes its propagation. Metallurgical stresses at the crack tip also provide energy to help the corrosion along. If hydrogen is evolved as the cathodic reaction this may occur in the 330 Introduction to electrochemistry

Air

01'-./2 QW Solution

Figure 14.11 Corrosion at a crack in a metal crack itself, which usually has a pH of around 4 whatever the pH of any medium the metal finds itself in (why?). Hydrogen embrittlement (see below) then becomes a possibility. Measurement of pH and potential gives a point on a Pourbaix diagram that may be used to determine whether corrosion or hydrogen embrittlement is likely to occur.

74.3.2 Corrosion at scratches

Scratches in painted metal

Have you ever wondered why even the smallest chip in the paint on your car goes rusty in no time at all, followed by more and more of the paint lifting off? Electrochemistry has the answer, which is informed by similar considerations of where the most likely place for reduction ofoxygen is and then where the metal will corrode. Figure 14.12 reveals all. Most chipped

Solution

Figure 14.12 Corrosion at a paint chip Corrosion 331 paintwork is open to the atmosphere, and the maximum concentration of dissolved oxygen will be right in the middle of the film of moisture covering the chip. Oxidation ofiron will be relegated to the edges of the chip. As the corrosion proceeds, the paint around the chip loses the metal it was standing on and so the area of the chip grows.

Scratches in metal coatings

A coating of one metal on another is often used, either to minimise the amount used of an expensive metal by coating it on a cheaper one (e.g. silver plate) or to protect an underlying metal (e.g. galvanising using zinc). What happens is governed by which metal (the coat or the underlying metal) is most likely to corrode. In the case of zinc plate on steel, a scratch in the zinc exposing the underlying steel does not lead to corrosion of the steel. Oxygen can be reduced on the steel, but the anodic reaction is still the more favourable oxidation of zinc. Tin plate, on the other hand, is more electropositive, and a scratch will cause iron to dissolve with the tin, acting as the cathode for oxygen reduction.

(a)

(b)

Figure 14.13 Corrosion at a scratch in metal coatings: (a) zinc on steel; (b) tin on steel 332 Introduction to electrochemistry

74.3.3 Corrosion from a difference in oxygen concentration

Some of the examples given above can be seen as corrosion-driven by a difference in oxygen concentration (for example, corrosion in cracks). It is interesting to reflect on the fact that much corrosion occurs because of where oxygen is rather than the availability of metal to corrode. One more case explains why corrosion often occurs at joins between two pieces of metal, even if they are the same metal. The join (Figure 14.14) will harbour electrolyte depleted in oxygen. Hence, the preferred anodic site

Figure 14.14 Corrosion at the join of two pieces of a metal will be in the join, and this is where metal will corrode. Another example comes from the corrosion of structures standing on metal piles driven into the ground or, even worse, into the sea-bed. The oxygen concentration falls rapidly going from the air into the ground. A metal leg will therefore corrode just under the surface of the ground, while the upper part will act as a cathode. Metal parts dipping into the sea will corrode at the furthest from the surface, where the oxygen concentration is lowest. Corrosion in heat exchanging pipes can occur under the loose scale that develops. Again there is a difference in oxygen concentration between areas with and without scale, and corrosion results.

74.3.4 Corrosion at the contact of different metals

The situation of two different metals in contact is even worse. The choice of anodic and cathodic sites is no longer left to chance. The more electro­ positive metal will survive and become the cathode at which oxygen is Corrosion 333 reduced or hydrogen evolved, while the luckless electronegative metal will corrode away. The way this can be turned to advantage in cleaning silver is disc1Jssed in the panel.

14.4 Corrosion protection and inhibition

14.4. 1 Protection by applied potential

Cathodic protection

As the potential becomes more negative, the current for the oxidation of a metal becomes less. This is a fundamental statement ofwhat happens when the potential of a half-cell is moved away from equilibrium (see Chapter 6). Therefore, to slow down corrosion, the potential of the corroding metal must be made more negative. This may be done directly using a battery or indirectly by connecting the metal up to another, more electronegative, metal that will corrode instead. In the latter case the second metal acts as a sacrificial anode. How these two examples of cathodic protection work is shown in Figure 14.15. The potential that is applied to the metal must be less than the corrosion potential, and if it is less than the open-circuit potential of the metal, then corrosion will be totally prevented. The cost is in the current that must flow to maintain the voltage. This current is supplied by the battery. The metal of a sacrificial anode must be more likely to corrode. When it does, although the corrosion rate (of it, not the protected metal) is greater, the corrosion potential is more negative than previously experi­ enced by the protected metal corroding away without the benefit of the sacrificial anode. The effect on the protected metal (don't forget the sacrificial anode is in electrical contact with it) is to lower its corrosion rate. Again you never get something for nothing. The total rate of corrosion has gone up, but now it is the corrosion of a metal you do not want rather than one you do. In practice, sacrificial anodes of scrap iron are used to protect oil pipelines. These are buried along the length of the pipe. Zinc strips are also bolted to the sides of ships. In fact galvanising using a zinc coat is precisely a form of cathodic protection. See Problem 14.2.

