Some Aspects of the Energetics and Kinetics of Electrochemical Proton Transfer

Salomon, Mark; Enke, Christie G.; Conway, B. E.

doi:10.1063/1.1696631

Cited by 15 publications

(12 citation statements)

References 41 publications

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“…This often-quoted conclusion was originally made,7 and subsequently reaffirmed,8-10-32 by workers primarily concerned with the proton discharge reaction. As the formation of the activated state for this particular electrode reaction has been considered (at least under some conditions) to involve proton transfer from HsO"8 to the metal surface with only subsequent charge neutralization,32 theoretical calculations of the barrier height using this model need to be compared with experimental ideal enthalpies of activation evaluated for the condition = 0, where the presence of the electrode will not affect the energetics of the proton transfer act.10- 32 However, for simple electrochemical reactions controlled by electron rather than atom transfer, quite a different situation is encountered. At the standard potential, E°, for the overall reaction 13, the standard electrochemical potential of the reacting electron, will equal the difference in the standard electrochemical potentials for There is a clear parallel between the heterogeneous and homogeneous "reductants" M(e~,E°) and Red* in that both serve to maintain the standard free energy of the overall reactions 13 and 15 at zero at all temperatures.17 As Marcus has shown,17 a close parallel therefore exists between the standard free energies of activation for corresponding electrochemical and chemical self-exchange reactions when the former are evaluated at E°.…”

Section: IVmentioning

confidence: 99%

Interpretation of activation parameters for simple electrode reactions

Weaver¹

1976

J. Phys. Chem.

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Interpretation of Activation Parameters made using a 0.5 M K2SO4 electrolyte with added H2S04 or NaOH to adjust the pH between 2.5 and 13. The pH was measured with a Corning pH meter.The values of No were determined from the slope of C"2 vs. potential. The Nd values are given in the table and were calculated using the following values for the dielectric constant *: Ti02 (173);21 Sn02 (23.4);21 SrTiOg (310);22 KTa03 (243).23The dielectric constant of KTao.77Nbo.23O3 has not been reported, but KTao.65Nbo.35O3 is ~600024 and we thus calculatedNo for the KTao.77Nbo.23O3 for = 243 and = 6000 assuming these to represent the limits. The two limits are given in Table I. In calculating No using eq 3 the value of e used was 8.854 X IQ-12 F/m> and the value of q used was 1.602 X 10-19 C.

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Section: IVmentioning

confidence: 99%

Interpretation of activation parameters for simple electrode reactions

Weaver¹

1976

J. Phys. Chem.

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“…This is rather high for this type of vibration (e.g. in I;I-11;-us,, = 600 cm-I) and is attributed to the calculated result that the (I-Ig-I I-OH2)+ coii~plex is asymmetric (22).…”

Section: Ratios Discussionmentioning

confidence: 99%

“…This method has been she\\-n to predict activation energies to ~vithin &2 ltcal mole-' for hydrogen trmsfer reactions and is therefore considered to be superior to the semien~pirical method. The syn~metrical stretching mode for the electroche~i~ical proton transfer was found (22) to have a frequency u s , , = 1 503 cm-l. This is rather high for this type of vibration (e.g.…”

Section: Ratios Discussionmentioning

confidence: 99%

“…[ I ] by eval~~nting qH*/q,l. * as follo\\s: lirsl, the activated complex is assumed to be immobile (22); second, a7e can iise the frequencies found for the (I Ig-1-1-01 I2)+ activated complex lo calculate the corresponding frequeilcies for the (I-Ig-T-OM2)+ complex. I t is found that u s , , = 870 cm-' for the stretch and U + , T = 384 cin-l a t -0.9 1. and v+ , = (i!…”

Section: Ratios Discussionmentioning

confidence: 99%

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ISOTOPE EFFECTS IN MIXTURES OF LIQUID H₂O AND T₂O

Salomon¹

1966

Can. J. Chem.

