J. Chem. Soc., Faraday Trans. I, 1988, 84(1), 97-109 Mechanism of Electrohydrodimerization of Cyclohex-2-en- 1-one on Mercury from Aqueous Solutions Part 1.-Results obtained in the Absence of Surfactants M. Yolanda Duarte Department of Chemistry, Nordeste University, Corrientes, Argentina Corrado Malanga and Lamberto Nucci Department of Chemistry and Industrial Chemistry, Pisa University, Pisa, Italy M. Luisa Foresti and Roland0 Guidelli" Department of Chemistry, Florence University, Florence, Italy The diffusion-controlled one-electron wave (wave I) due to cyclohex-2-en- 1 - one (R) electroreduction on mercury from aqueous solutions in the range 2.5 < pH < 4 is shown to be consistent with the following mechanism : R+ HA+ RH+ +A- RH+ + e $ RH' ( 1 4 ( 1 4 2RH' r - R2H2 ( 1 c) where HA is a proton donor and the rate-determining coupling step (1 c), denoted by rds, proceeds in the adsorbed state.Double-potential-step chronocoulometric measurements indicate that R adsorption lies below the limits of sensitivity of the method, whereas R2H2 adsorption is appreciable at all potentials positive to - 1.4 V us. SCE. The limiting current of wave I in the range 4 < pH < 6 is controlled by the protonation step (1 b), which is shown to proceed both heterogeneously and homogeneously. The con- tribution of the various proton donors, including adsorbed water, is pointed out. The diffusion-controlled one-electron wave (wave 11), which develops at the expense of wave I at pH > 7, is shown to be consistent with the R + e+ R'- (7 4 following mechanism : R'- +HA e RH' +A- (7 4 2RH' rx R,H2 (7 c) for 7 < pH < 10, and with the mechanism R+ e s R'- (lOa> 2R'- Rip (lob) ( W for pH > 11.For mechanisms (7) and (10) the rate-determining coupling step is homogeneous. The mixtures of isomeric forms of the hydrodimer R2H2 obtained at pH 5 uia the heterogeneous coupling step (1 c) and that obtained at pH 9 uia the homogeneous coupling step (7c) have practically the same composition. Ri- + 2H20 e R2H2 + 20H- 97 4-298 Electrohydrodirnerization of Cyclohex-2-en- 1 -one A systematic investigation of the mechanism of electrohydrodimerization (EHD) of diactivated alkenes on mercury from aqueous media has been carried out in this laboratory.'" As distinct from a number of diactivated alkenes which undergo EHD only in the presence of strong surfactants, chalcone undergoes EHD in aqueous media both in the presence4 and in the absence5 of strong surfactants such as Triton X-100.While chalcone EHD in the presence of Triton X-100 takes place in the non-adsorbed state, that in the absence of strong surfactants takes place in the adsorbed state and yields a different mixture of hydrodimer isomers. To verify whether this behaviour is shared by other a, B-unsaturated carbonyls, we have thoroughly investigated the mechanism of EHD of cyclohex-2-en- 1 -one by direct current (d.c.) polarography and chronocoulometry. This paper reports the results obtained in the absence of surfactants, whereas Part 2 deals with cyclohex-2-en-1-one EHD in the presence of Triton X-100.The electroreduction of cyclohex-2-en- 1 -one (henceforth denoted by R) has been the subject of several studies in aqueous,'. ' hydroalcoholics and non-aqueous lo The studies in aqueous' and hydroalcoholic' media agree in ascribing the diffusion- controlled one-electron wave observed at pH < 4 (wave I) to electronation of the protonated form RH+ of the reactant followed by coupling of the RH' radicals and hydrodimer formation. The one-electron wave (wave 11), which develops progressively at the expense of wave I and the pH is gradually increased above 4, is instead ascribed to direct electronation of the reactant R followed by further steps yielding the h ydrodimer . Experimental All chemicals were analytical reagent grade supplied by either Merck or Fluka, and were used without further purification.All solutions were prepared from triply distilled water treated with active charcoal. Mercury was purified by a wet process followed by three distillations. All potentials were measured against a saturated calomel electrode (SCE). Polarographic measurements were carried out at 25 f 0.25 "C with an Amel model 473 polarograph. In all measurements the drop time, t,, was kept equal to 2 s. Double- potential-step chronocoulometric measurements were carried out with a computerized apparatus described in