AWLECATEGN G? THE CURRENT-iMPULSE RELAXATEQR TECE—ZMGUE '50 $45 MERCER? (E3 S‘f‘gfiM “west: {or flee Degree cf M. S. MECHIGAR STATE UNIVERSE? Jane‘s ‘Viae Kuéirka W68 THESlS .O- '''' .1- -. —L— Mirthfgui Mate Umvcrsity ....-___ ABSTRACT APPLICATION OF THE CURRENT-IMPULSE RELAXATION TECHNIQUE TO THE MERCURY(I) SYSTEM BY Janet Mae Kudirka Because kinetic results of investigations of the elec- trochemical reduction of mercury(I) by many different methods were very inconsistent this process was re-investi- gated using the current-impube relaxation technique. In the current-impulse technique an electrochemical system is displaced from equilibrium by a constant current impulse of brief time duration. The double layer is linear- ly charged to overpotentials of not more than a few milli— volts. The differential capacitance can be calculated from the slope of the charging curve and the applied current. The charge from the impulse is consumed by the electro— chemical reaction and charge-transfer kinetic parameters can be determined from the overpotential-time curves. Using this technique, the electrochemical reduction of mercury(I) at a hanging mercury drop electrode in 1.0 M perchloric acid at 25° C was investigated at concentrations —2 6 to 1 x 10 g_mercurous perchlorate. The from 5 x 10' differential capacitance was observed to rise sharply over the range of potentials corresponding to these concentra- tions. The kinetic parameters deduced from the relaxation Janet Mae Kudirka measurements were higher than the results of previous in- vestigations because of the absence of mass-transport control at short times. APPLICATION OF THE CURRENT-IMPULSE RELAXATION TECHNIQUE TO THE MERCURY(I) SYSTEM BY Janet Mae Kudirka A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemistry 1968 VITA Name: Janet Mae Kudirka Born: July 9, 1944, in Hastings, Michigan Academic Career: Lake Odessa High School Lake Odessa, Michigan 1958-1962 Michigan State University East Lansing, Michigan 1962-1966 Degree Held: B.A., Michigan State University (1966). ACKNOWLEDGMENT The author wishes to express her appreciation to Professor Christie G. Enke for his guidance and encourage- ment throughout this study. Thanks are also given to Paul J. Kudirka, the author's husband,for his encouragement and understanding. ii I. II. III. IV. TABLE OF CONTENTS INTRODUCTION . . . . . . . A. Brief Explanation of Current-impulse Technique . . . . B. Chemistry of Hg(I) - C. Previous Studies of Kinetics for Reduction of Hg(I) and Results . . . . . . . . . . . D. Summary of Results of This Study Compared to Previous Studies EXPERIMENTAL . . . . . . . A. Reagents . . . . . . B. Solutions . . . . . . C. Cell and Electrodes . D. Instrumentation . . . RESULTS . . . . . . . . . A. Capillary Data . . . B. Capacitance Data . . 1. Variance with current for charging capacitance . . 2. Comparison of charging and relaxation values of capacitance 3. Capacitances compared to those of Weir and Sluyters-Rehbach and Sluyters 4. Current density calculated from capaci- tance and change with concentration to determine a of Hg:+ . .o 5. Comparison of values of 1 those of previous investIgations CONCLUSION . . . . . . . . BIBLIOGRAPHY . . . . . . . and a with Page 10 29 32 32 33 33 34 38 38 39 39 42 42 45 52 54 55 LIST OF TABLES Table Page 1. Comparison of the present kinetic results with the results of previous studies . . . . 31 2. Drop period, drop mass, and spherical drop area in solutions of varying concentration of H92(ClO4)2 in 1.00MHC104 . . . . . . . . 38 3. Differential capacitance data from charging _6 and from relaxation experiments for 5.12 x 10 , 1.026 x 10 3, 1.026 x 10 g ng(ClO4)2 in 1.00 M HClO4, pulse duration 200 nsec . . . . 41 4. Zero-current capacitance from charging and _ from relaxation data for 5 x 10 6 to 1 x 10 MH92(ClO4)2 in 1.00MHC104 . . . . . . . . 43 2 5. Values of apparent exchange current density for 5 x 10 5 to 1 x 10 2 M_H92(C104)2 in 1.00 M HClO4 . . . . . . . . . . . . . . . . 49 6. Corrected values of apparent exchange current density for 5 X 10-6 to 5 x 10-5 M;H92(C104)2 in 1.00 E HC104 o o o o . o . o o . . o o o 0 iv LIST OF FIGURES Figure Page 1. Potentiostatic arrangement for Gerisher and Staubach's potentiostatic measurements . . 13 2. Arrangement for Gerisher and Krause's double-pulse galvanostatic measurements . 15 3. Circuit for Weir's adsorption model . . . . 28 4. Electrode system for the present investi— gation . . . . . . . . . . . . . . . . . . 34 5. Schematic representation of interconnection of cell and instruments in the present investigation . . . . . . . . . . . . . . 37 6. Differential capacitance from charging and relaxation procedures . . . . . . . . . . 4O 7. Differential capacitance as a function of potential . . . . . . . . . . . . . . . . 44 8. Typical charging curves .. . . . . . . . . . 46 9. Typical relaxation and log q‘yg t curves . . 47 10. Reaction order plot in 1.0 g HClO4 at 25° C. 50 I . INTRODUCTION A. Brief Explanation of Current—impulse Relaxation Technique The current-impulse relaxation technique is a relatively new method of studying the kinetics of fast electrode reac- tions. It is a variant of the charge step method proposed simultaneously by Delahay (6,7) and Reinmuth (24,25). The principle is as follows: The electrode being studied is initially at equilibrium. The charge density on the elec— trode is changed abruptly by applying a constant current impulse of brief duration in such a way that the electro- chemical cell is essentially at open circuit once charging is completed. The potential departs from the equilibrium value as a result of the change of charge density. The in— crement of charge applied to the electrode is consumed pro— gressively by the electrode reaction, and the potential drifts back to its initial equilibrium value. The over- voltage-time variations depend on the coulombic content of the impulse, the double layer capacitance, and the character- istic electrode process. By restriction of the coulombic content of the impulse and reduction of the time interval before relaxation data are acquired the kinetic parameters of the charge-transfer process are found without correction for mass—transport contributions. Study of electrode 1 2 kinetics from overvoltage-time curves is therefore possible. The increment of charge is: Aq = q0 - qi (1) where qi is the charge density at the equilibrium potential for the electrode reaction 0 + ne- = R and q0 is the charge density immediately after charging. It is assumed that the charging time is so short that leakage by the Charge transfer reaction can be neglected during charging. The overvoltage n (n = E - Ee, where E6 is the equilibrium potential) at time t after charging is: where q is the charge density at time t and Cd is the differential capacitance of the electrode. It is usually assumed that variations of E are so small (Incl < 5 mv. approximately) that C is constant. The signs in Eqn. 2 d are consistent with the definition n = E - Be and the dependence of q on E, namely, n : O for q - qi i O. The charge density q is: q = q0 + f: i dt (3) where i is the faradaic current density for discharge of the double layer and the integral is equal to the quantity of electricity used by the electrode at time t. .The integral is preceded with a plus sign, i.e. q i qO for i Z O, in agreement with the convention of regarding a net cathodic current as positive and a net anodic current as 3 negative. It follows from Eqns. 1 to 3 that n = [/cd1 + (l/cd> f: 1 dt (4) qt=o + (1/Cd) f: i dt where nt=o=Aq/Cd (5) is the overvoltage after charging at t = O. The derivation of the solution of Eqn. 4 in which Cd is supposed to be constant requires the explicit form of i as a function of n. The linearized i - n characteristic in the absence of mass transfer is: o i = ia(nF/vdRT)n (6) o where ia is the apparent (i.e., not corrected for the effect of the double layer) exchange current density, Vd is the stoichiometric number, and F, R, and T are as usual. Note that i Z O for q 2 0 and that Eqn. 6 holds well