Nemst potential difference

The concentration overpotential rjc is the component directly responsible for the steep increase in potential observed as the current approaches the limiting current, since the Nemst potential difference (Eq. 6) becomes very large as the concentration of the reacting ion at the electrode approaches... 

Once current passes tluough the interface, the Galvani potential difference will differ from that expected from the Nemst equation above the magnitude of the difference is temied the overpotential, which is defined heiiristically as... 

As the Nemst equation suggests, concentration variations in the electrolyte lead to potential differences between electrodes of the same kind. These potential differences are concentration polarizations or concentration overpotentials. Concentration polarizations can also affect the current distribution. Predicting these is considerably more difficult. If concentration gradients exist, equations 25 and 27 through 29 must generally be solved simultaneously. 

The principle of pH electrode sensing mechanisms which are based on glass or polymer membranes is well investigated and understood. Common to all potentiometric ion selective sensors, a pH sensitive membrane is the key component for a sensing mechanism. When the pH sensitive membrane separates the internal standard solution with a constant pH from the test solution, the potential difference E across the membrane is determined by the Nemst equation ... 

QB For this cell because the electrodes are identical, the standard electrode potentials are numerically equal and subtracting one from the other leads to the value c°dl = 0.000 V. However, because the ion concentrations differ, there is a potential difference between the two half cells (non-zero nonstandard voltage for the cell). [Pb2+] = 0.100 M in the cathode compartment. The anode compartment contains a saturated solution of Pbl2. We use the Nemst equation (with n = 2) to determine [Pb2+] in the saturated solution. 

If solutions of two electrolytes are brought into contact there is, generally speaking, a potential difference between them, just as there is one at the interface mercury-electrolyte in the capillary electrometer. This potential difference has been shown by Nemst to depend on the differences in the concentrations and the migration velocities of the ions. Smith uses dilute solutions containing equivalent amounts of KI and KC1 the kation is thus the same in both solutions, and the migration velocities of the I and Cl ions are nearly equal, so that, according to Nemst s theory, there should be no potential difference or double layer at the interface. These... 

As a result of these experiments Smith concludes that (a) the simple Helmholtz theory of the double layer is insufficient to account for all the observed facts. The potential difference mercury-electrolyte is not purely electrostatic, but depends on the nature of the ions, as, according to Nemst s theory, it should do. This theory, it will be remembered, involves the " solution pressure of the ions, which varies with their chemical nature. (6) The potential difference mercury-electrolyte is not necessarily zero when the interfacial tension is a maximum, although in the particular case of dilute KC1 this condition is very nearly fulfilled. 

The movement of solute across a semipermeable membrane depends upon the chemical concentration gradient and the electrical gradient. Movement occurs down the concentration gradient until a significant opposing electrical potential has developed. This prevents further movement of ions and the Gibbs-Donnan equilibrium is reached. This is electrochemical equilibrium and the potential difference across the cell is the equilibrium potential. It can be calculated using the Nemst equation. 

Schofield Phil. Mag. March, 1926) has recently verified this relation by direct experiment. In order to appreciate the significance of this result, it is necessary to consider in more detail the electrical potential difference V and the manner in which it arises. Instead of regarding the phenomenon from the point of view of the Gibbs equation, it has been, until recently, more usual to discuss the subject of electro-capillarity from the conceptions developed by Helmholtz and Lippmann. These views, together with the theory of electrolytic solution pressure advanced by Nemst, are not in reality incompatible with the principles of adsorption at interfaces as laid down by Gibbs. 

The maximum open-circuit photo voltage, attainable in a dye-sensitized solar cell, is the difference between the Fermi level of the solid under illumination and the Nemst potential of the redox mediator. However, for these devices this limitation has not been achieved and Voc is in general much smaller. It appears that Voc is kinetically limited and the diode Equation 17.12 can be applied for an n-type semiconductor in a regenerative cell.23... 

The nonpolarizable interface has been defined above (Section 6.3.3) as one which, at constant solution composition, resists any change in potential due to a change in cell potential. This implies that (3s Ma< )/3V)jl = 0. However, the inner potential difference at such an interface can change with solution composition hence, Eq. (6.89) can be rewritten in the form of dM7ds< > = (RT/ZjF) d In a, which is the Nemst equation [see Eq. (7.51)] in differential form for a single interface. 

