Optical and electrochemical study of cation adsorption on oxide layers on gold and platinum electrodes

Optical and electrochemical study of cation adsorption on oxide layers on gold and platinum electrodes


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OPTICAL AND ELECTROCHEMICAL STUDY OF CATION ADSORPTION ON OXIDE LAYERS ON GOLD AND PLATINUM ELECTRODES R. R. AD~IC and N. M. MARKOVIC Institute of Electrochemistry, KTM and Center for Multidisciplinary Studies, University of Belgrade, Njegokva 12, P. 0. Box 815, 11000 Belgrade, Yugoslavia (Received 25 February


Abstract-It has been shown that the adsorption of Bi” * and Tlf cations occurs on oxide layers of Au and Pt electrodes in acid solutions. The initial stages of oxide formation and reduction are inhibited. The effect increases with increasing cation concentration, but diminishes with increasing anion concentration. The adsorption ofeations originates in their interaction with the dipoles of the oxide species on Auand pt surface. A hydrophilic nature of oxidized surface also facilitates this adsorption. Cations apparently a&t the state of adsorbed water and decrease the lateral repulsion of oxide spies and the electric field in the double layer. This causes a retardation of the place-exchangemechanism, leading to a stabilization of oxides, fe, their more irreversible reduction.

INTRODUCTION The adsorption of cations (Zn”, Cu”, Co’+, Ni2* and Mg2 ‘) has been known ta occuron high area bulk oxides such as MnO,, Si02, AlzOs and TiOz[l, 21. It has been explained by the ion exchange adsorption on hydrated surfaces of these oxides. In electrochemical systems Erdey-Gruz and Shafarik[3] have shown that oxygen overvoltage on smooth plantinum in 0.5 M HzS04 increased in the presence of large amounts (0.3-1.0 M) of K, Al, Zn, Na, Mg, Li and ammonium cations. Kozawa[4] has found that oxygen overvoltage on platinum and some other metals increases in the presence of Ba’ + , Ca’ + and Sr’ + cations in 1 M NaOH. This has been attributed to the adsorption of these cations on Pt oxide. Kazarinov et al.[5] have found evidence of adsorption of Cs’ on Pt oxide in NaOH solution. It has been shown recently that Bi3+, Pb’+ and Cd2+ cations interact with oxide layers of gold and platinum electrodes[6]. The adsorption of these cations at such high positive potentials is rather surprising. It affects the oxide formation-reduction process. Because of the importance of such surfaces for oxygen and chlorine evolution and oxygen reduction, this paper reports in more detail the investigation of such an interaction.

EXPERIMENTAL The experiments have been carried out in an opticalelectrochemical cell with optical system which consisted of a Jobin-Yvon H-10 monochromator, a R-374 photomultiplier Hamamatsu and a tungsten-halogen light source. All reflectance measurements have been done with parallel polarization at an angle of incidence of 45”. Electronic equipment included a Stonehart BC-1200 potentiostat, PAR-173

programmer and 129A lock-in amplifier, a Nicolet digital oscilloscope and Hewllet-Packard X-Y recorders. A standard procedure was used in polishing and cleaning the electrodes and cell. A saturated mercttrous sulphate electrode served a.s the reference. All potentials are given against a standard hydrogen electrode. Some experiments have been performed with a rotating electrode disc-ring. Cations were added to the electrolyte as perchlorates obtained by oxide disolution in HClO,. The electrolytes have been prepared from triply distilled water and Merck’s HC104 and HzS04. The Same results have been obtained with the water obtained by a catalytic pyrodistillation.

RESULTS Adsorption of cations on gold oxide

A direct recording of reflectivity and modulated reflectivity in conjuction with a linear sweep voltammetry have been used throughout the work. Both techniques show evidence of interaction of the cations with oxides of Au and Pt. Figure 1 displays the effects of various concentrations of Bi” on oxide formation and reduction on Au in 0.1 M HClO,. The formation and reduction of oxide are considerably changed. A more pronounced change is seen in the oxide reduction which is more irreversible in the presence of Bi3+ indicating the stabilizing effect of adsorption of bismuth ions. The effect increases with the increase in concentration of Bi’ + The cathodic potential limit has been selected in such a way as to avoid the underpotential deposition (UPD) of metals. The reflectivity measurements offer additional information on cation adsorption of Au and Pt oxides. Besides voltammetry, Fig. 1 shows corresponding reflectivity-potential curves. The reflectivity has been