for |n|.: 5 mv., approximately. The combination of Eqns. 4 and 6, and the solution of the resulting equation yield the equation ”/Wt=o = eXp[-(i:/Cd)(nF/vdRT)t] (7) which is identical to the relationship for the voltage—time variations for discharge of a capacitor across a constant resistance. The overvoltage decays exponentially with time, and a plot of log |n| against t is linear. i: is readily computed from the slope of the plot if n/vd and Cd (per 4 cm2) are known, and the transfer coefficient is deduced from the variations of i: with the concentrations of O and/or R. The differential capacitance Cd which is needed in the computation of i: is obtained from the slope of the charging curve and the measured current or may be determined from Eqn. 5 with qO known and no determined by extrapo— lation of the log Iql versus t plot to t = 0. B. Chemistry of Hg(I) The chemistry of Hg(I) is complicated by two factors: (1) the fact that it is a dimer and (2) its disproportiona- tion. Both of these factors have long been realized. There have been many lines of evidence showing the bi- nuclear nature of Hg:+. A few of these may be noted: ((1) Mercurous compounds are diamagnetic both as solids and in solution, whereas Hg+ would have an unpaired electron. (2) X—ray determination of the structures of several mercurous salts shows the existence of individual 2+ ions. 2 H9 (3) The Raman spectrum of an aqueous solution of mercurous nitrate contains a strong line which can only be attributed to an Hg - Hg stretching vibration (39). These and other historical evidence are discussed by Sidg— wick (31). 5 The dissociation of the Hg:+ dimer has been postulated to occur in solution chemistry of the mercurous ion. Higginson (15) on studying the ultra-violet absorption of mercurous perchlorate in dilute (10-2 - 10-3 g) per- chloric acid solutions observed deviations from Beer's law below 10-6 M_mercurous perchlorate and suggested this was because of a significant degree of dissociation of the dimer at these concentrations. This led to a value of Kdiss = 7 and limits of 10'8 - 10'“. [Hg+]2/[Hg:+] = 1.6 x 10' Interference from perchloric acid was not detectable. Cartledge (5) also postulated the existence of Hg+ as a chain carrier in Eder's reaction. He calculated a normal potential of the half reaction Hg(fi) :3_Hg+(aq) + e- as -1.71 volts. Combining this potential with other mercury potentials he showed that the dissociation of the ordinary mercurous ion Hg:+ in solution is attended by a standard free energy change of 42 Kcal., from this pKd = 31 can be derived, which is much larger than that of Higginson. Kolthoff and Barnum (17) in studying the anodic waves of cysteine at the dropping mercury electrode postulated the existence of a species HgSR, the anodic reaction given by the equation RSH + Hg = HgSR + H+ + e_. They postu- lated that at mercurous concentrations of the order of 10-20 M practically all of the mercurous is present in solu- tion as Hg+ and not as Hg:+. From their data a pKd = 18 can be estimated. 6 In 1957 Moser and Voigt (22) using 2°3Hg and determining the ratio of this in an aqueous phase and an equilibrated organic phase calculated a dissociation constant Kd = 10-7 for the reaction Hg:+ = 2Hg+. The Hg+ ion has also been postulated as a reaction intermediate in the reaction of mercury(I) with cerium(IV) studied by McCurdy and Guilbault (21). Using 2.5 - 0.28'mM Ce4+ and 1.32 — 0.161 mM Hg:+ in 2.0 g perchloric acid at 50° C they found the reaction rate to be directly proportional 2 . to the ng+ and Ce4+ concentrations but not to be affected when H92+ was added. They postulated the following mechan— ism: k + 1 2 Ce4+ + (Hg-Hg)2 Slow > Ce3+ + Hg + + Hg ‘1' 4+ 1+ k2 3+ 2+ Ce + Hg m> Ce + Hg where the rate determining step is the breaking of the (Hg-Hg)2+ bond, concomitant with transfer of an electron. On studying the reaction of Co(III) with ng+ in aqueous perchloric acid Rosseinsky and Higginson (27) also postulated the Hg+ ion as an intermediate though also stating the pos— sibility of Hg:+. The concentration of ClO4_ ion was found not to affect this reaction. They postulated the following mechanism: 3+ 2+ + 2+ 3+ C0 + H92 2 ) , 1 + > Co + Hg + H9 (or H92 3+ 2+ Co + Hg1+ (or Hgg+) > Co2+ + (2) Hg . . . . 2 On studying the kinetics of the reaction between ng+ and T13+ in 3 M HClO4 at 25° C Higginson and coworkers (1) 7 suggested that what Higginson had observed earlier in his ultraviolet studies was not the dissociation of Hg:+ but the dismutation reaction: k + 1 2+ Hg: < > Hg + Hg . k-1 They postulated the following reaction scheme: 2+ k1 2 H92 < > Hg + + H9 k2 2+ 1+ _—> Hg + T13+ < Hg + T1 . In this reaction they found a dependence on the concentration 2+ of C104- and explained it by the complexation of H92 and C104". They determined Ka = 1.0 I-moie'1 for 2+ H92 + C104- ——> H92C104+ o < Moser and Voigt (23) undertook the study of this dis- mutation reaction using highly dilute mercurous nitrate solutions. -Radioactive tracer techniques were used to permit measurements in the 10-7 g range. The free mercury was extracted into non-polar organic solvents to measure the extent of dismutation. The equilibrium constant for the dismutation reaction was found to be 5.6 x 10-9. The solubility of mercury in aqueous solutions was found to be (3.0 i 0.1) x 10"7 M'at 25° C. Hietanen and Sillen (14) used emf methods to measure the equilibrium constants for the reaction: ng+ + Hg(E) = Hg:+ at an H+ concentration of 0.01 M_in various nitrate and perchlorate solutions. The equilibrium constant at infinite dilution was calculated to be 88 i 3 at 25° C 8 which agrees well with Schwarzenbach and Anderegg's value of K = 84.8 i 2 (29). The equilibrium constant varied little with nitrate concentration but increased strongly with perchlorate ion concentration. They calculated . -1 . Ka = 0.9 liter mole for the reaction Hg§+ + ClO4- = ngclo4+ which agrees well with that determined by Higginson. Wolfgang and Dodson (38) have suggested that the very rapid isotopic electron exchange between ng+ and Hg:+ i.e. 2+ 2+ H92 + Hg*2+ > Hg32+ + Hg proceeds through the mechanism 2+ + H92 > Hg + H92 + + H9 + H9"2 > Hg;2 Their results support the conclusion that the Hg§+ dismuta- tion is rapidly established. The dismutation of Hg:+ has been postulated to contri- bute to reaction mechanisms. The homogeneous reduction of mercuric salts in aqueous solutions by molecular hydrogen i.e. 2Hg2+ + H2 ——> Hg:+ + 2H+ as studied by Korinek and Halpern (18) has been postulated to proceed through the mechanism: + Hg2 + H2 > Hg + 2H+ (slow) > Hg:+ (fast). Hg + ng+ Rosseinsky (26) also postulated the dismutation of Hg:+ in his study of the reaction between mercury (I) and 9 manganese (III) in aqueous perchlorate. He postulated that the reaction occurred through the following mechanism: 2+ k' + H92 < > H90 + H92 2+ k" 4+ 2+ 2Mn < > Mn +Mn 3 ' 2 1 Mn++Hg° k>Mn++Hg+ 1 2 2 . Mn3+ + Hg + > Mn + + Hg + Rapid + 2+ 2+ Mn4++Hg§ > Mn +2Hg . Using the data of Sillen and Hietanen a value of the equilibrium constant for the disproportionation of Hg (I) to Hg (II) and the liquid metal in unimolar perchloric acid + can be calculated. For unimolar HClO4 H92 + Hg(fi) > 2+ H92 K = 165 i 10 liter mole-1 or K =1: 0.0061 mole liter-1 > ng+ + Hg(z). From this value and the value <— for Hg;+ for the solubility of mercury a disproportionation constant > ng+(aq) + Hg (aq) in 1.0 M HClO4 of <-——- for Hg§+(aq) — —1 1.8 x 10 9 mole liter can be calculated. Thus the pertinent equilibria of H92(ClO4)2 in 1.0 M HClO4 are as follows: System Medium K Hg§+(aq) = ng+(aq) + Hg(z) Infinite dilution 0.011 ! Hg§+(aCI) = H92+(aq) + Hg(fl) 1.0 y; HClO4 0.0061 g Hg§+(aq) = ng+ (aq) + Hg(aq) Infinite dilution 5.5 x 10"9 g Hg§+(aq) = ng+(aq) + Hg(aq) 1.0 MHClO4 1.8 x 10--9 g Hg(E) = Hg(aq) (independent of ionic strength) 3.0 x 10-7 fl Hg§+(aq) + ClO4—(aq) = Hg2C104+(aq) 0.9 Mil 10 C. Previous Studies of the Kinetics for Reduction of Hg(I) and Results Since the system Hg(I)/Hg has long been considered a prototype of reversible reactions in