Nemstian relationship

Ion-selective electrodes belong to the group of potentiometric methods. Many electrode systems, partly well known, partly in development and under investigation, show a Nemstian relationship between the measured electrode potential and the activity of a species in solution. Important conditions to be fulfilled for the development of ion-selective electrodes are the affinity of a membrane surface for a typical ion or molecule and a minimum ion conductivity over the membrane. If possible, but not necessarily, these conditions should be fulfilled at room temperature. 

A natural aqueous redox system may or may not be at total (internal) equilibrium (Q. How the redox status is characterized depends upon the state of the system relative to equilibrium. Regardless of whether the system is at equilibrium or not there is an individual, instantaneous pE for each redox couple in the system. Each pE corresponds to the relative concentrations of the oxidized and reduced species and is defined by Nemstian relationships (i). When a system of oxidants and reductants is at internal chemical equilibrium the pE of every couple is identical and this distinct value is the system pE. Only in this special case can the redox status be characterized by determining two of the following three factors pE, the total concentration of all components, and the relative concentrations of oxidants and reductants. When two of the factors are known, the third can be determined from Nemstian and mass balance relationships. Thus, only when the chemical system is at internal equilibrium and one of the redox couples of the system is electrochemically active and present in measurable concentrations can the system pE be calculated from an electrode potential. 

Unfortunately, the results can easily become too complex for practical application. For example, consider the simple mechanism in (3.5.8)-(3.5.10), where the pre- and postreactions are assumed to be kinetically facile enough to remain in local equilibrium. The overall nemstian relationships, (3.5.19), connect the surface concentrations of O and R to those of O and R. Thus, the current-potential characteristic, (3.5.11), can be expressed in terms of the surface concentrations of the initial reactant, O, and the final product, R. 

It is common practice to measure fb across a range of pH values. The Eq, of many semiconductors follows a Nemstian relationship as a function of pH (Rg. 6.4). This is due to the dynamic equilibrium of the surface hydride/hydroxyl terminations that generally cause the band edges to move by —59 mV/pH [8]. A common way to analyze data is to plot the measured fb values along with the OER and HER potentials versus pH. By plotting the fb data along with the reaction potentials (which also exhibit Nemstian behavior), the ability to shift the band edges of the semiconductor with pH can be evaluated. 

As the concentration is increased from 1.0 to 4.0 M HCIO4, there is a breakdown in the Nemstian relationship between CIO4 activity and (see Fig. 8.19). This breakdown is reflected in the increased normalized mass change observed at concentrations from 1.0-3.0-M electrolyte, i.e., in 2-M HCIO4 Aw is equal to 186 and in 3-M HCIO4, Am is equal to 479 Assuming that solvent... 

The calibration of ISEs using the tabulated activity values is especially simple when the dependence of the ISE potential on the determinand activity is Nemstian (3.1.5). If the liquid-junction potential is negligible or constant, the determinand activity flj+(X) can be found, using the standard activity [Pg.80]

These three relationships provide useful experimental criteria for reversible LSV waves. A plot of Ipjvl/2C0 vs. vx/1 is expected to be linear with zero slope. The peak and half-peak potentials for Nemstian charge transfer are independent of v and Ep — Epa is expected to be equal to 56.5/n mV at 298.1 K. 

Figure 9.20. Relationship between pH, surface potential, (or Coulombic term, log P, or Coulombic free energy, AGcoui) and surface charge density, o (or surface protonation), for various ionic strengths of a 1 1 electrolyte for a hydrous ferric oxide surface [P = exp(--Fi/ // 7 )]. (a) Dependence of the Coulombic term and surface potential on solution pH note the near-Nemstian behavior at low ionic strength, (b) xp versus or these curves correspond to the Gouy-Chapman theory, (c) o versus pH these are the curves obtained experimentally. (From Dzombak and Morel, 1990.)...

The potential of a glass cation-sensitive electrode is measured against an SCE. In a sodium chloride solution of activity 0.100 M, this potential is 113.0 mV, and in a potassium chloride solution of the same activity, it is 67.0 mV. (a) Calculate the selectivity coefficient of this electrode for potassium over sodium, using the relationship derived in Problem 21. (b) What would be the expected potential in a mixture of sodium (a = 1.00 X 10 M) and potassium (a = 1.00 X 10 - M) chlorides Assume Nemstian response, 59.2 mV/decade. 

This relationship is a very important general finding. It says that, for a kinetically facile system, the electrode potential and the surface concentrations of the initial reactant and the final product are in local nemstian balance at all times, regardless of the details of the mechanism linking these species and regardless of current flow. Like (3.5.17), (3.5.21) was derived for pre- and postreactions that involve net charge transfer, but one can easily generalize the derivation to include other patterns. The essential requirement is that all steps be chemically reversible and possess facile kinetics. 

Equation 1.109 has the same form as the Nemst equation. It indicates that the surface concentrations of species involved in the Faradaic process are related to the electrode potential by an equation of the Nemst form when the exchange current density is very large. Such electrode reactions are often called reversible or Nemstian, because the principal species obey thermodynamic relationships at the electrode surface. 

The paper of Erdey-Gruz and Volmer that appeared in 1930 [62] on the hydrogen overpotential was a seminal one, indeed (Fig. 12.23). It was the first time when the proper relationship between the current and the electrode potential was formulated. This paper can be considered as a landmark since the Nemstian (osmotic) equilibrium theory already hindered the development of electrochemistry. Even... 

---