Nemst equation concentration dependence

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

The chronoamperometric technique illustrates the principle that analytically useful current responses depend critically on the efficiency of analyte mass transport within the solution. The analyte mass transport in turn depends on the efficiency with which an appHed voltage can maintain the surface concentrations of oxidized and reduced species at values specified by the Nemst equation. It is generally the case in chronoamperometry that the bulk concentration of one of the species is zero whereas the surface concentration of the other species is forced to zero by the appHed potential, but this is not always so. 

The Nemst equation describes the dependence of the half-cell potential on concentration ... 

Potentiometry is suitabie for the analysis of substances for which electrochemical equilibrium is established at a suitable indicator electrode at zero current. According to the Nemst equation (3.31), the potential of such an electrode depends on the activities of the potential-determining substances (i.e., this method determines activities rather than concentrations). 

Reversal potentials for LSD were also determined over a range of external K+ concentrations. According to the Nemst equation, reversal potentials should shift approximately 60 mV per 10-fold shift in K+ concentration if K+ were the ionic species involved in a conductance change. Reversal potentials of LSD were found to shift almost exactly to the extent predicted by the Nemst equation for a K+-dependent potential. Of course, there are several different types of K+ conductances that could be activated by LSD, including the Ca2+-dependent outward current. To evaluate the latter possibility, midbrain slices were exposed... 

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. 

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

Abstract This chapter first explains the natural flotability of some minerals in the aspect of the crystal structure and demonstates the collectorless flotaiton of some minerals and its dependence on the h and pH of pulp. And then the surface oxidation is analysed eletrochemically and the relations of E to the composition of the solutions are calculated in accordance with Nemst Equation. The E h-pH diagrams of several minerals are obtained. Thereafter, electrochemical determination such as linear potential sweep voltammetry (LPSV) and cyclic voltammetry (CV) and surface analysis of surface oxidation applied to the sulphide minerals are introduced. And recent researches have proved that elemental sulfur is the main hydrophobic entity which causes the collectorless flotability and also revealed the relation of the amount of sulfur formed on the mineral surfaces to the recoveries of minerals, which is always that the higher the concentration of surface sulphur, the quicker the collectorless flotation rate and thus the higher the recovery. 

Equation (5.9) is the general Nemst equation giving the concentration dependence of the equilibrium cell voltage. It will be used in Section 5.4 to derive the equilibrium electrode potential for metal/metal-ion and redox electrodes. 

An internal electrochemical mechanism was proposed long ago for deposition on certain metal substrates, since the rate of deposition sometimes depended on the nature of the substrate [11].) The standard potential of Reaction (5.3) is -l- 0.08 V, considerably more positive than the rednction potential of S to (-0.45 V). Free sulphide, if formed, would be in a very low concentration, since it will be removed continually by precipitation of PbS this will move the S rednction potential strongly positive according to the Nemst equation [Eq. (1.32)]. This positive shift will be even greater than normal because of the non-Nemstian behavior of the S /S couple when [S] > [S ] (at least in alkaline solntion) [12]. In opposition to this, the solubility of S in the (slightly acidic) aqneons solntions is very low, which will move the potential in the opposite direction. Add to this the very small concentration of S in acid solution [Eq. (1.15)], and it becomes clear that it is not trivial to estimate the feasibility of the formation of PbS by free snlphide. The non-Nemstian behavior of the sulphur-rich S /S couple and the lack of knowledge of the solnbility of free S in the deposition solntion are the two factors that complicate what would have been a tractable thermodynamic calcnlation. 

Moreover, fG(r, qG) is a function which depends on the electrode geometry (see Table 2.3 for several common situations), c is the bulk concentration of species i, v is the scan rate (= AE/r), and Eeq is the equilibrium potential given by Nemst equation. The superindex or subindex G refers to the electrode geometry considered, and qG to the characteristic dimension of the electrode considered. 

By convention, the potentials of all half-reactions, E°, are found tabulated for the reduction process under standard conditions of temperature (298.15 K), pressure (1 atm), and solute concentrations (1 molar). For nonstandard conditions, the reduction potentials, and hence the cell voltage, will differ. The concentration dependence on the cell voltage is given by the Nemst equation ... 