ref. (1 l), using a pressurized hanging-mercury-drop electrode12 which was renewed under computer control. All measurements were carried out in buffered solutions in which the buffer concentration was no less than ten times the reactant concentration. The Na+ concentration in all solutions was kept constant at 1 mol dm-3 with NaCl. In this way the bulk concentration of the ions which predominate in the diffuse layer at the extremely negative potentials at which EHD takes place is kept constant, and the extent of ion pairing of the intermediate anion radicals is also kept constant.Results Cyclohex-2-en-1-one EHD was investigated over the pH range from 1.5 to 13. The pH was controlled with citric buffers from 1.5 to 3, formic buffers from 2.5 to 4, acetic buffers from 3 to 5, phosphate buffers from 5 to 7, borate buffers from 8 to 10 and with NaOH from 11 to 13. Higher pH values cannot be explored, since the height of the R- wave decreases in time because of reactant decomposition in the bulk.It is possible that at high pH values the ethylenic double bond of R undergoes hydration with formation of a hydroxy derivative, as observed with other a, B-unsaturated carbonyl comp~unds.'~~~* Polarographic Measurements The diffusion-controlled one-electron wave (wave I) observed in acidic solutions decreases in height as the pH is gradually increased above 4, while a more negative waveM. Y. Duarte et al. -1.30- -1.28 -1.26 - 1.24 99 - - - - - - - 1 I - I - 1 . 4 -1.3 w z ? - .I 4N 4 -1.1 # P r’ 1 /. b / / / / / / 1‘ 4 -1.7 w u m -1.6 2 > =+ 4 -1.5 I I I I I 4 6 0 10 12 PH Fig. 1. (a) Ei us. pH plot for mol dmP3 formic buffer (a), mol dm-3 phosphate buffer (m); the dashed line has a -60 mV slope. (b) Er us. pH plot for loP4 mol dmP3 R reduction from mol dm-3 borate buffer; the dashed line has a -40 mV slope.(c) Er us. pH plot for loP4 mol dmP3 R reduction from loP3 to lo-’ mol dm-3 NaOH solutions. mol dmP3 R reduction from mol dm-3 acetic buffer (0) and 5 x100 Elect ro h y dr odimer iza t ion of Cy clo hex- 2- en- 1 -one I f i I 0 2 4 6 8 [H']f/10-3 mol* dm-) Fig. 3. The solid curve (a) is a plot of </(fd - () us. [H+]i for phosphate buffer with [KH,PO,] = C,, = 5 x mol dm-3 R reduction from a rnol dm-3. For curves (b) and (c) see the text. 0 0.1 0.2 0.3 ciA /mola dm-* Fig. 4. </(id-<) us. dHA plot for mol dm-3 R reduction from a pH 5.46 phosphate buffer (HA = KH,PO,). (wave 11) develops and increases at the expense of wave I. Ultimately, at pH > 7 wave I vanishes and only the one-electron wave (wave 11) is left.Wave I At pH < 2.5 wave I splits into an adsorption prewave and in the corresponding 'normal' wave, provided the reactant concentration C: is > 2 x lo-* mol dm-3. The limiting height of the adsorption prewave points to a maximum surface coverage by the adsorbed EHD product of 3 x 10-l' mol as already observed by Denney and Mooney.6 AtM . Y. Duarte et al. 101 EIV us. SCE Fig. 5. (a) Plot of Aa'(E, + - 1.75 V) us. E, as obtained from a solution of 0.01 mol dm-3 NaOH + 0.99 mol dm-3 NaCl both in the absence and in the presence of mol dm-3 R; the polarogram in the presence of the reactant is also shown (a'). (b) Plot of AaM( - 1.75 V --* E,) us. Ef as obtained from a solution of 0.01 mol dmV3 NaOH + 0.99 mol dm-3 NaCl+ mol dm-3 R.(c) Plot of Ac'(-0.92 V + Ef) us. E, as obtained from a solution of 1 mol dm-3 mol dm-3 R, whose polarogram is shown in (c'). HCl+ pH values > 2.5 no adsorption prewave is observed. Under these conditions the plot of the half-wave potential Ei of wave I vs. pH at constant C$ has a slope of ca. -60 mV [see curve (a) in fig. 13. As the reactant concentration is gradually increased at constant pH, wave I shifts towards more positive potentials. The rate aE{/a log Cg of the half- wave potential shift increases with increasing log C:, attaining a maximum limiting value of 30 mV at Cg > mol dm-3 [see curve (a) in fig. 21. At pH values low enough to ensure a diffusion limiting current id for wave I, Ei is independent of buffer concentration. Thus, an increase in buffer concentration by almost two orders of magnitude under otherwise identical experimental conditions leaves Ei practically unaltered. As the limiting current 6 of wave I starts decreasing with respect to its diffusion- limiting value id because of an increase in pH above 4, it becomes dependent on the buffer concentration.Thus 6 