In Chapter 6 we have seen that metal M will be deposited on the cathode from the solution of M"+ ions if the electrode potential E is more negative than the Nemst potential of the electrode M/M"+. However, it is known that in many cases metal M can be deposited on a foreign substrate S from a solution of M"+ ions at potentials more positive than the Nemst potential of M/M"+. This electrodeposition of metals is termed underpotential deposition (UPD). Thus, in terms of the actual electrode potential E during deposition and the Nemst equilibrium potential (M/M"+) and their difference AE = E — (M/M"+), we distinguish two types of electrodeposition ... 

Under electrochemical equilibrium conditions (AG = 0), the interfacial potential difference is given by the Nemst equation (see Eqs. 1.34 and 1.36) ... 

The application of the Nemst equation for the reaction of cell (I) yields the potential difference Ei (corrected to 101325 Pa - partial pressure of hydrogen gas) given by Eq. (2). E1 can be rearranged to give the so-called acidity function so that there are only measurable quantities on the right side of Eq. (3). 

From the century s beginning, through its midpoint, the electrochemistry of electrodes was based upon the treatment given by Nemst (Section 7.2.36). This had been derived first, for an interface between a metal and its ions in solution, but the treatment had spread (Planck and Henderson, 1890-1907) to the potential difference between two liquids containing different concentrations of electrolytes. The first of these two treatments yields an equation (Nemst equation) identical in form to the... 

The method for measuring a membrane potential is simple. One places an electrode (e.g., a calomel electrode if the solution contains Cl") on either side of the membrane, which usually occupies a hole about 1 mm in diameter in a Teflon sheet. Since the potential of the calomel electrode is accurately known and varies according to the Nemst potential with log aa- (Section 7.2.7), the difference in potential arising from the two different Cl concentrations on each side of the membrane is easily known and can be subtracted from the total potential differences registered between the two electrodes to give the value due to the membrane. Most of the membrane potentials recorded in the literature lie within values of tens to hundreds of millivolts. 

A (more modem) approach to the membrane potentials observed in biology is to take account not only of the liquid junction (Nemst-Planckian) potential aspects, but also to model the net potential difference across the membrane as a bielectrode. On each side of the membrane it is supposed that (differing) electron-transfer reactions occur. The observed potential is the difference of these, plus IR components, of active electronic and ionic potential differences across the membrane. 

The unequal distribution of K+ and Na+ across plasma membranes gives rise to an electrical potential difference AE. It can be calculated by the Nemst equation (see Chapter 2) ... 

Assuming that (a) the rate of combination between hydrogen atoms in the adsorbed layer is proportional to the square of their concentration, cH there, and (6) the potential difference between electrode and electrolyte is a linear function of the concentration of hydrogen atoms on the surface, in lormal analogy with the Nemst solution pressure hypothesis, then... 

For an electrochemical reaction, O + ne R, at equilibrium, the forward reaction rate equals the backward reaction rate, the net reaction rate is 0, and no net electric current is produced. The potential at equilibrium is the Nemst potential or thermodynamic potential as expressed in Equations 1.30 and 1.31. To obtain a net current from the reaction, as shown in Equation 1.37, the potential apphed to the electrode surface should shift away from the Nemst potential the difference between the applied potential and the Nemst potential is called overpotential ... 

He refers to Equation 7.14 (Equation 2 in his paper) as the Nemst equation and states his approach explicitly as follows The only important point is that the Nemst equation should correctly be obeyed, if one is considering a constant surface potential problem. His criticism is clearly based on the idea that there exists a chemical potential difference A/ic between the two phases. Many colloid scientists think in this way, but few express it so elegantly. The idea resurfaces in Overbeek s criticism of SSS theory [17, 18]. 

The Nemst equation applies (if we neglect the activity coefficients of the ions, in keeping with PB theory) to the emf (electromotive force) of an electrochemical cell. The emf of such a cell and the surface potential of a colloidal particle are quantities of quite different kinds. It is not possible to measure colloidal particle with a potentiometer (where would we place the electrodes ), and even if we could, we have no reason to expect that it would obey the Nemst equation. We have been at pains to point out that all the experimental evidence on the n-butylam-monium vermiculite system is consistent with the surface potential being roughly constant over two decades of salt concentration. This is clearly incompatible with the Nemst equation, and so are results on the smectite clays [28], Furthermore, if the zeta potential can be related to the electrical potential difference deviations from Nemst behavior, as discussed by Hunter... 

Equation (36) suggests that the membrane potential in the presence of sufficient electrolytes in Wl, W2 and M is primarily determined by the potential differences at two interfaces that depend on ion transfer reactions at the interfaces, although the potential differences at interfaces are not apparently taken into account in theoretical equations such as Nemst-Planck, Henderson and Goldman-Hodgkin-Katz equations which have been often adopted in the discussion of the membrane potential [19,22-25]. 

---