electrochemical sys— tems there have been a variety of studies of it by different methods. Since these methods were not all adequate to study the kinetics of such a fast reaction a variety of kinetic parameters has resulted. In 1948, Rozental and Ershler (28) to determine the applicability of a faradaic impedance method proposed by Ershler (9,10), studied the behavior of a mercury drop elec— trode in 5 x 10—4 to 1 x 10-2 §_solutions of mercurous nitrate in 2.0, 0.2, and 0.02 §_perchloric acid. They resolved the cell impedance into series reSistive and reac- tive components. The electrolyte resistance (estimated by conductance measurements in 2 §_HClO4) was subtracted from the series resistance. By transforming the resulting series analog of the electrode impedance into its parallel equivalent a correction for the admittance of the double layer was obtained. A value of 40 microfarads cm-2 was taken for the differential capacitance at all concentrations in this calculation. Reverse transformation gave series— equivalent values C and R . R R According to the theory of Ershler R and 1/uCR, where R w is the angular frequency, plotted as functions of w should yield straight line plots of identical slope, the intercepts correSponding to O)——9 00 should be zero for the 11 reactive component and a value equal to the charge—trans— fer resistance for the resistive component. On the plots of Rozental and Ershler the points fall on straight lines, the reactive and resistive plots are however, not parallel but appear to extrapolate to a common zero intercept. The authors conclude that the charge—transfer resistance is thus less than the uncertainty in the measurement of re- sistance 0.03 ohm cm2. The faradaic impedance method was also used by Gerisher and Staubach (13) to determine the kinetics of the Hg(I)/Hg electrode. The authors also carried out a preliminary potentiostatic investigation. To determine the solution resistance in the presence of this highly reversible reac- tion they found it necessary to extend measurements to quite high frequencies (to 200 kHz). They also realized the necessity of measurement of the differential capacitance. They calculated the series capacitance corrected for trial values of the double layer capacitance, the value which, in accord with theory gave a constant difference between series resistance and reactance independent of frequency, was taken as the correct value, and the difference was the charge-transfer resistance. The impedance was determined in an equal armed bridge by comparison with a resistance and a capacitance in series connection. At the dropping mercury electrode the bridge was balanced so that in the instance of departure of the drop the potential difference was null. Determinations were made in 1, 2, and 4 x 10—3 M 12 mercurous perchlorate in 1 g perchloric acid and a plot of log Hg:+ gs, log i yields a straight line of slope 090 0.7 i 0.2. The ka calculated from this data is 0.00391 cm/sec. The potentiostatic measurements were observed on an electron beam oscilloscope connected to a potentiostat. Figure (1) shows the principal form of the potentiostatic arrangement. The amplifier had an amplication factor of approximately 2000 and a frequency up to 50 kHz, which be- cause of the large capacitance of the measured object was locally perhaps 10 kHz. The current was measured by an oscilloscope (S) after introduction to a direct current amplifier (V). Since the resistance Rv which served for current measurement had little influence on the potentio— static arrangement, it was varied without difficulty and adjusted to the actual current flow. The potentiostat used in these experiments had a time constant of 10-5 sec which causes the results to be rather uncertain. The values for the exchange current found by this method were consistently below those found by the faradaic impedance method. This was attributed to the onset of concentration polarization because of the rise time of the potentiostat. The reaction order plot of thexedata yields a slope of 0.6 i 0.1. By comparing the cathodic Tafel slope (=2.303vdRT/anF) with the slope of the reaction order plot, with the assumption that the rate—determining charge—transfer step is the only 13 .HOHMHHQE¢ n > .mmoomoHHHomo m mMUOHUUmHm wUCQHmmmm H mm .mUOHUUmHm Hmpcgou H Nm .mUOHUUQHm mCHVHHoz H Hm . mUCGEGHDmmmE oeumumOHucmuom m.£UmQSmum UGO Hmnmflnmo How ucmfimmcmuum UflumumOHucmuom .H musmflm HOHMHHQE< wmmuao> JT DCOHHSU uomufln filo ? MN m xm m \\\4o 6 o . emflwl I4 «m «E V\\\\\\ > 9|. > m 14 charge—transfer step in the overall process, the authors determined n/vd = 2 and 1 — a = 0.6 i 0.1. Because n/vd = 2 and thus v = 1, they concluded that the mercurous d ion traverses the phase boundary undissociated and hence that the charge transfer reaction for electrodeposition is Hg:+(aq) + 2 é- > 2 Hg + aq. metal with the assumption of a single charge—transfer step. In an attempt to resolve the discrepancy between the faradaic impedance and the potentiostatic-step results Gerisher and Krause examined the kinetics of electrodeposi- tion of mercury with the double pulse galvanostatic technique (12). The current impulse was produced with an electronic generator. The pulse was obtained as follows: A trigger circuit produced a differentiated short needle impulse which was then fed to a monostable multivibrator. At the output of the monostable multivibrator a rectangular impulse was obtained. This was improved in a discriminator, then the long and short pulses were overlapped to obtain the double pulse for the measurement. Impulses from 5ua to 400 mA could be obtained from the pulse generator. The authors state that the slope of the top with long impulses amounted to approximately 2% at 300 usec, the side steep— ness of the short impulse depending on the magnitude of the cut off resistance was between 5 x 10-8 and 2 x 10-7 sec. The arrangement for measurement is given in Figure (2). It consisted essentially of a bridge connection. The 15 .mucwEOHSmmmE OHumumocm>Hmm mmasmlmansop m.mm5mHM UGO Hmsmfiumo How pamEmmcmHH< .N mnsmflm ? \ . A HTHMHHQWM/I/ HOADGOHOMMHQ . mmoomoHHHomo mm Hm. HOUMHGCTU QmH 3m 16 electrolyte resistance could be reduced according to its relationship to the magnitude of the transfer resistance of the measurement sensitivity through compensation of the bridge resistance (R3) situated parallel to the cell. With the correct standard resistance the potential time curve would begin at the null point. The compensating resistance also permitted the measurement of the current. Current and potential measurements were measured with an oscillo- scope with a maximum sensitivity of 1 mv/cm. The authors state that equilibrium resulted on the average after 1.5 usec. At 25° C, exchange currents were determined for solu- tions from 5.9 x 10—4 M_to 3.5 x 10-3 M_mercurous perchlorate in 1 M perchloric acid. Thfifi data gave a reaction order plot with a slope of 0.70 i 0.03 and hence an apparent transfer coefficient of 0.30 i 0.03 for n/vd = 2. The ex- change currents were somewhat higher than those reported by Gerisher and Staubach. A k: = 0.011 cm/sec can be calculated from thae data. The incongruity of a mechanism involving dissociation of the mercurous dimer prior to charge with the experi- mentally derived Vd = 1 was demonstrated by Gerisher and Krause. In addition, they considered the possibility of a disproportionation 2+ H92 (aq) > H92+(aq) + Hg(aq)- The authors contended that the intermediacy of this reaction would give rise to abrupt concentration polarization for 17 the dissolution process due to insufficient supply of Hg(aq). Because this concentration polarization was not observed for anodic dissolution, even at high current densities, they concluded prior disproportionation is not involved and con- cluded the mechanism must be that identified by Gerisher and Staubach. Matsuda, Oka, and Delahay (20) also used the double pulse galvanostatic technique for study of the Hg/Hg(I) system. The double pulse generator was composed of two single pulse generators which