0.1 M HClO, __---. Au

I!’ rl


Au/l x Ib3M Ei” Au/l lO-4 M Ei”’ %

Fig. 1. Voltammetry and reflectivity-potential curves of Au in 0.1 M HCIO, in the absence and in the presence of Bi’ + Sweep fate 100mVs-‘, 1 = 410nm, parallel polarization.

normalized at 1 at the most negative potentials. A of reflectivity is caused by oxide formation on Au. Although the oxide peak is considerably suppressed the reflectivity is lower in the presence of Bi’+. This shows that a combined effect of oxide formation and BP+ adsorption on that surface causes a larger change of reflectivity than a formation of a larger oxide coverage in the absence of BP*. For the sake


of clarity the reflectivityypotential curve is given only for 1 x 10W3M BP+. In the reverse sweep the reflectivity is smaller in the presence of B?+ in the whole potential region of oxide reduction. Less oxide is formed on Au in the presence of Bi3’ in the electrolyte, and one would expect a higher reflectivity (A Q = 70,uC cm-’ for lo- 3 MB?‘). A decrease of reflectivity, however, is larger by 0.125%. This clearly shows a strong influence of Bi’+ adsorbed on Au oxide on the reflectivity of that surface. The re&ctivity of Au changes linearly with coverage of oxide (insert, Fig. 2). This can be used to calculate the reflectivity- potential curve in the presence of Bi’+, by taking the oxide coverage from voltammetry. The calculated curve shows a much higher reflectivity than the experimental one, indicating again the adsorption of Bi3 ’ on Au-oxide (Fig. 2). The change of reflectivity is defined as A (A R/R,) = (AR - AR,)/R, (1) where AR and AR0 are the changes of reflectivity caused by oxide formation in the presence and in the absence of Bi3+; R,, is lOO%, a value of a normalized reflectivity. It should he noted that the difference in the charge associated with oxide formation in the presence,Q,andintheabsenceofBi3*,Q,,AQ =Q-Q,,, has a negative sign. This reflects the fact that a smaller oxide coverage together with adsorbed Bi3’ causes a larger decrease of reflectivity than a somewhat larger oxide coverage in the absence of Bi3+. The linearity of both (AR/RJ and AQ as a function of log CBi” suggests the Ten&in behaviour of this adsorption. This also suggests a linear relationship between (AR/Ro) and AQ. The effect of Bi3+ cations on the oxidation/reduction of Au depends on the concentration of anion of supporting electrolyte. Both (AR/R,,)and AQ decrease with the increase in CHClo In 1 M HClO, the effect of Bi3* on oxide forma&n is not seen. The oxide reduction, however, is somewhat shifted to more negative potentials. Apparently a high concentration of ClOiprevents the interaction of Bi3+ during initial stages of oxide formation, while at a full monolayer coverage that interaction takes place causing a stabilization of oxide.


Fig. 2. Experimental and calculated reflectivity-potential curves for Au in the potential region of oxide formation in the presence of 1 x 10v4M Bi 3* Inserted figure gives a change of reflectivity with the charge associated with oxide formation on Au obtained from Fig. 1.


Optical and electrochemical study of cation adsorption 02 -

0.1 M H*so~ _____A”



Ol0: 5


2 -5 -0.1 -

-0.2 -

-0.3 -










E/V Fig. 3.

VoltammetrycurvesofAuinO.1 MH2S04withoutandwith 1 x 10-j MBi”.Anodicpotentiallimit progressively increased, sweep rate SOmV s- ‘.