decreases not only with a decrease in H30+ concentration at constant concentration C,, of the acid component HA of the buffer (see fig. 3), but also with a decrease in C,, at constant pH (see fig. 4). The more 6 decreases with respect to id the more the plateau of wave I deviates from horizontal behaviour, causing ( to become progressively more dependent on potential. In plotting fig. 3 and 4, the arbitary procedure of measuring il at a potential E = El - 100 mV was adopted.Wave II In well buffered solutions of pH ranging from 8 to 10, when the limiting current of wave I1 has already attained its diffusion-limiting value id, the half-wave potential Ef of this wave shifts towards more negative values by 40 mV per each unitary increment of pH [see curve (b) in fig. 11. Then, as pH is increased above 1 1 , Eil tends to become102 Electrohydrodirnerization of Cyclohex-2-en- 1 -one I I I o o o o o o o o o o o o o o o ooooo 0 0 O O O O O t/ms Fig. 6. Q(t) us. t curve as obtained from a solution of 0.01 mol dm-3 NaOH + 0.99 mol dm-3 NaCl+ mol dm-3 R upon stepping the applied potential from E, = - 1.75 V to Ef = - 1.00 V at t = 0 and then backward at t = z = 50 ms. independent of pH [curve (c) in fig.11. Provided that over the pH range 7-10 the solution is well buffered (buffer concentration 2 10 Cz), El' is independent of the buffer concentration. In well buffered solutions of pH 7-10 and at NaOH concentrations 3 lOCg, El' at constant pH shifts towards more positive values by ca. 20mV per unitary increment of log C;lt [see curves (b) and (c) in fig. 21. Chronocoulometric Measurements The presence of an adsorption prewave in acidic solutions denotes a notable adsorption of the electrode-reaction product, at least over the potential range covered by wave I at these low pH values. Single and double-potential-step chronocoulometric measurements were performed to determine the potential dependence of product adsorption and to ascertain whether the reactant R is also appreciably adsorbed.Curve (a) in fig. 5 shows the changes AaM in capacitive charge involved in a series of potential jumps from a variable initial potential Ei to a fixed final potential Ef = - 1.75 V us. SCE in a pH 12 solution free from reactant, as plotted against Ei. The slope of this plot is almost constant, and corresponds to the differential capacity on mercury at potentials negative to the P.Z.C. in the absence of specific adsorption (ca. 17 pF cm-2). The same single- potential-step chronocoulometric measurements were then performed in the presence of mol dm-3 reactant, which under these conditions yields wave I1 with Ei* = - 1.61 V [see fig. 5(a)]. The resulting plots of the time-dependent charge Q(t) flowing at Ef us. the square root ti of the electrolysis time are linear, in agreement with the fact that Ef lies $long the diffusion-controlled plateau of wave 11.The intercepts of these plots on the ti = 0 axis at different values of the initial potential Ei yield AoM (Ei) at the interphase between mercury and the reactant solution. The resulting AaM us. Ei plot practically coincides with curve (a), indicating no detectable adsorption of R. Double-potential-step chronocoulometric measurements carried out under the same experimental conditions show that the charge Q(t-z) following the backward potential jump at t = z fromM. Y. Duarte et al. 103 Ef = - 1.75 V to Ei decreases abruptly and then remains perfectly constant in time. This indicates that the primary reaction product is converted into the electroinactive hydrodimer R2H2 so rapidly as not to give rise to a detectable reoxidation current to the reactant.To detect product adsorption, double-potential-step chronocoulometric measure- ments were performed in which the mercury drop was kept at a fixed initial potential Ei = - 1.75 V along the plateau of wave I1 for the majority of drop life. Towards the end of drop life the applied potential was then stepped to a more positive value Ef for a time period z = 50 ms during which adsorption equilibrium of the hydrodimeric product at Ef was established (see fig. 6). Note that the diffusion layer produced by R2H, diffusion towards the bulk at Ei = - 1.75 V before the potential jump is much thicker than that produced by any R2H2 diffusion towards the electrode surface following its adsorption at Ef during z.Hence we can safely assume that, as far as the