The equilibrium constant expression is in the same form as the ratio in the Nemst equation (Chapter 17). The square brackets mean the molarity of the substance they enclose, and the constant K is called the equilibrium constant. The entire equation is known as the equilibrium constant expression. No matter what the initial concentrations of reactants or products, the ratio of the concentrations at equilibrium will be equal to the constant K. The value of K depends only on the specific chemical equation and on the temperature. It does not depend on any of the other factors that can affect the rate of a reaction. For example, if different quantities of the same reactants and products are introduced into different reaction vessels, they will react with one another until, at equilibrium, the same ratio of concentrations, each raised to the appropriate power, is established. 

Axial-Ugand binding constants, for example to Fe and Fe porphyrins, can be measured in favorable cases by measuring the Ei/2 values for the Fe /Fe and Fe /Fe waves by cyclic voltammetry as a fimetion of the concentration of axial ligand and then fitting the ligand concentration dependence of the reduction potential observed for each half-reaction to the full Nemst equation, ... 

The shape of the transient shown in Fig. 13K depends on electrode kinetics, althougli the transition time T is independent of it. For the reversible case, this can be obtained by introducing the time-dependent concentrations of reactants and products at the electrode surface, C (0,t) and Cj (0,t), respectively, into the Nemst equation. The result is... 

There is a very strong dependence on pH, and the two species should be found at equal concentration at pH = 5.07. This should be represented by a vertical line, like the equilibrium between H O and OH in Fig. 13M. In the case of aluminum this is irrelevant because in the range of about 4.0 < pH < 8.6 only the solid phase is thermodynamically stable. There are two chemical equilibria, represented by the vertical lines in this figure, between the hydrated oxide hydrargillite and the two ions, and three electrochemical equilibria between metallic aluminum, the two ions, and the oxide. We shall write here only the electrochemical equilibria and the corresponding Nemst equations. 

Its dependence on concentrations in solution is expressed by the Nemst equation, which has the general form... 

Moreover the electrodiffusion potential gradient is likely to cause electroosmotic transfer of the solution, whose local content is not in equilibrium with that of the counterions [5]. In this case, as it is pointed out in Ref. 5, the ion mobility and concentration depend on the prior history of the process which can bring about non-Fickian diffusion. The application of Nemst-Planck equations to the real system may require inclusion of additional terms that account for the effect of activity coefficient gradients which may be important in IE with zeolites [4,5]. 

These topics are discussed in Chapter 3, Volume 1. The potential difference across the interphase is A(M, S) = m — I s-This potential difference cannot be measured directly (see Chapter 1 in Volume 1). The electrode potential E of the metal/metal-ion electrode (with respect to the reference electrode) depends on the concentration (more exactly, the activity) of the metal ions Mz+ in solution according to the Nemst equation... 

Q in the Nemst equation for the cell reaction above will depend only on the unknown concentration of if the Cl" concentration in the calomel electrode is fixed at a value determined for a saturated solution of KCI and the pressure of H2 gas is kept constant at 1 bar. 

Again H" ions show up in the balanced half-reaction. Thus, this reaction s potential is going to depend on H" concentration. Writing the Nemst equation ... 

The mid-point potential of the redox couple is given by the Nemst equation, and is therefore dependent on the relative concentrations of iodide and iodine. The concentrations of these species required for efficient device function are in turn constrained by kinetic requirements of dye regeneration at the working electrode, and iodide regeneration at the counter electrode, as discussed below. Typical concentrations of these species are in the range 0.1-0.7 M iodide and 10-200 mM iodine, constraining the mid-point potential of this electrolyte to -0.4 V vx. NUE. It should... 

The simplest potentiometric technique is based on the concentration dependence of the potential, E, at reversible redox electrodes according to the Nemst equation ... 

The dependence of concentration for the cell potential at 298 K is given hy the Nemst equation (named after the German chemist Hermann Nemst) given as ... 

Further we looked at galvanic cells where it was possible to extract electrical energy from chemical reactions. We looked into cell potentials and standard reduction potentials which are both central and necessary for the electrochemical calculations. We also looked at concentration dependence of cell potentials and introduced the Nemst-equation stating the combination of the reaction fraction and cell potentials. The use of the Nemst equation was presented through examples where er also saw how the equation may be used to determine equilibrium constants. 

The potentials listed in Table 12.1 were determined for the case when the concentrations of both the oxidized and reduced forms (and all other species) were at unit activity, and they are called the standard potentials, designated by E. Volta originally set up empirical tables under very controlled and defined conditions. Nemst made them practical by establishing quantitative relationships between potential and concentrations. This potential is dependent on the concentrations of the species and varies from the standard potential. This potential dependence is described by the Nemst equation ... 

---