Figure 3 displays the voltammograms obtained with a successive increase of the anodic potential limit for Au in 0.1 M H,SO, in the absence and in the presence of 1 x 10e3 M Bi’+. The oxidation apparently commences very slowly at potentials less positive than in H,SO.+. Other initial stages of oxide formation, bowever, are suppressed and the amount of oxide decreases. The effect of stabilization amounts to - 1OOmV. Figure 4 shows the effects of ‘II’ on oxidation and reduction of Au. This system is complicated by Tl+/T13+ redox reaction withE” = 1.247V. It givesan anodiccurrent at potentials less positive than the oxide formation which causes large differences in the voltammetry curves. Therefore, it would be impossible to establish the adsorption of Tl+ by voltammetry. The measurement of reflectivity offers more reliable information. It shows that the oxide formation is less affected by adsorption of TI * than the oxide reduction. This appears to be due to the fact that Tl’ is not stable at that potential; it undergoes oxidation to T13+. The latter cation apparently does not adsorb on Au oxide. The redox process itself does not affect the optical properties of gold electrode. The irreversibility of oxide reduction places this process in the region of the stability of Tlf , which adsorbes on oxide, thus shifting its reduction to more negative potentials (Fig. 4). The adsorption of TIC exibits a dependence on CT,+ and concentration of anions similar to that observed with Bi3+. Adsorption of cations on Pt oxide A study of cation adsorption on Pt oxide is complicated by the underpotential deposition of these metals which takes place at the oxide-free Pt. A dissolution of adatoms formed in that way usually coincides with the onset of oxide formation on Pt. For these reasons a linear sweep voltammetry and a direct recording of reflectivity offer little information on this process. A problem with a direct recording of reflectivity lies in its normalization in the presence of


QIM Ii&O., -0,3 -






Fig. 4. Voltammetry and reflectively-potential curves of Au in 0.1 M HzS04 in the absence and in the presence of II +. C,, = x IO-’ M. Sweep rate 1W mV s-‘, i = 410nm, parallel polarization. cations. There is no potential window where it can be done on an oxide-, or adatom-free surface. A modulated reflectivity is a more suitable technique for such systems. Figure 5 shows voltammetry and corresponding modulated reflectivity curves of Pt in 0.05 M H$O., in





N. M.





Lsi + ‘I


i_> ’ ;







. .








~Mchsor ____ pt Pt/Ei”

Fig. 6. As in Fig. 5 but for 1 x lO+M Tl+. Fig. 5. Voltammetry and modulated rellectivity-potential curves of Pt in 0.05 M HISO. without and with 1 x IO-’ M Bi’+. Sweep rate 2OmV E.-‘, modulation potential AE =lGOmVpp,70Hz.

the absence and in the presence of 1 x 10m3M Bi3+. The in-phase component of the electromodulation coefficient x = l/R dR/d E is shown. A cathodic potential limit has been selected so as to avoid a multilayer deposition of Bi. Because of the problem with a dissolution of Bi adatoms it is difficult to say whether the voltammetry curve in anodic scan indicates any adsorption of Bi’* on Pt oxide. The oxide reduction is partly obscured by the current of the underpotential deposition of Bi adatoms. The modulated reflectivity-potential curves show that the beginning of oxide formation is shifted to more positive potentials. The electromodulation coefficient is smaller in the presence of Bi3 l throughout the oxide region. It is too large to be caused by different amounts of oxide formed in these electrolytes and is a clear indication of the interaction of Bi3* with Pt oxide. It is a complex quantity determined by several properties of the metal/electrolyte interface. The value of x depends on Gail+ and the concentration of the anion of supporting electrolyte. It increases with Cai,+, but decreases with the concentration of ClO; or SO:-. At themost positive potential in 0.5 M HZSOI, where Bi adatoms are oxidized, the values of x for the two surfaces show only a small difference. This supports the view that the change in x is caused by the adsorption of Bi”+. An indication of adsorption of Bi3’ on Pt oxide has been observed by Bruckenstein[?] by the disc-ring measurements. Figure 6 displays the results obtained with Tl+. The UPD of Tl shifts considerably the oxide formation on

Pt. The peak of Tl dissolution is well into the oxide region. The pair of peaks at _ 1.2 V corresponds to Tl* /T13 + redox reaction. This further complicates the interpretation of the optical measurements, but nevertheless, as shown below, the adsorption of Tl+ can be easily seen. The reflectivity measurements also indicate a shift of oxide formation to more positive potentials. At still more positive potentials, the curve differs from the curve for Pt in the absence of Tl+ and appears to reflect the redox reaction. This is possible if at least one component of the redox couple is adsorbed on Pt oxide. If they were in the outer Helmholtz plane the modulation of their concentration would not much affect the optical response. The peak of x at 1.2 V diminishes with an increase in concentration of H,SO, and in 0.5 M it is practically absent. Since the voltammetry still shows the redox reaction this clearly means that Tl l is adsorbed on Pt oxide in 0.05 M HISO and the modulation of its coverage is a cause of the peak. The adsorption of T13+ is less probable because of its higher charge.