were triggered manually with another pulse generator. The two pulses were mixed in a twin- triode circuit with common cathode. A bridge circuit was used for compensation of the ohmic drop in the cell (2). It was inserted in the cathode circuit of the mixer. Pulse heights were adjusted by variation of the grid voltages of the mixer with separate battery supplies. Cer— tain precautions were taken to obtain minimum rise and cut off times. The pulse height ratio varied from 2 to 12 in this study. The low residual plate current through the bridge in the absence of pulse generation was compensated with a potentiometer. The rise and cut off time was approximately 0.2 micro sec for any pulse length. The pulse generators that were used had approximately a 0.2 microsec rise and cut off time and distortion thus resulted from the pulse generators rather than the mixer. The combination of the preamplifiers 18 used in this study, at maximum gain, had a linear response for input voltages up to 80 millivolts. The input voltage did not exceed 50 millivolts in this study (cell resistance of approximately 5.0 ohms). The maximum sensitivity was 0.5 millivolt per centimeter deflection. Matsuda, Oka, and Delahay, by means of a complete solution of the boundary problem take into account concen— tration polarization in the galvanostatic technique. They reconsidered the data of Gerisher and Krause and concluded that serious errors in the apparent exchange currents re- ported by these authors had been introduced by their simpli— fied treatment which assumed concentration polarization to be negligible for preimpulses of one microsecond duration. Delahay and coworkers determined the exchange current densities for solutions from 2.5 x 10—4 to 2 x 10.3 g mercurous perchlorate in 0.98 szerchloric acid at 25° C. Their corrected exchange current density for 1 x 10-3 M mercurous perchlorate is approximately twice the value determined by Gerisher and Krause. Imai and Delahay (16) in order to illustrate the ap- plication of the faradaic rectification technique of Senda, Imai, and Delahay (30) to very rapid charge-transfer re— actions made a study of the discharge of mercurous ions. The general equation for the rectification voltage for control of the mean faradaic current to zero has the follow- ing form in the particular case of the discharge of Hg(I) on Hg 19 AEOO = nFlza _ 1 _.Q 1 + ctn 6a :1 (A) V2 RT 4 2 1 + ctn2 6a where AEOO is the rectification voltage for t -2 00; VA the amplitude of the sinusoidal voltage across the faradaic impedance; a the transfer coefficient; 6a the phase angle between the resistive and capacitive components of the faradaic impedance; n = 2; and R, T, and F are as usual. At sufficiently high frequencies Imai and Delahay derived .o 1 + ctn 6a :3 1 : la 1 (B) 1 + ctn2 6a ctn ea 2172 nFCDl/2 w1/; where i: is the apparent exchange density; C the bulk concentration of Hg(I); and w = 2wf, f being the fre_ quency. When the faradaic impedance Z is very large in f comparison with the double layer impedance 1/wc1 (c1 dif— ferential capacitance) one has VA gsIA/dcl (IA current amplitude) and there follows from the above equations: " 2 .0 [33000) ,3 1 n_F_ 2a — 1 _ Ola 1 (C) I: c 2 RT 4 23/2 nFCD1/2 w1;2 Imai and Delahay assumed that (a) the differential capacitance c1 is not affected by variations of the Hg(I) concentration in the presence of a large excess of Support- ing electrolyte; (b) that Cl is constant in the range of potentials corresponding to the variations in C; and (C) that Cl is frequency independent. They stated that the 20 first two assumptions were realistic and the third one o verified experimentally. Further they assumed that ia in this case is: .0 _ O 1-(1 ia - anaC (D) where k: is the apparent rate constant. It then follows from Eqn. C that the ratio of the slopes of the plot AEOOCF/I: against wl/Z for two concentrations of Hg(I) C1 and C2 is (CZ/C1)Q. The coefficient a can then be evaluated from the directly measurable quantities Afiaa’ IA, and w without independent determination of the differential capacitance CI. The latter was then evaluated from the intercept of the line AEGDwz/I: against w-l/z for w—l/z = 0. Finally 1: was calculated from the slope of the line AEOOCP/I: against w-l/z. Rectification voltages were measured directly from a cathode ray oscilloscope display. Because of the three assumptions stated above Imai and Delahay used a differential capacitance of 43 micro- farads cm-2 in all calculations. The experiments were carried out at 24 i 2° C in 0.1 and 0.2 M_perchloric acid . -5 for concentrations of mercurous perchlorate from 5.8 x 10 to 4.7 x 10-4 M_and in 1.1 g_perchloric acid for 6.7 x 10-5, 3.5 x 10-4, and 7.3 x 10-4 M mercurous perchlorate. A transfer coefficient a = 0.28 was determined and rate constants of 0.28, 0.36, and 1.3 cm sec-1 for 0.1, 0.2, and 1.1 M_acid media, respectively. 21 To explain the large difference in rate constants found in 1.1 M_perchloric acid by this technique from that found in 1.0 szerchloric acid by the double—pulse galvanostatic method the authors suggest that a coupled chemical reaction may be involved, that for the very high frequencies employed in their rectification study the effect of the chemical re- action is minimized or eliminated, while on the time scale of the galvanostatic experiments the effect is present and essentially constant. The authors did not determine what chemical reaction could be occurring. Sluyters and coworkers, using the principles of com- plex-impedance pIane analysis of faradaic impedance data, investigated the behavior of mercury electrodes in perchloric acid solutions. Sluyters-Rehbach and Sluyters (32) measured the differential capacitance at the dropping mercury elec- trode at 25° C for solutions containing mercurous perchlor- ate in 1 M_perchloric acid from -0.305 to +0.717 volts versus the normal hydrogen electrode, and at frequencies from 420 to 5000 cps. The differential capacitance was shown to undergo a quite rapid increase for potentials anodic of +0.400 volt as had been shown by Grahme (11). The same authors then repeated this work with a hanging mercury drop electrode and with closer attention to the cor- rection for electrolyte resistance (33). The resulting capacitances were somewhat lower than those previously de- termined, but the increase in capacitance with increasing anodic potential was still present. From the absence of 22 charge-transfer polarization they concluded that for 1 x 10-3 M mercurous perchlorate in 1 M_perchloric acid at 25° C, the exchange current density must be in excess of 0.46 A cm-z. The same conclusion was obtained for 1 x 10- 3 M mercurous perchlorate in 0.1 fl perchloric acid (33). These authors also compared the results of this complex plane analysis with those of the double-pulse galvanostatic and faradaic rectification techniques (34). They attri- buted the lower exchange current density values from the double-pulse galvanostatic technique to a consistent sys— tematic error in the galvanostatic data. Based on the ab- sence of any indication from the faradaic impedance data at intermediate frequencies of the intervention of any process other than diffusion they discredited Imai and Delahay's attempt to explain this by a coupled chemical reaction. From a numerical evaluation of the approximations made by Imai and Delahay in their faradaic rectification study Sluyters-Rehbach and Sluyters calculated that the error in measurement of exchange currentcbnsity in the ex- periments of Imai and Delahay was within ten percent only if ctn 9a - 1 is greater than four. Thus Eqn. B was only significantly justified with the results obtained for the highest Hg(I) concentration in 0.1 M_perchloric acid. In all other cases the assumptions of Imai and Delahay were unjustified and their conclusions based on incorrect inter— pretation of their data, especially for the measurements in 1.1 M perchloric acid. Sluyters-Rehbach and Sluyters, on 23 the assumption of pure control by diffusion of reactants, calculated values for the