diffusion and adsorption of R2H2 at Ef is concerned, the electrode behaves as though it were immersed in a solution of R2H, of bulk concentration C:. After z, the potential was stepped back from Ef to Ei = - 1.75 V. As shown in fig. 6, the charge Q(t - z) following the backward potential jump first decreases abruptly by an amount equal to the capacitive charge AaM at the interphase between mercury and a mol dm-3 solution of R2H2, and then more slowly on account of R electroreduction at - 1.75 V. The quantity AaM(Ef) corresponding to the various Ef values was obtained by graphical extrapolation to t = z. Such a procedure involves an error no greater than 0.5 pC cm-2.The resulting plot of AaM(Ef) us. Ef is shown in fig. 5(6). This curve has the typical shape of charge us. potential curves of neutral organic surfactants. The intersection point of curves (a) and (h) locates the potential Em,, = -0.6 V of maximum adsorption for the product R2H,, whereas the merging of curves (a) and (b) at E < - 1.4 V denotes the lack of detectable R,H2 adsorption at these negative potentials. The differential capacity of an R2H2 solution in contact with mercury at Emax amounts to ca. 7 pF cm-2. The same value was obtained by performing double-potential-step chronocoulometric measurements anal- ogous to those in fig. 6 with a lop3 rnol dm-3 solution of R in 1 mol dmP3 HC1, upon jumping from an initial potential Ei = -0.92 V along the plateau of the adsorption prewave [see the profile of the whole wave I in fig.5 (c')] to more positive final potentials. The resulting AaM(Ef) us. Ef plot is shown in fig. 5 (c). The potential Emax = -0.6 V has the property that a potential jump from Emax to a final potential negative enough to exclude R2H2 adsorption (say < - 1.4 V) involves a capacitive charge AaM which does not depend upon the concentration of R2H2 around the electrode. By performing a double-potential jump from Ei = Emax to t3, = - 1.75 V in a pH 12 solution of mol dmP3 R, the capacitive change in charge, Q(z + dt) - Q(z - dt), following the backward potential jump Ef -+ Emax is practically e,qual to the cfiarge, ca. 17.2 pC cmp2, obtained from the intercept of the Q(t < z) us.ts plot on the ti = 0 axis, where Q(t < z) is the charge flowing at Ef before the backward potential jump. This confirms unequivocally the absence of detectable reactant adsorption, at least at Cz < mol dmP3. Higher reactant concentrations were not investigated pecause of the rapid decrease in the accuracy of the extrapolation of Q(t < z) us. tz plots with increasing CE. Macroscale Electrolysis Macroscale electrolysis was carried out in a conventional cell described in ref. (5). Cyclohex-2-en-1-one EHD was carried out both in a pH 9 borate buffer (0.16 mol dmp3 Na,B,O, + 0.68 mol dmd3 NaCl) at - 1.6 V, where the coupling reaction takes place homogeneously, and in a pH 5 acetic buffer (1 mol dm-3 CH,CO,H+ 1 mol dm-3 CH,CO,Na) at - 1.4 V, where the coupling reaction takes place mainly in the adsorbed state.During electrolysis in the borate buffer solution the pH value was controlled by104 Electrohydrodimerization of Cyclohex-2-en- 1 -one a glass electrode immersed in the cathodic compartment ; whenever pH increased beyond 9.2-9.3, the original value was restored by adding a few drops of 6 mol dm-3 HC1. A coulometric analysis at controlled potential yielded a value of almost unity for the number of electrons per molecule of the reactant in both buffer solutions. Electrolysis was conducted up to 91 YO conversion in the pH 9 borate buffer and up to 77% conversion in the pH 5 acetic buffer. After electrolysis, the cathode-compartment contents were extracted with ethyl acetate in a separation funnel. The organic phase was washed with water up to neutrality and dried with Na,SO,. The extracts were then stripped of the organic solvent under vacuum ( mmHgt). The oily crude product so obtained was examined by thin layer chromatography (t.1.c.) on silica and by high- performance liquid chromatography (h.1.p.c.) on a Lichrosorb Si60 column using an ethyl acetate-hexane 80/20 (v/v) mixture as eluent.This crude product turned out to consist of three different compounds and to be practically the same no matter if obtained from borate or acetic buffer. The main compound obtained by fractionating the crude product in a Lobar Lichropur Si60 column yielded the same lH-n.m.r. and i.r. spectra and the same chromatographic response as the starting crude product. This behaviour denotes the establishing of a slow equilibrium between this compound and the other isomers of the crude reaction mixture.It is possible that the attainment of this equilibrium is favoured by the silica employed for the chromatographic separations. Lr., 'H-n.m.r. and m.s. analyses were therefore carried out directly on the crude product. 