DI!SCUSSION Surfice oxidation of Au and Pt The adsorption of cations at high positive potentials at oxide surfaces is rather surprising. Before further discussing this adsorption, the processes of the oxide formation and reduction on Pt and Au should be considered. An extensive literature exists on the formation and reduction of oxide layers on Pt and Au. The reference will be made here only to the papers of some relevance to this work. Angerstein-Kozlowska et al.[X, 9] haive proposed a mechanism of oxide forma-

Optical and electrochemical study of cation adsorption tion on Pt which involves three distinguishable stages of surface oxidation of Pt up to a monolayer coverage by OH species which undergo a place-exchange with Pt atoms, followed by further oxidation to PtO. Vetter and Schultze[ 10,l l] proposed that electrosorption of 0 species in the surface oxidation of Pt and Au in acid solutions proceeds by specific adsorption of 02- ions which are exchanged for the metal ions from the first atomic layer. This results in the electrosorption valence of O*- equal to 2. Allen et al. [12] interpreted ESCA measurements in terms of the anodic film consisting of single species Pt (OH),. On the basis of ellipsometric spectroscopy measurements Horkans et al. [ 131 have concluded that PtO species form the oxide monolayer on Pt. The surface oxidation of Au has also been thoroughly investigated. In acid solutions this process is more complex because of a strong anion adsorption at high positive potentials. As with Pt, the initial process involves deposition and reduction of OH or 0 species that are chemisorbed on the metal surface[9]. Extensive work has been done on Au single crystal electrodes [14-171. The works of Sotto[l4, 151 suggest three species formed in the oxidation of Au, viz Au203*nH20, or Au(OH)* and AulO, or AuOH, while Ferro et a/.[@ 191 suggest similar three reactions stressing evidence of the ageing process. Spectroscopy data of Kolb and McIntyre indicate the existence of Au,O,[20]. The adsorption of cations on high-area hydrated oxides has been explained by Kozawa[S] by an ionexchange reaction. This has been proposed only for alkaline solutions, while for acid solutions the exchange of anions with H from M-OH has been assumed. This work shows, however, that certain cations can interact with surface oxides ofAu and Pt in acid solutions even in the presence of anions which exhibit a weak specific adsorption. Surface oxidation ofAu and PC in the presence ofcations A detection of cation adsorption on Au and Pt oxides is based on the comparison of the curves obtained in the base electrolyte and the curves obtained upon addition of cations. The shift of the very beginning of the oxidation of Au (Figs 1 and 4) to less positive potentials is least understood. It may be caused by the ion-pairing at those high positive potentials which could cause a decrease of adsorption of Clod and SO:; and consequently facilitate the oxidation of Au at less positive potentials. More work is needed to explain this effect. The oxide formation associated with the main peak is considerably inhibited. It appears that this is not due to a blocking effect, since cations are not adsorbed on the oxide-free gold surface. Their adsorption is concurrent with the oxide formation. Once they are adsorbed, they change double layer properties and the place-exchange mechanism. This will be discussed below. A stabilization of oxide is the most striking effect of these cations. With Bi3+ it does not disappear even in 1 M acids. It is probably mostly due to a retardation of the place-exchange mechanism. The reflectivity of these surfaces indicates a strong interaction of cations with oxide layers. If cations were in the ionic double layer such a charge of reflectivity


could not be produced. These species are probably predominantly ionic. This is indicated also by the Temkin behaviour of their adsorption inferred from Fig. 9. The Temkin adsorption is corroborated by the experiments in which the concentration of supporting electrolyte (HCIO,) was varied. AR/R0 decreases linearly with log C,,o+ for constant Cai,.. It is clear that anions at such lugh positive potentials easily displace cations from the surface and the inner double layer. The exact state of adsorbed cations is difficult to depict on the basis of these experimental data. Because of the UPD of adatoms of these metals it is not possible to study the effects of cations on initial stages of surface oxidation of platinum. Modulated reflectivity measurements provide clear evidence of the interaction of cations with oxide existing after the initial stage. The electromodulation coefficient can be defined as[21, 221:

where r is the surface concentration of adsorbed species. The first term is due to the intrinsic electroreflectance effect and depends on the nature of electrode and the adsorbed species. The second is due to the modulation of the surface concentration of the adsorbed species. For low modulation frequencies the second term is much larger than the first[22].Therefore, the modulated reflectivity curves are predominantly determined by thechanges in thesurfaceconcentration of OH or 0 species, roX, ie the oxide coverage and cations coadsorbed on it. Equation (2) assumes that the modulation of potential simultaneously modulates ToXand r,, the surface concentration of cations, determined by Fax. That is why only one 8 R/a r term appears in Equation (2). The modulated reflectivity is used here only to monitor the oxide coverage whose formation coincides with a dissolution of metal adatoms, illustrating again the usefulness of this technique. The authors refrain from making a detailed optical model of the interface and kinetic model of the oxidation reduction process which would require the measurements in a broader frequency and wavelength range. Origins of cation adsorption and analysis of the eflects The cations investigated in this work are susceptible to hydrolysis and the question of the nature of the species in solution arises. Bi3+ exhibits the highest tendency toward hydrolysis. It is believed that in 0.5 M acid solution Bi3+ does not hydrolyse[23]. For small Bi3+ concentrations (10-5-10-” M) the hydrolysis is negligible even in 0.1 M acid solutions used predominantly in this work. It is possible, however, that Bi’+ forms BiOH’+[3], which is again a cation, but with lower charge. A polymerization of these species is not likely under these conditions. Tl+ is less susceptible to hydrolysis and is in such a form in 0.1 M acid solutions. A model of the interaction of the cations with oxidized metal surfaces is given in Fig. 7. The oxide species MOH, M(OH), or MO are dipoles with a negative end pointing to the solution side. The cations, despite a high positive charge on the electrode, may












+ +












+0 +






-E t





Fig.7. Model of c&on interaction with oxidized metal surface. Hydration

come in the, inner part of the double layer at the distance small enough to interact strongly with these dipoles, according to Scheme 1. The cations probably lose most of their hydration sheet in this interaction. It appears that the bondis not completely electrostatic, but has a certain covalent character. This is indicated by different magnitude of the effect of various cations. The explanation given by Kozawa[5] for alkaline solutions, involving an ion-exchange, may be possible for the unrearranged states of electrodeposited OH. It is difficult, however, to establish such a reaction on a submonolayer of oxide. In order to determine the amount of Bi3+ adsorbed on gold oxide the disc-ring measurements have been used. A ring has been potentiostatted at E = 0.05V

shell of cation not shown

which facilitated a deposition of Bi at a diffusion control. The flux at the ring has been followed as a function of the disc potential. Figure 8 shows the current at a ring as a function of a disc potential. For E, - 1.2 V a decrease of the current at open disc is due to theadsorption of Bi’+ at gold oxide. In the sweep in cathodic direction at E _ 1.OV the increase of the ring current is due to the desorprion of Bi3’ with the reduction of gold oxide. The processes at E = 0.5V are due to the UPD of Bi. The coverage of Bi’+ has been determined from these measurements. Figure 9

H 6+



O ‘\

2MOH + M’+ b+M _






\ H

’ 6+M _


fi+&j _



2MO + M’+ -






Scheme 1.

I a5


Fig. 8. Current of the ring as a function of the disc potential of rotating Au/Au disc-ring electrode. Ring potential E = O.OW, collection efficiency N = 0.21I; 900 rpm, IOV min-‘.

Optical and electrochemical

study of cation adsorption


For the low coverage of surface oxide, BOX Q 1, Equation (3) becomes, eon = kc exp(z FEIRT) exp ( - g,fk)


where k is an equilibrium constant; c, the concentration of HzO, g and g, are lateral interaction factors[9] in the film in the absence and in the presence ofcations. tic should be positive, corresponding to an unfavourable field effect due to co-adsorbed cations, which diminishes Boxat a given E and c. Equation (4) does not take into account the enhancement of oxidation caused by the ion-pairing effect, discussed above. The anions affect the oxide formation through blocking and a local field effect. From above analysis it appears that the cations act predominantly through a local field effect. Acknowledge~ntu-Financial support by the Research Fund of Serbia, Yugoslavia and the National Science Foundation, U.S.A. is gratefully acknowledged. REFERENCES Fig. 9. Coverage of Bi3+ adsorbed on gold oxide as a function of log C,;,, obtained from Fig. 7.