differential capacitance at equilibrium potentials corresponding to several Hg(I) con— centrations from the data of Imai and Delahay and found reasonable agreement with the results of their own complex- plane analysis. Birke and Roe (3) investigated the kinetics of the system Hg(I)/Hg to amplify an extension of the theory of the simple galvanostatic technique to permit rigorous ap- plication of a linearized n‘yg t1/2 relationship for extrapolation beyond mass-transport control in studies of systems in which the reduced component is of unit activity. A preimpulse to abruptly charge the double layer was applied in order to assure a linear plot over an extended period on which to base the extrapolation to zero time. The constant current was obtained from a 3 to 12 volt battery source. A mercury wetted contact relay applied a transient-free voltage step to the bridge (bridge circuit which balances out the resistance voltage drop of the cell). To control the charging spike it was necessary to shape the leading edge of the voltage step with a low pass filter. The current step was applied to the cell at a fixed time during the growth of a mercury drop. The time cycle was derived from two microsvvitches activated by motor driven cams. One microswitch controlled a relay which dis- lodged the drop through a shearing force. The other switch, which was activated 4 seconds after the start of the growth 24 of a new drop, triggered a wave form generator. The gate output of the generator activated the mercury wetted con- tact relay and the sawtooth output triggered the sweep of an oscilloscope. The duration of the sawtooth was about 6 msec and the sweep was initiated about 10 nsec before the relay contacts closed. The closing time of the relay was about 3 msec and was reproducible to about i 10 nsec. A zero base line of one to three centimeters could thereby be observed on the oscilloscope screen. The oscilloscope was equipped with a Tektronix Type D preamplifier. At maximum sensitivity the upper band pass limit of this unit was adequate to produce accurate measure- ments after two or three microseconds. The initial portion of the overpotential-time curve was somewhat attentuated and therefore unuseable. These authors assumed the differential capacitance to be constant at 36 microfarads cm-2. Kinetic data were taken for the anodic dissolution process in solutions 4 x 10-4, 2 x 10-3, and 4 x 10-3 M mercurous perchlorate at 24 i 1° c. Apparent exchange currents were determined at three current densities for each solution with satisfactory repeatability. A transfer coefficient of a = 0.25 was determined. A k: = 0.06 i 0.02 cm sec.1 can be determined from their data. The most recent investigation of the kinetics of the system Hg(I)/Hg is that of Weir (36) using the current impulse technique (37). To supply the current impulse to the cell a General Radio 1217—B pulse generator with its 25 associated power supply was used. The pulse generator was coupled to the cell through a 1-kiloohm load resistor to assure constant impulse current and two 1N-914 switching diodes with polarity appropriate to pass a pulse but to re— ject counterflow of current. With this input arrangement, current pulses continuously variable in amplitude from 0 to 20 ma and of duration as brief as 100 nsec were applied to the cell. The overpotential response to the constant perturbation was amplified by a Tektronix 1121 amplifier (rise time 21 nsec). The amplified signa1.was cabled to a Tektronix 535A sweep-delay oscilloscope with a type H plug-in pre- amplifier (rise time 31 nsec). With this system an over-all deflection sensitivity as great as 5 uv cm—1 was achieved on a 100 nsec cm—1 time base. With appropriate calibration, current, overpotential, and time could be measured with an accuracy of 1%. The system 10 - 90% rise time was less than 100 nsec; however, overshoot and transient ringing due to uncompensated inductance and stray capacitance prohibited reliable (i100 uv) observation of relaxation for an interval of up to 400 nsec following termination of the current pulse. Ringing was evident only following the pulse and did not obscure charging response. Experiments were performed on seven concentrations from 2.05 x 10—5 to 5.15 x 10-.3 M mercurous perchlorate in 1.00 M_perchloric acid at 25° C. Estimates of differential 26 capacitance were determined for each concentration by two different methods: (1) by direct calculation from the ini— tial slope of the charging curve and the value of the con- stant charging current, and (2) by extrapolation of the relaxation data on a plot of log n against t to determine no and calculation of the capacitance from this value and the coulombic content (current x pulse duration) of the pulse. Estimates of differential capacitance obtained by the direct technique depended upon the current density at which the determination was carried out. The zero-current value of the capacitance was used as the appropriate dif- ferential capacitance at each concentration. A difference between the zero values found by the two different methods was observed which increased as the concentration increased. The differential capacitance was observed to increase with increasing anodic electrode potential, in striking agree~ ment with the measurements of Sluyters—Rehbach and Sluyters. A reaction order plot showed excellent linearity in the low concentration region for both charging and relaxation data, but marked systematic departure from linearity was evident at higher concentrations for the points corresponding to the capacitance values determined in charging experiments. The s10pe of the reaction order plot established at low and intermediate concentrations is 0.68 i 0.02. From the i: values and a an apparent standard rate constant k: = 0.019 i 0.002 cm sec-1 is calculated. This slightly higher result than obtained by the other transient methods was 27 explained by the absence of partial mass transport control of the rate of the electrochemical reaction at short times. To resolve the anomolies of the dependence of differ- ential capacitance calculated from charging curves upon current density and significant deviation from linearity in electrochemical reaction order plots for the higher con- centrations, Weir developed a model (Figure 3) appropriate to the description of electrochemical processes involving adsorption of reactant and/or intermediate. Detailed analysis of the behavior of this network resolved the anomolous observations of his investigation and suggested the cause of the marked disparity between the kinetic re— sults of the transient and the periodic relaxation techniques for this system. Weir found no definitive mechanism could be determined directly from the predictions of this model and the experi- mental results. But through a re-evaluation of the data of Gerisher and Krause two unit charge—transfer steps were identified and rate control assigned to the first. Weir concluded that from this reaction sequence and the require— ments of the model that the electrodeposition of mercury requires adsorption of reactant Hg:+ or intermediate H92+ prior to the charge transfer and postulated two alternate mechanisms: _ + + _ A) Hg:+ + e > H92 ; H92 + e > 2Hg 2+ - + + + > H92 7 H92 + _ Hg + e B) H92 + e > Hg + Hg ; > Hg 28 E l g l\ a) where discharge Re requires adsorp— A A A tion of reac- tant species. Ca R1 R2 Rs Cf 1 \ b) where primary R discharge of non- e specifically ad- __—flvAvAh- sorbed species C R precedes adsorp- a 2 tion and dis— " ++/\/\/\— charge of inter— vl) mediate. R1 RS C 1% 1‘ c) general state- Re ment of both __4\/\/\_ cases. a {.L MAJ Figure 3. Circuit for Weir's adsorption model. CE = electrochemical double-layer capacitance, Re = elec- trolyte resistance, Ca = capacitance due to discharge of ad- sorbed species, Ra = charge—transfer resistance for discharge of adsorbed reactant or intermediate, RS = adsorption re- sistance. 