Activity coefficient , equilibrium electrode

If the Nernst equation is applied to more concentrated solutions, the terms in the reaction quotient Q must be expressed in effective concentrations or activities of the electroactive ionic species. The activity coefficient y (gamma) relates the concentration of an ion to its activity a in a given solution through the relation a = yc Since electrode potentials measure activities directly, activity coefficients can be determined by carrying out appropriate EMF measurements on cells in which the concentration of the ion of interest is known. The resulting Es can then be used to convert concentrations into activities for use in other calculations involving equilibrium constants. 

Formal potential — Symbol Efr (SI Unit V), has been introduced in order to replace the standard potential of -> cell reaction when the values of - activity coefficients of the species involved in the cell reaction are unknown, and therefore concentrations used in the equation expressing the composition dependence of ceii instead of activities. It also involves the activity effect regarding the -+ standard hydrogen electrode, consequently in this way the formal electrode potential is also defined. Formal potentials are similar to conditional (apparent) equilibrium constants (-> equilibrium constant), in that, beside the effect of the activity coefficients, side reaction equilibria are also considered if those are not known or too complex to be taken into account. It follows that when the logarithmic term which contains the ratio of concentrations in the -> Nernst... 

ACTIVITY AND ACTIVITY COEFFICIENTS In our deduction of the law of mass action we used the concentrations of species as variables, and deduced that the value of the equilibrium constant is independent of the concentrations themselves. More thorough investigations however showed that this statement is only approximately true for dilute solutions (the approximation being the better, the more dilute are the solutions), and in more concentrated solutions it is not correct at all. Similar discrepancies arise when other thermodynamic quantities, notably electrode potentials or chemical free energies are dealt with. To overcome these difficulties, and still to retain the simple expressions derived for such quantities, G. N. Lewis introduced a new thermodynamic quantity, termed activity, which when applied instead of concentrations in these thermodynamic functions, provides an exact fit with experimental results. This quantity has the same dimensions as concentration. The activity, aA, of a species A is proportional to its actual concentration [A], and can be expressed as... 

The parameter R is the gas constant, T is the temperature, F is the Faraday constant and n is the number of electrons consumed in the electron transfer step (Eq. 2). The standard potential, Eq of the redox couple O/R is defined as the reduction potential of O when the activity coefficients for both O and R are equal to one. Once Fq is known, the electrode potential can be used to measure concentrations in solutions or to calculate equilibrium constants, for redox equilibria (Eq. 3) involving two or more redox couples as shown in Eq. 4. 

Thus HCO3 is decomposed to CO2 in the thin decomposition layer, the resultant CO2 diffuses to the Hg electrode, then electro-chemically reduced to HCOO. The equilibrium CO2 pressure of NaHCO3-Na2CO3 (1.0-0.05) given in Fig. 5 is estimated at 0.03 atm from Table 2 with an assumption of the activity coefficient 0.5. The rate of decomposition of HCO3 limits the supply of CO to the electrode, and the reduction of HCO3 stays at a low value as shown in Fig. 5. 

The formation of Hg(SeCN)4 is well established by the potentiometric work of Toropova [56TOR], while her experimental data pertaining to the formation and the formation constant of Hg(SeCN)3 only comprise a few points. In their polarographic work Murayama and Takayanagi [72MUR/TAK] studied the anodic mercury wave in the presence of 0.001 to 0.003 M SeCN . The electrode process was assumed to comprise the charge transfer Hg(l) Hg + 2e combined with the formation of Hg(SeCN)2(aq) and Hg(SeCN)3. No primary data are provided and the evaluation procedure is rather involved, which makes the assessment difficult. The results are mixed equilibrium constants, since an activity coefficient correction was applied to the Hg ion. The following complexes are thus proposed to prevail in the Hg -SeCN system ... 

Parker, Tice, and Thomason [97PAR/T1C] measured the Ca activity in solutions containing total Ca concentrations in the range 20 x 10 to 200 x 10 M and the selenate concentration 0.004, 0.01, or 0.03 M with a carefully calibrated ion-selective Ca electrode. Activity coefficient corrections were made by Davies equation. The equilibrium constant of the reaction ... 

Thermodynamics is used in the analysis of electrochemical cells (1) to predict which electrode reactions occur spontaneously in the anodic and cathodic directions if the two electrodes are in equilibrium with their respective adjacent solutions and are connected to one another via an external wire, and (2) to quantify chemical potentials and activity coefficients in nonideal electrolytic solutions. 

Colombier measured the potential of NiSO4(0.5 M) Ni against a calomel reference electrode at 20°C. When the electrolyte was appropriately degassed and kept air-free the same equilibrium potentials were found for massive or powdered nickel, the latter having been electrolytically deposited or prepared by hydrogen reduction of NiO. As the author presented no details about the experimental data, the reference potential selected, how the liquid junction potential and the activity coefficients were accounted for, the final result, °(Ni Ni, 293.15 K) = (0.227 + 0.002) V, cannot be recalculated and was not being considered any further. 

The splitting of redox reactions into two half cell reactions by introducing the symbol" e , which according to Eq.(II.28) is related to the standard electrode potential, is arbitrary, but useful (this e notation does not in any way refer to solvated electrons). When calculating the equihbrium composition of a chemical system, both e , and can be chosen as components and they can be treated numerically in a similar way equilibrium constants, mass balance, etc. may be defined for both. However, while represents the hydrated proton in aqueous solution, the above equations use only the activity of e , and never the concentration of e . Concentration to activity conversions (or activity coefficients) are never needed for the electron cf. Appendix B, Example B.3). 

Activities and/or activity coefficients are not available for ionic species in most corrosion solutions. Therefore, as a practical expedient, the concentrations of the species are used in place of the respective activities when computing equilibrium electrode potentials. ... 

Provided A , the product of the polarographic reduction, has a negligible ability to function as an acceptor with D, a study of the shift in half-wave reduction potential of the A-l-e - -A system with donor concentration may be related to the free energy of formation of DA. The conditions which must be satisfied for successful use of the method are (i) chemical equilibrium for the formation of DA must be rapidly achieved (//) the rate of electron transfer to A or (DA) at the electrode must be high and (hi) the solvation energy of A must be unchanged by addition of the donor. The fulfillment of these conditions may be tested experimentally . When these conditions are fulfilled an expression of the form (5) may be derived. Here we have written activity coefficients equal to one for... 

The definition of certain quantities that play an important role in corrosion and in electrochemistry, notably the equilibrium potential of an electrode (Section 2.2) and the pH, require knowledge about the activity of individual ions. By invoking certain non-thermodynamic hypotheses, it is possible to estimate these in certain cases. We present here two examples, namely the establishment of the pH scale and the estimation of activity coefficients in weakly concentrated aqueous solutions. 

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