gives the plot of charge associated with a desorption of Bi”+ us the log C,,a+. The linear dependence clearly shows the Temkin behaviour of this adsorption. At 1 x 10W4M Bi3+ in solution that charge is 19OpC cm- ‘. Taking 605 $cm- 2 as a monolayer charge gives tr,,,, _ 0.3. This suggest a low electrosorption valence of this species, ie a species with a considerable ionic character. The wetting properties of oxide layers may play a role in cation adsorption. At a hydrophobic metal surface the adsorption of anions is facilitated. The oxide formation certainly makes the surface more hydrophilic, ie more suitable for cation adsorption. Cation adsorption the oxide may a&et formation/reduction process in the following ways: (i) modifying the innerblayer potential profile; (ii) influencing the kinetics of place-exchange mechanism: (iii) stabilizing the states of deposited 0 species; (iv) affwting the state of adsorbed water. Adsorbed cations considerably change the potential profile in the inner part of the double layer (local field effect). The potential gradient is decreased and consequently the place-exchange is retarded. The placeexchange is also retarded by lowering the lateral coulombic repulsion between OH or 0 by coadsorbed cations. Angerstein-Kozlowska et a!.[91 have given the expression rekting the formation of oxide in presence of specific adsorption of anions and electrode potential. A similar expression can be written for the case of cation adsorption which relates the oxide coverage, B,,, cation coverage 0, and applied potential, E, @,A1 [email protected],I = kcexp(tFEIRT)exp(-88,-gc8,). (3)

1. A. Kozawa, J. inorg. Chem. 21, 315 (1961). 2. A. Kozawa, J. electrochem. Sot. 106. 55 (1959). 3. T. Erdey-Gruz and I. Shafarik, So&t Elecrrochemistry, Proc. 4th Conf. on Electrochemistry, Vol. 2, pp. 145. Consultants Bureau, New York (1961). 4. A. Kozawa, J. electrood. Chem. 8, 20 (1964). 5. V. E. Kazarinov, N. A. Balashova and M. 1. Kuleznevs, Elektrokhimiya 8, 975 (1965). 6. R. R. Adzit and N. M. Markovif, J. electroannl. Chem. 102, 263 (1979). 7. S. H. Cadle and S. Bruckenstein. An&t._ Chem. 44. 1993 (1972). 8. H. Angerstein-Kozlowska, B. E. Conway and W. B. A. Sharp, J. electrormol. Chem. 43, 9 (1973). 9. H. A&erstein-Kozlowska, B. E. Conway, B. Barn&t and J. Mozota, J. electroad Chem. 100, 417 (1979). 10. K. J. Vetter and J. W. Schultze, J. electroonal. Gem. 34. 131; 141 (1972). Il. K. J. Vetter and J. W. Schultze, 2. Elektrochem. 62, 378 (1958). 12. G. C. Allen, P. M. Tucker, A. Capon and R. Parsons, 1. electroanal. Chem. 50, 335 (1974). 13. J. Horkans, B. D. Cahan and E. Yeager, Surj Sci. 46, 1 fl9741. 14. &l. S&to, J. electroanal. Chem. 69, 229 (1976); 70, 291 (1976); 72. 287 1976. Acad. Sci., Paris, 276c, 141 15. M. Sotto, C. hebd. St%znc+. (1973). 16. G. Valette and A. Hamelin, J. electrwd Chem. 45, 301 (1973). 17. D. Dickert-n, J. W. Schultze and K. I. Vetter, J. electronal. Chem. 55, 429 (1974). 18. C. M. Ferro, A. J. Calsndra and A. J. Arvia J. electroand. Chem. 50, 403 (1974). 19. C. M. Ferro, A. J. Calandra and A. J. Arvia, J. electroad Chem. 65, 963 (1975); 85, 213 (1977). 20. D. M. Kolb and J. D. E. Mcintyre, Surf. Sci. 28, 321 (1971). 21. R. Ad&?, B. D. Ghan and E. Yeager, J. them. Phys. 58, 1980 (1973). 22. R. Ad& E Yeager

and B. D. C&an, J. electrochem. Sot. 121, 474 (1974). 23. C. F. Baes and R. E. Mesmer, 7’he Hydrolysis ofcations, pp. 379427. Wiley, New York (1976).