J. Chem. SOC., Faraday Trans. I, 1984,80, 781-788 Square-wave Amperometric Monitoring of Reaction Rates BY BRIAN G. Cox* Chemistry Department, University of Stirling, Stirling FK9 4LA AND WOJCIECH JEDRAL* Chemistry Department, Warsaw University, 02-093 Warsaw, Poland Received 25th May, 1983 The application of square-wave amperometry, an analytical technique involving the use of two indicator electrodes polarized by a square wave, in the determination of reaction rates is described. Kinetic measurements have been made on the bromination of anisole in aqueous solution. Square-wave amperometry in conjunction with a stopped-flow apparatus equipped with Pt electrodes in the observation tube was used to monitor the disappearance of bromine in dilute solutions. Reaction rates with half-lives down to ca.5 ms can be measured using relatively high-frequency square waves (ca. 800-1000 Hz). The results are in good agreement with values measured spectrophotometrically at higher bromine concentrations. The rate of dissociation of Ag+ from its macrobicyclic cryptand 21 1 complex was also measured, using a pair of silver indicator electrodes. Free Ag+ may be monitored selectively in the presence of its cryptate complex by using a low-amplitude square wave (& 150 mV). The advantages and limitations of the amperometric technique for kinetic measurements are discussed. Square-wave amperometry is potentially a very useful technique for conventional analytical applications and for monitoring reactions over a wide range of reaction rates.l The principle of the method is illustrated in fig.1. When an alternating potential [fig. 1 (a)] is applied to a pair of identical polarizing electrodes immersed in a solution containing a suitable reversible redox couple (e.g. Br2/Br-) the resulting current is the sum of the faradaic current and the capacitance or charging current [fig. 1 (b)]. The capacitance current depends upon the rate of change of potential, dE/dt, and with a square-wave potential a large capacitance current is observed immediately following the change in sign of the polarizing potential. This current decays rapidly during the time of constant polarizing potential. The faradaic current requires the presence of both (or all) species involved in the electrode reaction and depends upon the concentration of the limiting reagent governing the electrode reactions, e.g.Br, in the presence of excess Br- (anode : Br- + $Br2 + e ; cathode : $Brz + e + Br-). The faradaic current also decays with time, owing to the depletion of depolarizer (Br, in the above example) in the vicinity of the electrode, but more slowly than the capacitance current [fig. 1 (b)]. It remains at a significant level prior to change in sign of E, and if the current is sampled at the end of each square-wave period [fig. 1 (c)] the measured value will be predominantly equal to the faradaic current. Both the capacitance and faradaic current depend upon the amplitude of the applied alternating potential. Full details of the technique have been discussed ear1ier.l A major advantage of the square-wave method over conventional d.c.amperometric methods is that when the square-wave potential is symmetrical (i.e. no d.c. bias is present) the measured current is independent of stirring. This is essential for use in 78 1782 MONITORING OF REACTION RATES (4 + .+ kg 0 I I I I I I time I (cl I I time Fig. 1. (a) Square-wave signal, generator output; (b) square-wave signal, cell output: (-) total current, (. . . . .) capacitance current; (c) delay (id) and sampling time (2,) of measuring circuit . conjunction with techniques which require measurements on still solutions. For example, in the stopped-flow technique measurements are made on virtually still solutions, generated by stopping rapidly flowing solutions just after mixing. The use of high-frequency square waves should, in principle, allow very fast reactions to be monitored.In practice, however, the usable frequency range will be limited by the decay of the capacitance current, because