1.r. spectra obtained from a liquid film of the crude product showed a band at 3460 cm-', ascribable to OH bond stretching, and a band at 1730 cm-l, ascribable to C=C and/or C=O double-bond stretching. 1.r. spectra of a solution of the crude product in CDC1, showed four distinct bands at 3650, 3600, 3460 and 3150 cm-l. A comparison with i.r. spectra of analogous compounds in CDC1,15~'6 permitted us to ascribe this behaviour to a mixture of the following hydrodimers.0 This conclusion was supported by m.s. analysis carried out by direct introduction of the raw product, which showed a spectrum identical to that reported for diketone 111.'' Combined gas chromatography-mass-spectral analysis of the raw product, carried out using a 2 m x 0.29 cm column filled with 8 YO CW20M + 2 YO KOH on 80-100 mesh Chromosorb W DMCS (CW20W) and helium as carrier gas, yielded four chro- matographic peaks having retention times of 7.12, 7.90, 11.80 and 18.02 min. The compound with 7.12 min retention time was ascribed structure I (M+ = 194, M+- H,O = 176), that with 7.90 min retention time structure I1 (M' = 194, M+-H20 = 176, M+-2H20 = 158), whereas the compounds with higher retention times were identified as degradation products of structure 111.'H-N.m.r. analysis of the crude product yielded signals at 6.0-5.4 and 3.4-2.6 ppm, which are ascribable to olefinic and alcoholic t 1 mmHg = 13.5951 x 980.665 x lo-' Pa.M. Y. Duarte et al. 105 EIVvs. SCE -1.50 -1.55 -1.60 1 I I \ h \ \ \ \ \ ~ ~~ -1.25 -1.30 -1.35 E/V us. SCE Fig. 7. (a) Plot of log [(I - i/~;)~/(i/i~)] us. E for buffer. (b) Plot of log [( 1 - i/id)/(i/i:)i] us. E for mol dmP3 R reduction from a pH 4.6 acetic mol dm-3 R reduction from a pH 8.8 borate buffer. protons, respectively, as well as signals at 2.6-0.8 ppm, which are ascribable to the cyclohexane and cyclohexene rings of structures I, I1 and 111. Upon addition of D,O to the reaction mixture, the signals due to the alcoholic protons disappeared. On the other hand DCl addition caused a slow conversion of product I into product IV: Formation of the latter compound was deduced from the disappearance of the signals of the H, and Hb.protons and the appearance of a structured doublet (5.5-5.3 ppm) and of a large multiplet (4.0 ppm) ascribable to the H, and H, protons, respectively. 'H-N.m.r.spectra of the crude product, as recorded in pyridine, showed several similarities in chemical shifts with the spectra of analogous compounds under the same experimental ~0nditions.l~ In particular, the alcoholic protons of structures I and I1 resonate at 5.0 ppm, whereas the Ha and Hb protons resonate at 6.2-5.6 ppm. On the basis of the above spectroscopic evidence, the 'H-n.m.r. spectra of the crude product allowed us to conclude that such a product consisted of compounds I and I1 in equilibrium as well as of compound I11 in a 60/40 approximate ratio.106 Electrohydrodimerization of Cyclohex-2-en- I -one The experimental observation that heterogeneous coupling at pH 5 and homogeneous coupling at pH 9 yield the same mixture of hydrodimers seems to contrast with chalcone EHD,5 which leads to different isomeric forms of the hydrodimer depending on whether the coupling reaction takes place in the adsorbed or non-adsorbed state.However, chalcone EHD in the absence of strong surfactants such as Triton X-100 takes place at an electrode surface which is almost fully covered by reactant and product. Under these conditions the neutral radicals which undergo coupling in the adsorbed state are likely to have a well defined orientation imposed by the high surface coverage.On the other hand, cyclohex-2-en- 1 -one is adsorbed very weakly. Hence the adsorbed neutral radicals RH' which undergo heterogeneous coupling are almost certainly free to assume quite different orientations relative to the electrode surface, and hence they behave towards coupling as though they were in the non-adsorbed state. Discussion