Hydrogen embrittlement

A blot on the cathodic protection horizon comes when in an excess of zeal the material has been made too negative and the cathodic reaction be­ comes the evolution of hydrogen. This can happen quickly if oxygen 334 Introduction to electrochemistry

1.23~--....

v

o1------;;1£------"\!--­ log In

V I-__~~ -:-:-----~r--- cp

V.. I--__~

Figure 14.15 Cathodic protection: (a) Evans diagram showing the lowering or elimination of corrosion by an applied potential; (b) Evans diagram showing the effect of a sacrificial anode reduction is limited or if the pH is low. As we saw in Chapter 8, hydrogen is evolved by a mechanism in which the first step is the discharge of a proton on the surface of the electrode to give an adsorbed hydrogen atom:

~ H20 + e Hads + OH- (14.14) I spent some time in Chapter 8 developing the possibilities for what happens next, but did not let on that for some metals (including iron), if the hydrogen atom hangs around for long enough, it can, because of its exceedingly small size, burrow into the metal. Small amounts of hydrogen atoms can sit quite happily in the lattice ofthe metal. This itself does not do Corrosion 335 a lot for the strength of the lattice, but it can get worse if there are small voids in the metal that can accumulate hydrogen gas. The pressure that is generated is huge and enough to propagate a crack in the metal, causing catastrophic failure. See Problem 14.2.

Anodic protection

Anodic protection is possible if the metal passivates. The potential of the metal is raised quickly past the Flade potential and into the region in which the metal corrodes only very slowly. It may be that the metal is naturally passive at the corrosion potential (Figure 14.16a). If it finds itself in the active corrosion region, then its potential must be made more positive until it passivates (Figure 14.16b). With any luck, the passive film will be permanent, as happens with aluminium.

01------+----.+---\------log (I)

Figure 14.16 Anodic protection. Evans diagrams (a) for a metal that is naturally protected, (b) for a metal requiring the application of a positive potential 336 Introduction to electrochemistry

74.4.2 Protective coatings

A passive oxide film described in the last section is an example of a protective coat. As well as an electrochemical method (this is known as anodising), the oxide layer can be generated by chemical oxidation (for example, with dichromate) or by adding small amounts of an alloying electropositive metal (e.g. copper or palladium in steel) that will provide cathodic sites to set up a cell that drives the metal to passivate. Reaction of steel in phosphoric acid leads to a coat of a complex phosphate that provides good protection. Paints or polymers that form sturdy and continuous coats prevent corrosion by excluding air and moisture from the metal. However, we have seen what happens when local chips or scratches occur so these must be used with caution.

74.4.3 Additives and inhibitors

For metal articles that are to be in contact with a solution, small amounts of additives that do not affect the quality of the medium can have desirable consequences for corrosion. The removal of dissolved oxygen is clearly desirable, and this may be done by purging with oxygen, by pumping the air above the liquid or by the addition of reducing agents such as sulphite ions or hydrazine. Organic additives that are adsorbed at the corrosion potential can inhibit either the anodic or cathodic reactions. The action of inhibitors may be to physically block sites on the surface, or they may enter into reactions with the surface to produce an inactive layer.

• PROBLEMS

14.1 From the information given below construct the Pourbaix diagram for nickel. What is the most acidic solution that nickel may exist in without corrosion (a) in an oxygen-saturated solution and (b) in deaerated solution?

Reaction E~/V Nj2+ + 2 e ;= Ni -0.25 Ni(OH)2 + 2 H+ + 2 e ;= Ni + 2 H20 +0.11 Ni 30 4 + 2 H20 + 2 H+ + 2 e ;= 3 Ni(OH)2 +0.73 3 Ni20 3 + 2 H+ + 2 e ;= 2 Ni30 4 + H20 + 1.305 2 Ni02 -+ 2 H+ + 2 e ;= Ni20 3 + H20 + 1.434 2 Ni30 4 + 8 H+ + 2 e ;= 3 Ni + + 4 H20 + 1.977 Ni 20 3 + 6 H+ + 2 e ;= 2 Ni2+ + 3 H20 + 1.753