of an increasingly high background level relative to the faradiac current as the frequency increases. It is also possible that the establishment of a steady current proportional to the depolarizer concentration will take a finite time and hence influence the observed kinetic behaviour. The present paper describes a study of the use of the square-wave amperometric method to monitor the bromination of anisole in aqueous solution with an all-glass stopped-flow apparatus containing a pair of Pt electrodes in the observation tube. Reactions with half-lives down to ca. 5 ms could be followed using square-wave frequencies of up to 800 Hz.This is very close to the lower limit (1-3 ms) possible from rapid-mixing techniques, the application of which has until now been limited almost exclusively to reactions that may be followed using optical or conductimetric detection. The application of the method to monitoring free Ag+ in rapid equilibrium with its complex (cryptate) with the macrobicyclic cryptand 21 1 ligand (cryp) (I) has also been studied using two Ag electrodes: kP Ag+ + cryp t Ag(cryp)+. kdB. G. COX AND W. JEDRAL 783 It was found that Ag+ may be measured selectively in the presence of its cryptate complex, and this has been used to monitor the rate of dissociation of Ag+ from Ag(cryp)+ on the addition of excess acid : H+ Ag(cryp)+ -+ Ag+ + (cryp)H$+.(2) H20 Rates were measured at total Ag+ concentrations down to mol dmP3. (1) rO1 L o *J N L O ~ N U EXPERIMENTAL AND RESULTS MATERIALS Anisole was treated with FeSO,, washed with aqueous sodium hydroxide, dried over calcium sulphate and fractionally distilled under reduced pressure.2 No impurities were detectable in the n.m.r. and i.r. spectra. Cryptand 211 (Merck) was used without further purification. All inorganic chemicals were high-purity commercial grades. APPARATUS Square-wave signals were provided by a Farnell LFM4 Sine-Square generator, and the cell signal was measured using a sample-and-hold integrated circuit triggered by a delayed signal from the generator, as previously described.l The stopped-flow system was an all-glass apparatus, originally constructed for conductimetric dete~tion,~ containing a pair of Pt electrodes ca.0.2 cm2 in area. The signal amplitude from the generator was normally +250 mV for bromine detection and + 150 mV for Ag+ detection, at a frequency in the range 50-800Hz. Measured rate constants were independent of the generator frequency. It is clear from fig. 1 (c) that the sampling frequency is determined by the frequency output of the generator, and thus ideally the frequency should be high relative to the rate constant to be measured. Rate constants up to ca. 100 s-l were measured (4 x 7 ms) and on this time-scale signals recorded at 800 Hz (1.25 ms per sample) the output appears as an exponentially decaying step function. This, together with the increasingly high background capaci- tance current sets a lower limit of ca.5 ms on the half-life of reactions that can be conveniently followed using the present electronic circuit. Bromination reactions were also followed by observing the decrease in absorbance at 350 nm due to Br,/Br; using a Durrum Gibson stopped-flow apparatus. This equipment, when fitted with the temperature-jump cell containing a pair of stainless- steel electrodes, could also be used for current measurements on the Br2/Br- system. However, it was difficult to avoid small leaks from the drive and stop syringes providing an independent connection between the reaction solution and earth, which led to severe distortion of the kinetic traces. Output signals from the sample-and-hold circuit (current measurements) or the photomultiplier (optical measurements) were fed into a Commodore 30 16 microcom- puter via a Data Lab DL 901 transient recorder. The data were analysed by standard methods to yield the required first-order rate constants (see below).Silver-ion concentrations were monitored using a pair of silver wire electrodes sealed through soda glass (electrode area ca. 0.3 cm2) dipping