The behaviour of wave I over the pH range 2.5-4, where no adsorption prewave is observed and the limiting current is diffusion-controlled, is consistent with the following mechanism : 1 R + HA RH+ +A- (1 a ) EtJ RH+ + e + RH' (1 b) where the rate-determining coupling step (1 c), denoted by rds, takes place in the adsorbed state. In eqn (1) HA is a proton donor and A- its conjugated base.The diffusional problem for mechanism ( I ) under the assumption that the reactant is weakly adsorbed (Henry-isotherm behaviour) is entirely analogous to that examined in ref. (9, the only difference being represented by the fact that here the rate-determining heterogeneous coupling step is preceded by the protonation step ( l a ) in quasi- equilibrium. The presence of this further step is readily accounted for by applying the equilibrium condition to both steps (1 a) and (1 b) under the assumption that the protonation equilibrium (1 a ) is almost completely shifted towards the unprotonated form R in the bulk solution: (2) CRH+/CRH = exp HE- E,)] = C,[H+]/(K,, CRH). H e r e f r F/RT, the C denote volume concentrations at the electrode surface and Kd = CR[Hf]/CR,+ is the dissociation constant of RH'.Using eqn (2) in place of eqn (A 4) of ref. (9, the final current us. potential characteristic of eqn (A 7) of ref. ( 5 ) is modified as follows: E = E, +f-' In ([Hf]/Kd) + (2f)-' In (k6/?kH Cg/D) + (2f)-' In [( 1 - i/Ld)2/(f/fd)]- (3) Here Cc is the bulk reactant concentration, PltH is the adsorption coefficient of the RH' intermediate, 6 is the diffusion-layer thickness and D is the diffusion coefficient, assumed to be the same for all diffusing species. According to eqn (3), the half-wave potential of wave I is given by (4) E$ = E,, + (2f)-l In [kdp2,,/(2D g)] - 2.3 f-' pH + (2f)-' In CE. The predictions of this equation are verified. Thus (t3EI/t3pH),; is = -60 mV as shown in fig.1, whereas (aE[/a log C*,),, is =-30 mV as &own in fig. 2. A further confirmation comes from the plot of log [ ( l -i/id)2/(i/id)] us. E in fig. 7(a), which is linear and has a slope of (30 mV)-', in agreement with eqn (3). This experimental behaviour does not agree with any of the most familiar homogeneous EHD mechanismsM. Y. Duarte et al. 107 (radical-radical, radical-substrate and ion-substrate coupling mechanisms)." Eqn (3) and (4) also hold in the case in which protonation follows charge transfer rather than preceding it. However, this mechanism is inconsistent with the decrease of the limiting current of wave I below its diffusion limiting value cd as observed at pH > 4. The heterogeneous nature of the coupling step is confirmed by the effect of an addition of lo-* mol dmP3 Triton X-100 to a pH 4 solution of mol dm-3 R.Such an addition causes a moderate negative shift of wave I (ca. -20 mV) and a change in wave shape. Thus the difference (I$ - 4) between the potentials at which i = </4 and 3i,/4 passes from 41 to 47 mV. In Part 2 it will be shown that the presence of Triton X-100 causes wave I to satisfy the requirements for a homogeneous radical-radical coupling step (e.g. &?!/a log Cc becomes ca. 20 mV). Triton X-100 concentrations as low as rnol dmP3 are indeed sufficient to remove both the reactant and the intermediate products completely from the adsorbed state, thus deactivating the heterogeneous pathway to radical-radical coupling in favour of the homogeneous one. The slight shift of El following Triton X- 100 addition denotes that the rates of the two parallel homogeneous and heterogeneous pathways are only slightly different. This is not surprising since the surface concentration of the protonated radical RH' should not differ much from that of the reactant R, which lies below the limit of sensitivity of the double-potential-step chronocoulometric technique (ca.0.3 ,uC cm-2, corresponding to a surface coverage 0 x 0.005 if the maximum surface concentration is taken as equal to that deduced from the limiting height of the adsorption prewave). The slope of the El us. log C;F. plot being less than 30 mV at Cg < lo-* mol dmP3 [see curve (a) in fig. 21 is explained by noting that the homogeneous coupling step is characterized by 8E!/a log Cg = 20 mV, whereas the heterogeneous one is characterized by log CE =' 30 mV.For Cc 6 lo-* rnol dmP3 the homogeneous pathway may therefore yield a more positive 4 value, and hence a higher current at any given potential, than the corresponding heterogeneous pathway. Under these conditions the homogeneous pathway will prevail over the parallel heterogeneous one, yielding &!?!