29 D. Summary of the Results of this Studinompared to Previous Studies The current-impulse relaxation method used by Weir in his investigation was also used in the present investiga— tion of the kinetics of the Hg(I)/Hg reaction. Constant current impulses of 0.2 usec duration were applied to a hanging mercury drop electrode with a platinum gauze counter electrode in a solution of Hg2(ClO4)2. The voltage- time relaxation curve was observed on an oscilloscope. A pulse of 1 usec duration was used to obtain the charging curve. Concentrations of mercurous perchlorate from 5 x 10‘6 to 1 x 10‘2 in 1.0 g HClO4 at 25° C were used. Estimates of the differential capacitance were obtained by the same two methods used by Weir. And as observed by Weir the differential capacitance obtained by the direct method was dependent upon the current density at which the determination was carried out. The zero—current value of the capacitance was used as the appropriate differential capacitance at each concentration. Also as observed by Weir and Sluyters—Rehbach and Sluyters the differential capacitance increased with increasing anodic electrode po— tential. A reaction order plot showed excellent linearity in the intermediate and high concentration regions but de— parted from linearity at low concentrations. The slope of the reaction order plot established at intermediate and high concentrations is 0.67 i 0.02. The i: values were slightly higher than observed by Weir. This is explained by the fact 30 that his relaxation datavere obtained 0.6 usec after the impulse whereas in the present investigation data wag ob- tained starting at 0.2 usec after the impulse hence a steeper slope was obtained. From the i: values an ap- parent standard rate constant k: = 0.0297 i 0.002 cm sec-1 was determined. The kinetic results of the present investigation and of previous studies of the electrochemical reduction of Hg(I) are summarized in Table (1). 31 .mHOGuGO ma UOuOHGoHOo uoz II :0G=* mm.o hmmo.o No.0 H mm.o own: «.0 II OOHGQEHIDGOHHGU OxHHUGx om.o mHo.o No.o H mm.o 0mm: v.o mm OmHGQEHIUGOHHGU HHOB . . . I . GOO: I OAuODOOGO>HOm mm 0 mo o mo 0 + mm o m m m UOHMHUOS Oom UGO Oxuflm . I. OUGOUOQEH mnmumsam UGO we 0A *0G *0G II mm UHOUOHOm GOOQGOmlmumumsam . . I . II GOHDOUHMHDUOH ma m H mo 0 + mm o UH UHOUOHOm mOGOHOD UGO HOEH . . . I . . OHUODOOGO>HOm MOGOHOQ mm o vao o No C + cm 0 COO: mIN on OOHGQIOHQGOQ UGO .Oxo .OUGmuOS . . . I . own: I UHUODOOGOPHOm mH o moHo o mo 0 + on o m N NH OOHGQIOHQGOQ Omsmux UGO HOGOHHOO no.0 mfioo.o H.o H v.0 omm: OH mH oeuOumoHquuom GOOQGOum UGO HOGOHHOO . . . I . II OUGOUOQEH ma o mmoo o m o + m 0 ma UHOUOHOm GOOQGOum UGO HOGOHHOU «IEUIQEO «£28 «Sr 2 mIOHxH huHmGOQ uGOHHGU HIUOOIEOIDGOHOHMMOOU uGOEOHGmOOE OmGOGoxm GGOHMGOU HmmmGOHB OHOMOQ OEHD .mmm OGOHGGOOB mGoHpOmaumOPGH uGOHOmmd ODOH .Upm uGOHOmm< OuOEHxOHmmm I .mOHUGum mGoH>Oum mo muasmmu OLD GDHB mpaGmOH OHDOGHM uGOmmum mo GOmHHOmEOU .H OHQOB II. EXPERIMENTAL A. Reagents The mercury used in this investigation was purified in this laboratory by repeated washings with 1 M nitric acid, 1 M NaOH, and distilled water, and filtering. The red mercuric oxide used in the preparation of solutions of mercurous perchlorate was Matheson, Coleman and Bell A.C.S. Reagent grade, perchloric acid was G. Frederick Smith double—distilled lead free acid at 70% strength. The dis- tilled water used in the preparation of solutions and in cell rinsing was obtained by redistillation over KMnO4 and NaOH in an all Pyrex apparatus, of laboratory distilled water. Nitrogen gas introduced into the cell was Liquid Carbonic prepurified gas, treated and passed into the cell by a glass and teflon purification train. The nitrogen was dried over calcium chloride, then passed through an oven containing copper turnings at 350° C to remove traces of oxygen, then through a multiple element trap containing activated coconut charcoal at liquid nitrogen temperature, and finally presaturated by bubbling through 1 M perchloric acid before introduction into the cell. 32 33 B. Solutions Aqueous perchloric acid used as supporting electrolyte was prepared volumetrically to approximately I‘M concentra- tion, then determined by titration with 2-amino-2-hydroxy- methyl-1-3-propanediol, and was found to always be 1.00 i 0.01 g and was used without further adjustment of concen— tration. A stock solution of mercurous perchlorate was obtained by preparation of a solution of mercuric oxide in 1.00 M_perchloric acid and its reduction by mercury metal. The solution was assayed gravimetrically as the chloride (8), and its concentration, in agreement with calculation, was. 0.0515 i 0.0004 M, Working solutions were prepared by volumetric dilution of this stock solution with 1.00 g perchloric acid. All solutions were stored over mercury and in the dark. C. Cell and Electrodes A two electrode system similar to that used by Weir (35) was designed and constructed (Fig. 4). Simply a tube of copper connected through a pyrex support to a platinum gauze counter electrode concentrically surrounding the plat- inum wire which terminates in the drop contact. A second contact is provided near the drop contact but outside the copper tube. The pulse current is applied through this contact with the copper tube held at ground, and the re- sponse is observed between the platinum inner conductor and 34 Test Electrode Counter Electrode Pulse Input S 24/40 Inner Member Pt wire, 13 mil Copper tube ( I d , - i-_,, KL. Ag sol er Pt Cu Ag solder, Pt—Pt L——————-Pt gauze (52 mesh) Figure 4. Electrode system for the present investigation. 35 the copper tube. The drop contact was polished flat and Hg plated according to Brubaker and Enke (4). A Pyrex cell with standard taper ground glass fittings to accomodate this electrode, the dropping capillary, a teflon spoon, and a gas inlet was constructed. The dropping capillary was a 6 - 12 sec drop time capillary from Sargent. It was fed from a 10 cc syringe as a reservoir, connected to a stand tube by a length of teflon tubing. The height of the mercury column was fixed at 610 i 1 mm. Capillary data were established by measure- ment of period and mass for the discharge of 20 drops. ~The period was established using an electric stopclock (The American Time Co., Type S—1) and mass by weighing. D. Instrumentation The pulse generator used in this study was an Inter- continental Instruments Model PG-33. The maximum rise time/fall time is.:6 ns depending on source impedance. The pulse duration of the generator is continuously variable from 30 ns to 1 sec, and frequency is variable from 0.1 cps to 10 mo and single shot. There are both positive and negative outputs from which current pulses adjustable from 10 ma to 200 ma can be obtained. This was connected to the electrode auxiliary contact by a tektronix 010-120 1X probe. The detection system for the current—impulse experi— ments was composed of a Tektronix 556 sweep-delay oscilloscope 36 with a Tektronix type 1A5 plug-in differential amplifier (8 nsec rise time). This was connected to the drop contact wire by a Tektronix 010-120 1X probe. Connectors of the BNC type were used for all terminations. The pulse generator was triggered from the delayed— trigger output of the oscilloscope. All current determinations for calculation of differ- ential capacitance were made by connecting a 10.047 ohm resistor (its value determined by measurement with an ESI model 300 used as a Wheatstone bridge) between the pulse generator and the oscilloscope and measuring the voltage drop across it produced bYEiPUISe of current. Charging and relaxation curves were recorded photo— graphically. A Tektronix type 350 camera with Kodak Tri- X1ASA 4001 35 mm film was used. The results from the nega— tive strip were projected onto ruled graph paper and traced. All exposures were made with manual shutter control. 37 .GOfluOmemm>GH uGOmOHm Oz» GH muGOEGHumGH UGO HHOU mo GOHDUOGGOUHODGH mo GOHDOUGOOOHQOH UHuOEOnom .m musmfim mm filL Onoum NH ONHIOHO xHGOHuMOB M..----III:.I-I-I.- ..... -IIII-I--I----I ........ I .AN .1 t n _ H . . _ . . . . m _ . _ -—--.-- -——-—u-—-‘- : I I I. IIIIIIIIIIIIIIIIII I- I- I I.411 I t Hmmmflnerv_ u e .0 HI. __ UOSOHOG ._.