into a glass, jacketed cell. Reactions were sufficiently slow (ti x 20 s) to be recorded with a conventional chart recorder.784 MONITORING OF REACTION RATES 0 1 .o 2 .o 3.0 4 .O [ anisole] /lo-' rnol dm-' [Br-] = 0.1 mol dm-3. Fig. 2. Rate of bromination of anisole in water at 25 "C: initial [Br,] x 7 x mol dm-3, All kinetic measurements were carried out at 25.0 f 0.2 "C ( & 0.5 "C for the Durum Gibson stopped-flow apparatus).BROMINATION OF ANISOLE Initial measurements using amperometric detection were carried out with 5 x lo-, < [anisole]/mol dm-3 d 4 x lo-,, ionic strength = 0.2 mol dmh3 (NaClO,) and [Br,] = 5 x 10-5-1 x lo-, mol dm-3. Under these conditions, pseudo-first-order kinetics were observed : [Br-] = 0.1 mol dm-3, - d[Br,]*/dt = k, [Br,]* (3) where [Br,]* = [Br,] + [Br,] represents the total bromine concentration. The observed first-order rate constant, k,, was directly proportional to the anisole concentration : k, = k,[anisole] (4) as shown in fig. 2. The initial bromination products are much less reactive towards bromine than the original so that no correction is necessary for further bromination. Product analysis was not attempted, but there is good that bromination takes place predominantly (> 90%) in the para position.Rate constants were then measured at varying concentrations of Br- over the range 0.02 d [Br-]/mol dm-3 d 0.3. Provided that Br, is much more reactive towards anisole than Br;,, the observed second-order rate constant, k,, should be represented by k2 = k,r2/(l +K[Br-I) ( 5 ) where kPr2 is the second-order rate constant for reaction of anisole with Br, and Kis the equilibnum constant [Br;]/[Br,] [Br-1. Values of k, measured at various bromide concentrations are listed in table 1, together with kBr, values obtained from eqn (9, using K = 16 dm3 mol-l.' The kBr, values show no systematic trend with [Br-1, inB. G. COX AND W. JEDRAL 785 Table 1.Rate of bromination of anisole in water at 25 'Ca WBrl k2 k2( 1 + nBr-1) kk( 1 + qBr-1) /mol dm-3 / 1 O4 dm3 mo1-l s-l / 1 O4 dm3 mol-1 s-l / l O4 dm3 mol-1 s-lb - 0.02 2.24 2.95 0.05 1.69 3.05 3.55 0.10 1 . 1 1 2.87 2.90 0.15 0.851 2.91 3.02 0.20 0.681 2.87 3.08 O.3Oc 0.524 3.04 3.15 a Ionic strength, I = 0.20 (NaC10,). k;l is the rate constant measured spectrophoto- metrically. I = 0.3. agreement with the assumption that Br; is much less reactive towards anisole than Br,. The average value [kBr, = (2.95 0.07) x lo4 dm3 mol-1 s-l] is in good agreement with earlier reported values: kBr, z 2.6 x lo4 dm3 mol-l s-l (measured using ring-disc electrodes);* kBr, = 2.7 x lo4 dm3 mol-1 s-' (electrochemical generation of Br, at low anisole concentration^);^ kBr2 z 4 x lo4 dm3 mol-1 s-I (approximate extrapolation from results obtained at 0 "C using cell-potential measurements at anisole concentra- tions of ca.lod5 mol dm-3).4 The reactions were also checked using optical measure- ments as described above and the results are included in table 1 for comparison. The agreement between the two sets of data is satisfactory. At low bromide concentrations, < 0.05 mol dm-3, it was very difficult to observe the reaction optically because of the low concentrations of the more highly absorbing Br; species present. However, note that difficulty was also experienced with ampero- metric measurements at low bromide concentrations (< 0.02 mol dm-3). Separate measurements suggest that at these low bromide levels linear response to bromine concentration is limited to bromine concentrations < 5 x mol dm-3 (cf.linear response to [Br,] 2 lop3 mol dm-3 at [Br-] = 0.1 mol dm-3).1 DISSOCIATION OF Ag(cryp)+ In the presence of an excess of acid, metal cations may be displaced quantitatively from cryptate complexes [reaction (1)].1°9 l1 It can be readily shown that for a reaction scheme represented by kd Ag(cryp)+ f Ag+ + cryp kr cryp + H+ 4 (cryp)H+ (7) i.e. the acid is acting as a scavenger for free cryptand in equilibrium with Ag(cryp)+, the observed rate law is given by - d[Ag(cryp)+l/dt = k, [Ag(cryp)+I k, = k, k[H+]/(k,[Ag+] + k[H+]). Provided k[H+] & kf[Ag+] eqn (9) simplifies to k , = k,786 MONITORING OF REACTION RATES 3 . 