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Calculations are presented for the equilibrium tritium isotope effect involving w:.ater, h y d r o l~i u~i~ ion, and hydroxide ion. The results are msed to predict the kinetic isotope effect i l l the transfer of protons to a mercury cathode.The use of t r i t i~~m for studying the kinetics of proton transfer reactions has some major advantages over the deuterium isotope. This is particularly true for reactions \\;hich proceed by small amounts of proton tunneling. The use of deuteriunl to evaluate proton tunneling contributions may not, in this case, be cri~ical enough unless the kinetics are studied dou-11 to veq-lo\\ temperatures. In aqueous solutions one is severely limited to a relatively small temperature range. Hence criteria inore diagnostic than the 1-1/11 isotope effect is sought. Rl, emp1o)ring the tritium isotope, which gives larger isotope effects, the experin~ental confirmation of proton tunneling nlay indeed be more significant. It is of interest, therefore, to calculate the solvent isotope effects for equilibria involving nlixtures of 1-120 and T20 and to apply these calculatio~~s to a kinetic mechanism involving a proton transfer. CALCU1,XTION 01: EQUILIBIIIUM CONSI'r\STSThe calculations presented belon-\\.ere performed by the method of Bader (1, 2). This method was used recently by Thornton (3) to calculate the equilibrium properties for n.ater containing the 'Q-lV isotopes. This method, applied to hydrogen and t r i~i u m , has enabled the follo\ving equilibrium constants (for aqueous ~)~s t e l n s a t 25 " C ) to be calculated.These equilibriun~ constants \yere caclulated by first evaluating the partition fullction ratios, q T / q H , for the various isotopic species involved. The rotational partition function is calculated by Bader's method (1, 2) of treating the librations of the solvated I H and T species as harmonic oscillators. The librational and vibratioilal frequencies for H?O and 01-1-were talien from Bader's work (1) and the corresponding frequencies for T20 \\>ere calculated froin I-Ierzberg's equations (4). The force constants for 1-1 ?O given by I-Ierzberg (4) were used in this calculation. The force constants and vibrational frequencies for I-I3of \\;ere obtained from Wolfsberg (5). The force constants for I-130+ are: k, = 4.915, k$ = 0.5, k , = 0.06, and k,,, = -0.4896 ~n d y n k'. The subscripts s, 4, \\;, and int refer., respectively, to the 0-1-1 stretch, the f1-0-1-1 bend, the 0-H mag, and the 01-1 . . . . 01-1 interaction. The corresponding vibrational frequencies for T30+ were caIculated fro111 I-Ierzberg's ecluations (6).

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“…Despite some serious objections to either method (26)(27)(28), there is no doubt as to their general usefulness. In order to construct the potential energy surface for an electrochemical reaction, one would have to know the "real" activation energy so that the adjustable parameters in the theory could be properly utilized (23,(29)(30)(31).…”

Section: _ Qd30+ )2mentioning

confidence: 99%

Primary and Solvent Isotope Effects in the Anodic Evolution of Oxygen

Salomon¹

1967

J. Electrochem. Soc.

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This equation is plotted for x = 0 in Fig. 8 and is plotted as a function of x for different values of t/T in Fig. 9.The above examples were intended to illustrate the general procedure for employing the lumped parameter models in the computation of concentration transient responses. Even though we have restricted these examples to a constant current excitation, other types of current excitations can readily be considered in a similar manner. In particular, for other excitations the lumped parameter approach becomes even more attractive. This follows because the solution of the diffusion equation, Eq.[13], is practically intractable except for very few excitations, such as the constant current excitation. ConclusionsThe incremental model has been shown to be a convenient vehicle with which to study electrical conduction phenomena in the electrolyte of a reversible transference cell. The linear relationship between concentration and current, for the approximations set forth, suggests a tangible means for describing a distributed system with a circuit analog. This follows because the same system can be analyzed for different excitations without recourse to the exact partial differential equations which are, in general, more difficult to solve than differential-difference equations. Even though the lumped parameter model has its principal limitation in predicting rapid transients, such as the initial portion of the concentration transient for a constant current excitation, its iterative structure provides a convenient means for adding more increments to the model to improve the accuracy. For many applications, where the over-all transient is to be investigated, a two-increment model for the half-cell should be adequate.The possibility of extending and applying the lumped parameter model to other electrolytic systems should pose some challenging and interesting problems. ABSTRACTThe use of hydrogen isotopes in studying the oxygen evolution reaction (o.e.r.) is discussed. It is shown that along with other experimental data such as pI-I studies, Tafel behavior, etc., the H/D-isotope effects can be used as additional criteria for the elucidation of reaction mechanisms. Normal isotope ) unless CC License in place (see abstract).

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Some Aspects of the Energetics and Kinetics of Electrochemical Proton Transfer

Abstract: A model for low temperature electrochemical proton transfer: Temperature and isotope effects on kinetic parameters J. Chem. Phys. 106, 9523 (1997); 10.1063/1.473853Flow-drift tube measurements of kinetic energy dependences of some exothermic proton transfer rate constants

Cited by 15 publications

References 41 publications

Interpretation of activation parameters for simple electrode reactions

Interpretation of activation parameters for simple electrode reactions

ISOTOPE EFFECTS IN MIXTURES OF LIQUID H₂O AND T₂O

Primary and Solvent Isotope Effects in the Anodic Evolution of Oxygen

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Some Aspects of the Energetics and Kinetics of Electrochemical Proton Transfer

Abstract: A model for low temperature electrochemical proton transfer: Temperature and isotope effects on kinetic parameters J. Chem. Phys. 106, 9523 (1997); 10.1063/1.473853Flow-drift tube measurements of kinetic energy dependences of some exothermic proton transfer rate constants

Cited by 15 publications

References 41 publications

Interpretation of activation parameters for simple electrode reactions

Interpretation of activation parameters for simple electrode reactions

ISOTOPE EFFECTS IN MIXTURES OF LIQUID H2O AND T2O

Primary and Solvent Isotope Effects in the Anodic Evolution of Oxygen

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ISOTOPE EFFECTS IN MIXTURES OF LIQUID H₂O AND T₂O