|OI H..I.II- .OLMlusmuGo I FAG quGH IIHHLMJLH UGQGH pseudo + mmfi mama Hmmmflue o OmoomoHHHomo mmm mama xflGouuxOB III . RESULTS A. Capillary Data Because the electrode potential of mercury in contact with an aqueous solution of a soluble mercurous salt is determined by the concentration of mercurous ion, it is necessary to make a separate determination of drop mass in each solution. The results of drop period (t*) and drop mass (m*) determinations for solutions from 5 x 10'.6 to 1 x 10.2 M_mercurous perchlorate in 1.00 g_perchloric acid are summarized in Table (2). Table 2. Drop period, drop mass, and spherical drop area in solutions of varying concentration of ng(ClO4)2 in 1.0 fl HC104. Conc. ng(ClO4)2 Drop Period Drop Mass Approximate mole liter"1 (t*)_1 (m*)_1 drop area cm2 sec drop mg drop 5.12 x 10'6 5.950 5.352 0.02650 1.024 x 10‘5 5.893 5.301 0.02590 2.048 x 10"5 5.840 5.253 0.02570 5.12 x 10‘5 5.783 5.202 0.02555 1.024 x 10" 5.730 5.151 0.02540 2.048 x 10'4 5.682 5.114 0.02525 5.12 x 10" 5.605 5.042 0.02504 1.024 x 10’3 5.560 5.002 0.02490 2.048 x 10’3 5.505 4.953 0.02474 5.12 x 10’3 5.440 4.891 0.02454 1.024 x 10'2 5.394 4.853 0.02440 38 39 Estimates of the drop area for each solution concen— tration were obtained by calculating the spherical area from each drop mass by the equation: 211/ S = [36w(m*/ng) 3 taking the density of mercury at 25° C. The results of these calculations are also given in Table (2). These values were used for normalization of results to unit area. B. Capacitance Data Estimates of differential capacitance were obtained at each concentration by two methods: (1) by direct calcu- lation from the initial slope of the charging curve obtained using a 1 usec pulse and the value of the current and (2) by extrapolation of the relaxation data obtained using a 0.2 usec pulse on a log In] versus t plot to t = 0 to determine no ; and calculation of the capacitance from this value and the coulombic content of the pulse. As observed by Weir estimates of the differential capacitance obtained by the direct technique depended upon the current density at which the determination was carried out. The estimates obtained by the two methods were not at variance as observed by Weir until the two highest con— centrations. Typical data for low, intermediate and high concentrations are given in Table (3) and illustrated in Figure (6). These data show strong dependence of differ- ential capacitance from anodic charging current, increasing 40-- N E fl In 30* 1. o A . A 8 d A I? 20.. ‘9 e U :44 100- -I-I Q I + i I 20 10 0 10 20 anodic cathodic Current, ma 80“ 0 NE 9 E 60" ° W A 0 j— A A A z: 4' A o ‘- o 53‘ 40 ° 5 U 3:: 201— -:-I Q 30 15 0 15 30 anodic cathodic Current, ma N 30 E o \\ ”3250 o'. A A 315 A 3200*- O 3: o .8 150‘- O I 0 GI 30 0 30 60 anodic cathodic Current, ma Figure 6. 40 AACapacitance from relaxation data oCapacitance from charging data 5.12 x 10'6 g Hg;((ClO4)2 in 1.0 fl HC104 at 25 C. OCapacitance from charging data z>Capacitance from relaxation data 1.024 x 10'3 g Hg8(ClO4)2 in 1.0 9.4. HCIO4 at 25 c OCapacitance from charging data A Capacitance from relaxation data 1.024 x 10"2 g Hga(ClO4)2 in 1.0 y; HC104 at 25 -C. Differential capacitance from charging and relaxation procedures. 41 Table 3. Differential capacitance data from charging and from relaxation experiments for representative concentrations of ng(ClO4)2. Concentration Current, ma Differential Differential mole/liter E32. :3::;.., Ezigxiiiig fr°m curvesuf/cm2 plots uf/cm2 5.12 x 10’6 14 anodic 26.4 23.58 9.2 23.14 23.94 6.2 23.40 21.87 6 cathodic 22.64 22.64 9.8 21.13 23.48 15 20.58 22.31 1.024 x 10'3 29 anodic 72.5 51.5 24 68 50.3 17 62 52 10 56 50.6 15 cathodic 44 50 23 40.5 51 29 38.5 49.6 1.024 x 10’2 60 anodic 270 210 30 208 208 20 190 206 20 cathodic 150 210 30 142 208 60 118 208 42 with increasing anodic current, while for cathodic charging, the capacitance shows a distinct but decreasing trend with increasing cathodic current. The capacitance values ob— tained from the relaxation data do not show this trend but remain essentially constant for all currents. As demon- strated by Weir (36) the appropriate capacitance for either procedure is that corresponding to the zero current inter- cept of its current dependent values. Thus zero—current estimates of the differential capaci- tance were obtained for all solutions by both procedures. These values are summarized in Table (4). These values are the average of four determinations. Figure (7) shows the log differential capacitance plotted as a function of measured potential compared to the values of Sluyters-Rehbach and Sluyters obtained from their faradaic impedance study and to Weir's values of capacitance is. equivalent potential calculated using E° = 0.789 (19). The agreement is very good until high potentials. The dis- crepancy here is most likely because of the shorter time at which the present dataimne obtained. With longer time more Chxge will be consumed by the faradaic reaction and thus Aq will increase and hence Cd increases. This will be more apparent at high concentrations. Using a 2 usec charge duration Weir stated he observed a steep initial curvature in the charging curves which was more prolonged the higher the concentration and more evident with lower than with higher cathodic current density. A 43 Table 4. Differential capacitance estimates for solutions of varying concentration of ng(ClO4)2 in 1.0 g HClO4. Concentration Zero-current Cap. Zero-current Cap. mole/liter from relaxation plot from charging curve (if/cm2 (If/cm2 5.12 x 10‘6 25.7 27 1.024 x 10’5 28 27 2.048 x 10'5 28.1 29.1 5.12 x 10‘5 28.8 29.0 1.024 x 10'4 34.6 33.6 2.048 x 10" 33.8 35.4 5.12 x 10" 41.0 40.0 1.024 x 10‘3 50.0 52.2 2.048 x 10‘3 61.4 61.0 5.12 x 10‘3 118.4 102.5 1.024 x 10 203 161.8 44 1b— 500-" A 0 Calculated from charging data A Values of Weir 400 ‘- 9 Values of Sluyters-Rehbach and Sluyters 300 +— D 200-+ NE 0 o \\ ‘EI 8 A {3100 4— 0 ii 90 +— 8 I % 80 {- U 70 '0- B 73 A .3 60 ‘5 0 G G 2’, 50 ._ 9 .3 El I: a A I: 40 1% o E] A 0 E] D o A ‘ 30 .. A ‘3' m o O 2° + + + I 4 0.74 0.72 0.70 0.68 0.66 0.64 E ygn NHE Figure 7. Differential capacitance as a function of po- tential. 45 1 usec charge duration was used in the present investigation and the charging curves were observed to curve off. This was more marked at anodic currents and with higher concen- trations and was attributed to the onset of the faradaic reaction. Typical charging curves are illustrated in Figure (8). The initial slope of these curves was used in all capacitance calculations. Typical relaxation curves and semi-logarithmic decay plots with a pulse duration of 0.2 usec are illustrated in Figure (9). Slopes of the log n versus t plots were taken from the initial portion of the curve. Since no portion of these curves is essentially linear something more than charge—transfer must be occurring. Exchange current densities were determined for each concentration from graphically~estimated slopes of log n versus t plots prepared directly from the relaxation curves. The values of the apparent exchange current densities calcu- lated from the two sets of capacitance values are summarized in Table (5). A reaction order plot of these data is given in Figure (10). It shows excellent linearity with the exception of the low concentration region for both sets of data. The slope of the reaction order plot is found to be 0.67 i 0.02. On the basis of the simple reaction-order treatment given in the introduction, this corresponds to an apparent transfer coefficient of a = 0.33 i 0.02. From the \ 1 nsec I I 5 mV 5 mV ] 2 mV ] 5 mV 5 mV 5.12 x 10'6 g H92(C104)2 17.5 ma anodic current 1 cm = 5 mV 5.12 x 10'6 2.4. ng(c104)2 20 ma cathodic current 1 cm = 5 mV 1.024 x 10"3 _M_ Hg2(c10.,)2 27.5 ma anodic current 1 cm = 2 mV —3 1.024 x 10 £4. H92(0104>2 27 ma cathodic current 1 cm = 5 mV -2 1.024 x 10 L4 H92(C104)2 60 ma anodic current 1 cm = 5 mV —2 1.024 X 10 fl H92 (C104)2 60 ma cathodic current 1 cm = 5 mV Figure 8. Typical charging curves. C) 0 9 OIO O Z a . 3..