6 r Fig. 3. Dissociation of Ag+ from Ag(cryp)+ in the presence of excess acid: initial [Ag(cryp)+] = 3.2 x mol dmW3, [HClO,] = 2.0 x mol dm-3, [NaNO,] = 0.10 rnol dm-3. Table 2.Dissociation of Ag(cryp)+ in water at 25 "C" k,/ 10-2 s-1 [NaN03]/mol dm-3 . . . 0.008 0.028 0.1 0.3 1.0 0.1 [HClO,]/ loV3 mol dm-3 . . . 2.0 2.0 2.0 2.0 2.0 20.0 ~ ~~~~~ initial [Ag(cryp)+]/mol dm-3 9.0 x 10-5 4.6b 3.50b 3.34b 2.99 2.80 3.30 1.0 x 10-5 3.12 3.19 3.17 2.90 3.15 3.17 3 . 6 ~ - - 3.2 x 10-5 3.15 3.14 3.18 - 3.19 - - a Generator amplitude _+ 150 mV, frequency 200 Hz; silver electrode area 0.3 cm2. * Non- linear response of measured signal with concentration. i.e. the dissociation of the cryptate complex is the rate-determining step in the overall reaction. The stability of Ag(cryp)+ in water is relatively high, log K, = 8.5 l2 [corresponding to a difference in standard reduction potentials of free Ag+ and Ag(cryp)+of 500 m y , and the kinetic characteristics of the reduction of Ag+ and Ag(cryp)+ are presumably rather different. By applying a low potential difference across two silver electrodes (e.g. Ag (anode) -+ Ag+ + e Ag+ (cathode) + e -+ Ag 150 mV) a current controlled by the electrode reactions may be used to monitor Ag+ selectively in the presence of Ag(cryp)+.Reactions were initiated by adding a small aliquot of a concentrated solution of Ag(cryp)+ to an aqueous HClO, solution (normally 2 x mol dm-3) at varying ionic strengths (NaClO,). Fig. 3 shows a typical reaction trace. The increase in signalB. G. COX AND W. JEDRAL 787 corresponds to the increase in [Ag+] as Ag+ is displaced from Ag(cryp)+ by H+.Rates were measured for a variety of Ag(cryp)+ concentrations down to 3 x mol dm-3 and several different ionic strengths. The observed rate constant, k,, was independent of acid concentration, the ionic strength and the initial concentration of Ag(cryp)+ [table 2, cf. eqn (lo)]. The value obtained, k , = (3.1 kO.2) x s-l, may be identified with the dissociation rate constant, k,, for Ag(cryp)+ and compares favourably with an independent determination of this rate at low ionic strength with conductimetric detection, which gives (2.9 & 0.1) x s-l.13 When combined with K, (= k f / k d ) this gives a value of kf = 1.1 x lo7 dm3 mol-l s-l. It is expected that the use of silver-plated Pt electrodes in the stopped-flow apparatus will enable much faster reactions involving Ag+ to be monitored. DISCUSSION The stopped-flow study of the bromination of anisole shows that the amperometric method utilizing a square-wave polarizing potential can be used to measure reaction rates close to the stopped-flow limit.In this case we have used without modification a stopped-flow apparatus designed for conductimetric detection. It is clear from the agreement between results obtained with optical and electrochemical detection that the establishment of a faradaic current proportional to concentration is rapid on the stopped-flow time scale. The rapid response time combined with the very high sensitivity of amperometric methods1, means that it should be possible to measure second-order rate constants covering a very wide range.The time range of the present technique is limited by the decay rate of the capacitance current, which typically had a time constant of the order of 1 ms in our system (z = RC, where R is the resistance between the electrodes and C is the capacitance of the double layer). Experiments using pulsed potentials have reently been used to monitor reactions with half-lives approaching s,15 further emphasising the rapid response times possible using amperometric detection. This has been achieved in pulse polarographic experiments using i.r. compensation or charge-injection techniquesl5' l6 to charge the double layer in < s, allowing delays between charging the double layer and measuring the faradaic current as low as 7 ,us. This technique is of course limited to measuring rates of systems at equilibrium, rather