/a log C;F. = 20 mV. As Cg becomes sufficiently high, however, the opposite will be trbe, whereas at intermediate Cg values the slope of the Ef us. log Cg plot will gradually change from 20 to 30 mV. 'At pH > 4, when the limiting current 6 of wave I becomes lower than its diffusion- limiting value, the rate of the overall process is simultaneously controlled by the protonation step (1 a), by the coupling step (1 c) and by reactant diffusion towards the electrode. Naturally, the contribution of the coupling step to the control of the electrode process decreases as we proceed along the rising portion of the wave and ultimately vanishes along the plateau of wave I.Contrary to what was reported by Ivcher et al.,7 we found that the dependence of 6 upon pH and buffer concentration does not satisfy the requirements for a rate-determining homogeneous protonation step. To explain such a dependence we must assume that protonation takes place both homogeneously and heterogeneously. An approximate expression for a limiting current controlled by a mixed homogeneous-heterogeneous protonation is as follows : 6 /(id - i,) = A + 0.8 1 2( [ H+] t d k,/Kd)i ( 5 ) with The first and second terms on the right-hand side of this equation express the contributions from heterogeneous and homogeneous protonation, t d is the drop time, k, and k , are the heterogeneous and homogeneous protonation rate constants respectively, whereas PR and Tm are the adsorption coefficient and the maximum surface concentration of R.Eqn ( 5 ) is obtained from eqn (474) of ref. (19), which represents a slight improvement pver Mairanovskii's formula,2o upon disregarding PR Tm with respect to ( 12Dta/7n)1. The latter simplifying assumption is thoroughly justified in view of the weak adsorptivity of R.108 Electrohydrodimerization of Cyclohex-2-en- 1 -one In view of the principles of general acid-base catalysis, both rate constants k, and k, consist of contributions from all proton donors present in the solution.The mechanistic study of EHD reactions of activated alkenes in aqueous media has revealed that adsorbed water molecules are much stronger proton donors than non-adsorbed We will therefore assume that by far the major contribution to k, stems from adsorbed water molecules, whereas that to k, stems from both the H30+ ion and the acid form HA (6) of the buffer: The linear plot of </(i,-il) vs. &HA at pH 5.46 in fig. 4 agrees with eqn (5) and (6), provided that k,, HA CHA 9 kv, H+ [H+] at this relatively low hydroxonium ion con- centration. The positive intercept A = 0.45 of this plot points to a heterogeneous protona!ion pathway. The slope of the plot yields a (kv. HA/&)' value ofca. 2.6 x lo3 dm3 mol-1 s-2. With these A and (kv,HA/K,)i values we can draw a plot of ~+0.812([H+]- c,, 'dk,, HA/&)' at constant CHA against [H']', expressing the asymptotic behaviour of </(id-iJ at low [H+] values when the homogeneous protonation by HA prevails over that by H,O+.This plot is expressed by the dashed straight line (b) in fig. 3, which fits nicely the lower portion of the experimental curve (a). Deviations between curves (b) and (a) at the higher [H+]i values are then used to estimate the kv,H+/kv,HA ratio on the basis of eqn ( 5 ) and (6). The dashed curve (c) was calculated from eqn ( 5 ) and (6) for a kv,H+/ k,,,,value of 1.5 x lo3. The moderate potential dependence of the limiting plateau of wave I for tl c id is such that the unavoidably artibrary procedure for measuring < may affect the above rate-constant values by factors as high as 3.However, the mechanistic conclusions drawn from fig. 3 and 4 are not appreciably affected by the choice of the procedure adopted to measure I;. The behaviour of wave I1 over the pH range from 8 to 10 is consistent with a mechanism which differs from the mechanism of eqn (1) by the fact that the protonation step in quasi-equilibrium follows the electron-transfer step : kv = kv, H+ [H+I+ kv, H A CHA- Re- + HA e RH' +A- (7 b) 2RH' 5 R2H2. (7 4 Moreover, the rate-determining coupling step (7 c) is now homogeneous. The current us. potential characteristic for this mechanism is reported in ref. (4), where the Koutecky-HanuS-Mairanovskii equation21* 22 for a reversible electron transfer followed by a coupling step was modified to include a preceding protonation in quasi-equilibrium. The modified equation is written as E = E[* +f-1 ln [25 (1 - f/id)/(i/id)'] 4' = Eb + (3f)-' In {[k'62[H+]2C:/(3D K:)} (8) (9) with where Ki = C,-[H+]/C,,.. The experimental value of -40 mV for aE!'