Ni02 + 4 H+ + 2 e ;= Nj2+ + 2 H20 + 1.393 Corrosion 337

Reaction Solubility

Nj2+ + 2 H20 ;= Ni(OHh + 2 H+ -pcN ?+ = 12.2 - 2 pH Ni(OH)2;= HNiO; + H+ -PCHNiO = i -18.2 + pH

14.2 Iron corrodes in deaerated water at pH 2.8 to give a solution that is 0.01 3 2 2 mol dm- in Fe +. 10 for the oxidation is 0.01 A m- , the tr

14.3 Calculate the corrosion current for the previous example and determine 2 1 the corrosion rate of iron in kg m- yr- •

14.4 A pore inside a metal will crack if the pressure in the pore exceeds a critical value given by (16 Y Y / 3 d)ll2, where y is the surface energy of the metal, Y is Young's modulus and d is the diameter of the pore. If the corrosion potential at a sample of iron is -0.15 V (versus SHE), with the cathodic process being the evolution of hydrogen, determine whether or not the iron would be disrupted by hydrogen embrittlement. Y = 1.2 X 1011 N m-2; y = 1 N m-\ d = 1 IA-m. (Assume equilibrium and calculate the pressure of hydrogen that would give a potental of -0.15 V.)

14.5 At what pH will copper corrode in the presence and absence of air?

• ANSWERS

14.1 The diagram is constructed by plotting the lines of E against pH for the electrochemical reactions and vertical lines of solubilities between species. Potentials are calculated at a concentration of nickel ions of 1O-{; 3 mol dm- • See Figure 14.2. (a) In the absence of air the cathodic process is the evolution of hyd­ 6 rogen. The E of the nickel half-cell = - 0.25 + 0.059/ 2 log (10- ) = -0.427 V. Equating this to the potential of the hydrogen electrode, -0.427 = -0.059 pH, which gives pH = 7.26. Look at Figure 14.2 and you will see that the dotted hydrogen line crosses the Ni / Ni2+ line at about pH 7. (b) In the case of oxygenated electrolyte, the oxygen line is always above the Ni line, so nickel should always corrode. However, if NiO passivates the metal Ni should be protected between about pH 9 and 2 pH 12. Specifically if PCNi2+ = 6, then for Ni + / NiO gives pH = (12.2 + 6) / 2 = 9.1. HNiO; is soluble in alkali, so for PCHNiOi = 6; pH = 18.2 - 6 = 12.2. 338 Introduction to electrochemistry

14.2 We must equate the corrosion current of iron to the hydrogen current.

First calculate the rest potentials of each reaction. For iron EFe = - 0.66 + RT /2 F In(O.Ol) = - 0.60 V and for hydrogen EH = - 0.059 pH = - 0.165 V. Therefore Icorr = 0.01 exp {0.5 F / RT [Ecorr - (- 0.6O)]} = 0.05 exp {-2 RT / F [Ecorr - (-0.165)]). The rest, as they say, is algebra. I make Ecorr = - 0.39 V. For the iron to be protected the

potential must be lowered to EFe , i.e. - 0.6 V. This would require a hydrogen current of 0.05 exp {-2 RT / F [- 0.60 - (-0.165)]} = 0.051 A m-z.

14.3 The corrosion current is obtained by substituting the corrosion potential in either expression. It comes to 0.005 97 A m-z. Therefore, the rate is 3 7 z 1 0.00597/2 F x 55.9 X 10- x 3.154 X 10 = 0.0545 kg m- yr- •

6 8 14.4 The critical pressure is (16 x 1 x 1.2 X 1011 / 3 X 10- )112 = 8 X 10 N m-z or 7900 atm. This sounds high enough but let us now calculate the pressure of hydrogen in the pores. If the potential of the electrode is - 0.15 V this can be equated to - RT / 2 Fin pHz. s Therefore, pHz = 1.2 x lO atm. This does not look good for the pores.

14.5 Corrosion is taken to occur when the concentration of metal ions exceeds 3 10--6 mol dm- • Therefore, the potential of the copper electrode (~ = +0.34 V) that the oxygen or hydrogen line must exceed is + 0.34 + 0.030 x (- 6) = 0.16 V. The first point to note is that copper cannot dissolve in aqueous media, for which the cathodic process is the evolution of hydrogen. The oxygen potential reaches here when 1.23 - 0.059 pH = 0.16, or pH = 18.1! This is a meaningless calculation, as copper ions would not survive intact in high pH solutions. If we knew the solubility product of Cu(OH)z, we could calculate the pH at which ccu2+ was equal 6 3 to 10- mol dm- • Copper mostly corrodes by the formation of copper chloride complexes (verdigris), which adds even further complexity to the problem.