than the irreversible reactions that we have described.Equivalent double-layer charging rates may be very difficult to achieve during continuous monitoring of concentration levels. Compared with conductimetric methods, a significant advantage of electrochemical detection is the ability to monitor selectively a given electroactive species in the presence of high concentrations of other ions. This is illustrated clearly in reaction (2), in which the concentration of Ag+ is measured in the presence of Ag(cryp)+, excess HClO, and NaC10,. Because the electrode processes at the two electrodes are identical (Ag+ + e =t Ag), square-wave potentials with very low amplitudes can be used, thus allowing great selectivity. A disadvantage is the requirement of reasonably high background electrolyte levels ( to 10-l mol dm-3) to ensure rapid decay of the capacitance current. In practice the background capacitance current is relatively insensitive to electrolyte concentration.This is because as the electrolyte concentration decreases the fraction of capacitance current remaining after a given time increases (z increases) but the absolute level of the initial current decreases. An important distinction may be made between the two reactions described here. In the dissociation of Ag(cryp)+, the species monitored (Ag+) is not a reactant and its concentration does not affect the reaction rate. On the other hand the bromination of anisole is first order in bromine concentration and alteration in concentration as788 MONITORING OF REACTION RATES a result of the electrode reactions will in principle influence the rate.For such a first-order reaction, however, the depletion of the species (Br, in this case) during one half cycle will be cancelled by the increase during the second half cycle. The cancellation will not be exact for a reaction which is, for example, second order with respect to a particular component, except in the limit of low potential (and hence low current). It can be readily shown that such effects should be small; e.g. variations by as much as a factor of two in the concentration of the monitored species in the vicinity of the electrode during one a.c. cycle result in an error of only 1 1 % in the measured rate constant. It may also be noted that the stopped-flow technique is in general inconvenient for the determination of rates of reactions which are second order in the monitored component, irrespective of the analytical technique used.The principle of the amperometric method described is identical to that used in the familiar dead-stop titration method based on a d.c. polarizing potential. However, analytical work involving d.c. polarizing potentials is hampered by the stirrer-dependent decay of the faradaic current. Quantitative measurements using rotating indicator electrodess? 14? 1 7 7 l8 have been described, but these are often inconvenient and cannot be used in some situations, such as stopped-flow measurements of fast reactions. By contrast, when symmetrical alternating potentials with frequencies as low as a few Hz are used the measured currents are independent of stirring.Furthermore, the required faradaic current may be conveniently measured using a simple and inexpensive sample-and-hold circuit-l This should greatly enhance the applicability of amperimetric measurements to the measurement of reaction rates. We thank the Nuffield Foundation for a grant to W. J. and Prof. H. Schneider of the Max-Planck-Institut fur biophysikalische Chemie in Gottingen for assistance in the construction of the stopped-flow apparatus. B. G. Cox and W. Jedral, J , Electroanal. Chem., 1982, 136, 93. Press, New York, 1966), p. 74. B. G. Cox, D. Knop and H. Schneider, J . Phys. Chem., 1980,84, 320. R. P. Bell and D. J. Rawlinson, J . Chem. SOC., 1961, 63. L. M. Stock and H. C. Brown, J . Am. Chem. SOC., 1960,82, 1942. 1. Tanigucki, M. Yans, H. Yamaguchi and K. Yasukouchi, J . Electroanal. Chem., 1982, 132, 233. R. 0. Griffith, A. 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