/apH in fig.1 and that (20 mV) for aE['/a log C;it in fig. 2 (b), agree with the predictions of eqn (9), whereas they contrast with the predictions for homogeneous radical-substrate and ion-substrate coupling mechanisms1* and ,for any kind of heterogeneous coupling me~hanism.~ The plot of log [(I -i/&)/(t/t,)s] vs. E shown in fig. 7(b) is h e a r and has a (60 mV)-' slope, in agreement with eqn (8). The fact that the radical-radical coupling step is homogeneous along wave I1 whereas it is mainly heterogeneous along wave I is not surprising if we consider that RH' adsorption is likely to decrease towards increasingly negative potentials, in a way analogous to that shown by the resulting coupling product R2H2 (see fig. 5).Moreover, RH' adsorption is already small alongM. Y. Duarte et al. 109 wave I, where the rates of the two parallel homogeneous and heterogeneous coupling steps are almost comparable. At,pH values > 1 1 wave I1 is still characterized by a linear plot of log[(l -i/fd)/ (i/fd)'] us. E of slope (60 mV)-' in agreement with eqn (8), and by a value of aE!'/a log Cz of -20 mV [see fig. 2(c)]. This behaviour points again to a rate-determining homogeneous radical-radical coupling step. The tendency of to become pH independent as observed at 1 1 < pH < 13 can be explained on the basis of the following mechanism : R+e-GR'- (W 2R'- + Ri- rds Ri- + 2H,O e R2H2 + 20H-.(W Any protonation in quasi-equilibrium prior to the rate-determining coupling step, no matter the nature of the proton donor, would indeed cause the kinetics to be pH- dependent. Almost certainly the intermediate radicals R'- are not present around the electrode as negatively charged kinetic entities, but rather as ion pairs with the Na+ ion. The mechanism of eqn (10) in alkaline media was also hypothesized by Ivcher et al.' This work was supported by the Consiglio Nazionale delle Ricerche (Progetto finalizzato 'Chimica Fine e Secondaria'). Thanks are due to the Italian Ministry of Foreign Affairs for a fellowship to M. Y. D. during the tenure of which most of the present results were obtained. References 1 R. Guidelli, G. Piccardi and M. R. Moncelli, J. Electroanal. Chem., 1981, 129, 373. 2 M. R. Moncelli, F. Pergola, G. Aloisi and R. Guidelli, J. Electroanal. Chem., 1983, 143, 233. 3 C. Amatore, R. Guidelli, M. R. Moncelli and J. M. Saveant, J. Electroanal. Chem., 1983, 148, 25. 4 M. R. Moncelli, L. Nucci, P. Mariani and R. Guidelli, J. Electroanal. Chem., 1984, 172, 83. 5 M. R. Moncelli, L. Nucci, P. Mariani and R. Guidelli, J. Electroanal. Chem., 1985, 183, 285. 6 E. J. Denney and B. Mooney, J. Chem. SOC. B, 1968, 1410. 7 T. S. Ivcher, E. N. Zil'berman and E. M. Perepletchikova, Zh. Fiz. Khim., 1965, 39, 749. 8 E. Brillas and A. Ortiz, Electrochim. Acta, 1985, 30, 1185; J . Chem. SOC., Faraday Trans. I , 1986, 82, 9 P. Tissot and P. Margaretha, Helv. Chim. Acta, 1977, 60, 1472; Electrochim. Acta, 1978, 23, 104. 495. 10 P. Tissot, J. P. Surbeck, F. 0. GulaCar and P. Margaretha, Helv. Chim. Acta, 1981, 64, 1570. 11 M. L. Foresti, M. R. Moncelli and R. Guidelli, J. Electroanal. Chem., 1980, 109, 1. 12 M. L. Foresti and R. Guidelli, J. Electroanal. Chem., 1986, 197, 159. 13 P. Carsky, P. Zuman and V. Horak, Collect. Czech. Chem. Commun., 1965, 30, 4316. 14 P. Zuman, J . Electroanal. Chem., 1977, 75, 523. 15 J. Wiemann, S. Risse and P. F. Casals, Bull. SOC. Chim. Fr., 1966, 381. 16 E. Touboul, F. Weisbuch and J. Wiemann, Bull. SOC. Chim. Fr., 1967, 4291. 17 J. Dunogues, R. Calas, M. Bolourtchian, C. Biran and N. Duffaut, J. Organomet. Chem., 1973, 57, 18 L. Nadjo and J. M. Saveant, J. Electroanal. Chem., 1973, 44, 327. 19 R. Guidelli, in Electroanalytical Chemistry, ed. A. J. Bard (Marcel Dekker, New York, 1971), 20 S. G. Mairanovskii, E. D. Belokolos, V. P. Gul'tyai and L. I. Lishcheta, Elektrokhimiya, 1966, 2, 693. 21 J. Kouteckjr and V. HanuS, Collect. Czech. Chem. Commun., 1955, 20, 124. 22 S. G. Mairanovskii, Zzv. Akad. Nauk SSSR, Otd. Khim. Nauk, 1961, 12, 2140. 55. pp. 337-340. Paper 6/2499; 31st December, 1986