- .3" c' c- 2+- 2.... LI 1-- A .l .4 1 J i _5 _L A A L . n I .2 .4 .6 .8 110 112 1.4 .. .2 .4 .‘6 .‘8 110 112 1'.4 t, usec t, usec 5.12 x 10'6 111 H92 (C104)2 5.12 x 10'6 E ng(C104)2 17.5 ma anodic - 15 ma cathodic 53- 51,- 4r 4 > > E is. I... c- C‘ 2 _ 2+ 1“ 11 .2 .4' .'6 .‘8 1'.0 1'.2 11.4 I .2 .4 .6 .8 1.0 112 1.4 t, nsec t, usec 1.024 x 10'3 _N 1492(C10.,)2 1.024 x 10‘3 g Hg2 (C104)2 29 ma anodic - 29 ma cathodic 5 I- 5‘1‘ 4 - 4* > E e . 3-+ ~3.. C. _ 2 ‘I- 2 I- 1-0- 1.; .2 .4 .6 .8' 1.0 1.2 1'.4 .2 .4 .FE 1.0 1.2 1.4 t, nsec t, usec 1.024 x 10‘2 g Hg2 (c104)2 1.024 x 10‘2 g ng(C104)2 60 ma anodic ~ 60 ma cathodic Figure 9. (Cont.) 49 Table 5. Calculated apparent exchange current densities. Concentration i: from charging i: from relaxation mole/liter cap. amp/cm2 cap. amp/cm2 5.12 x 10‘6 0.0666 0.0636 1.024 x 10'5 0.0763 0.0791 2.048 x 10'5 0.0876 0.0871 5.12 x 10‘5 0.1040 0.0960 1.024 x 10‘4 0.1188 0.1233 2.048 x 10'4 0.2102 0.2006 5.12 x 10'4 0.3538 0.3564 1.024 x 10'3 0.5561 0.5345 2.048 x 10'3 1.0000 0.8994 5.12 x 10‘3 1.652 1.877 1.024 x 10’2 3.281 4.235 +0.64 +0.4-‘ amp/cm2 I ‘ I I I + H O O O O O o 0 o o o 0 O 00 03 IA N N I l l l 1 I. I H [\3 1 Log apparent exchange current density, L. L. J 50 (JCalculated with capacitance determined from charging experiments AsCalculated with capacitance determined from relaxation experiments CJCorrected values l J n . l -4 -3 -2 Log concentration H92(C104)2: fl; 3.» Figure 10. Reaction order plot in 1.0 fl_HClO4 at 25° C. 51 i: values and a, an apparent standard rate constant k: = 0.0297 1 0.002 cm/sec is calculated To explain the anomaly of the exchange current leveling off at low concentrations it was postulated that the mercurous monomer was contributing to the exchange current. A theore- o .o .o tical calculation of i = 1 + 1 atotal amonomer adimer dld show a positive deviation from linearity at the low concentrations but did not correspond to the experimental curve for any value of kd for the dimer kd = [Hg+]2/[Hg§+]. It was then observed that a constant added to the theoretical exchange current for the dimer corresponded very well with the experimental data. Since the measured potential did not deviate from the linear Nernst slope at low concentrations it was concluded that the constant was not a contribution from the chemical system but must re- sult from some other part of the experimental system. On placing a resistance in parallel across the scope impedance it was observed that the initial slope of the log n gs t curve became steeper as the scope impedance de- creased. Thus it was postulated that a system decay con— stant resulting from some reactance of the cell relaxing across the scope impedance is observed added to the decay of the electrode-solution interface. By using 1 x 10-7 §_mercurous perchlorate which has a much smaller exchange current than is equivalent to the sys- tem RC time constant, the system decay constant was measured. 52 From this (RC)S a slope for this relaxation was ys calculated. By subtraction of this slope from the experi— mental curve, a curve assumed to correspond to solution— interface relaxation alone was obtained. The slope of the resulting curve was used to calculate a new exchange cur— rent value. This was done for 5 x 10.6 to 5 x 10—5 g ng(ClO4)2 and the resulting exchange currents agree well with the theoretical exchange currents. These corrected values are given in Table (6) and plotted in Figure 10. Table 6. Corrected values of apparent exchange current densities for low concentrations of ng(ClO4)2 Concentration i: from charging io from relaxation mole/liter cap. amp/cm2 cap. amp/cm2 5.12 x 10’6 0.0161 0.0159 1.024 x 10'5 0.0249 0.0252 2.048 x 10"5 0.0386 0.0380 5.12 x 10'5 0.0795 0.0790 Comparison of the exchange current density result of 1.0 x 10—3 g mercurous perchlorate with that of previous studies shows that it is considerably higher than that found by any of the other methods except the faradaic rectifica- tion study of Imai and Delahay which has previously been disproved. It does agree with Sluyters—Rehbach and Sluyters' determination that it should be :_0.46 amp/cmz. The low results of the previous investigations can be explained by 53 lack of correction for mass—transport. Weir's low results from the current-impulse data can be explained by the fact that dataxmre not obtained until 0.6 usec after the impulse. CON CLUS ION Although the mechanism of reduction of mercury (I) cannot be established from the results of the present in- vestigation, it has presented new data from which further investigation can proceed. Significantly, results have been obtained at much shorter times than previously and also the deviation of the exchange current from linearity at high concentrations as observed by Weir has been dis- proven. By design of a more compact cell and use of a differ— ential probe from the cell to the scope it is hoped that more significant data can be obtained on further investiga- tion to explain why the differential capacitance increases with potentials anodic of +0.4OO and to obtain a mechanism for the reduction of mercury (I). 54 .h 0301 q 10. 11. 12. 13. 14. 15. 16. 17. BIBLIOGRAPHY Armstrong, A. M., J. Halpern, and W. c. E. Higginson, J. Phys. Chem., 69, 1661 (1956). Berzins, T., and P. Delahay, J. Am. Chem. Soc., 11, 6448 (1955). Birke, R. L. and D. K. Roe, Anal. Chem., _ZJ 455 (1965). Brubaker, R. L., C. G. Enke, and Ramaley, L. v., Anal. Chem., 3_5. 1088 (1963). _— Cartledge, G. H., J. Am. Chem. Soc., §§J 906 (1941). Delahay, P., J. Phys. Chem., 663 2204 (1962). Delahay, P., Anal. Chem., Q4, 1161 (1962). Erdey, L., "Gravimetric Analysis, Part II" International Series of Monographs on Analytical Chemistry, Pergamon Press, p. 62. Ershler, B. v., Disc. Faraday Soc., in 269 (1947). Ershler, B. v., Zhur. Fiz. Khim., _2__2_, 683 (1948). Grahme, D. c., Chem. Revs” :11, 441 (1947). Gerisher, H. and M. Krause, Z. Physik Chem. (Frankfurt) N.F., 1_4_, 184 (1958). . Gerisher, H. and K. Staubach, Z. Physik, Chem. (Frank- furt) N.F.. Q, 118 (1956). . Hietanen, S. and L. G. Sillen, Arkiv Kemi, 19, 103 (1956). Higginson, W. C. E., J. Chem. Soc. (London), 1438 (1951). Imai, H., and P. Delahay, J. Phys. Chem., 66, 1108 (1962). Kolthoff, J. M. and C. Barnum, J. Am. Chem. Soc., 62, 3061 (1940). 55 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 56 Korinek, G. J. and J. Halpern, J. Phys. chem., 285 (1956). 90.. Latimer, W. M.,"Oxidation States of the Elements and Their Potentials in Aqueous Solutions? 2nd Edition, Prentice—Hall, New York, 1952, p. 175. Matsuda, H., S. Oka, 9.1.. 5077 (1959). McCurdy, W. H., 64, 1825 (1960). Jr. and G. G. Guilbault, J. Phys. Chem., and P. Delahay, J. Am. Chem. Soc., Moser, H. C. and A. F. Voigt, U.S. Atomic Energy Comm. 1SC-892 (1957) (actual reference not seen). Moser, H. Reinmuth, W. H., Anal. Chem., 34, 1272 (1962). Reinmuth, C. and A. F. Voigt, J. Am. Chem. Soc., 19, 1837 (1957). W. H. 1159 (1962). and C. E. Wilson, Anal. Chem., 24. Rosseinsky, D. R., J. Chem. Soc., 1963, 1181-6. Rosseinsk , D. R. and W. C. E. Higginson, J. Chem. Soc., 31, (1960 . Rozental, 1344 (1948 . K. and B. V. Ershler, Zhur. Fiz. Khim., 223 ) Schwarzenbach, G. and G. Anderegg, Helv. Chim. Acta, §1J 1289 ( 1954). Senda, M., H. Imai, and P. Delahay, J. Phys. Chem., 951. 1253 ( 1961). Sidgwick, N. v.,"The Chemical Elements and their Com- pounds," Oxford Univ. Press, London, p. 289 ff. Sluyters-Rehbach, M., Chim., 82, 525 (1963). Sluyters-Rehbach, M., Chim., §§, 217 (1964). Sluyters-Rehbach, M., Chim., 83, 983 (1964). 1950, Vol. I, and J. H. Sluyters, Rec. Trav. and J. H. Sluyters, Rec. Trav. and J. H. Sluyters, Rec. Trav. Weir, W. D., Dissertation, Princeton University, Princeton, Ann Arbor, N.J., Mich. 1965; University Microfilms, 1966. Inc., 36. 37. 38. 39. 57 Weir, W. D. and C. G. Enke, J. Phys. Chem., 11, 280 (1967). Weir, W. D. and C. G. Enke, J. Phys. Chem., 11, 275 (1967). Wolfgang, R. L. and R. W. Dodson, J. Phys. Chem., 872 (1952). Woodard, L. A., Phil. Mag., 18, 823 (1934). .59. ”'TITifllflfllfiilfijlu(T)\11)))i)(il)MW)“ 939