Nemst equations defined

The Nemst equation defines the equilibrium potential of an electrode. A simplified thermodynamic derivation of this equation is given in the Sections 5.3-5.5. Here we will give the kinetic derivation of this equation. 

Cells create potential differences by pumping ions across membranes. The Nemst equation defines the electrical potential arising from differences in ionic concentration created by the various pumps. It relates the membrane resting potential to the charge and concentration of ions on either side of a membrane. 

The Nemst equation defines the single electrode (half-ceU) potentials in Eqs. (2.40) and (2.41). These are defined by the Nemst equation as ... 

If reactions (III.3.54) and (III.3.55) are reversible, the corresponding Nemst equations define the limits of the potential window ... 

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... 

Reducing and oxidizing conditions m a sediment determine the chemical stability of the solid compounds and the direction of spontaneous reactions. The redox state can be recognized as a voltage potential measured with a platinum electrode. This voltage potential is usually referred to as E or Eh defined by the Nemst equation, which was introduced in Chapter 5, Section 5.3.1 ... 

Electrode reactions are heterogeneous since they occur at interfaces between dissimilar phases. During current flow the surface concentrations Cg j of the substances involved in the reaction change relative to the initial (bulk) concentrations Cy p Hence, the value of the equilibrium potential is defined by the Nemst equation changes, and a special type of polarization arises where the shift of electrode potential is due to a change in equilibrium potential of the electrode. The surface concentrations that are established are determined by the balance between electrode reaction rates and the supply or elimination of each substance by diffusion [Eq. (4.9)]. Hence, this type of polarization, is called diffusional concentration polarization or simply concentration polarization. (Here we must take into account that another type of concentration polarization exists which is not tied to diffusion processes see Section 13.5.)... 

The essence of the technique is as follows [239]. The cathode reduces the mediator which then reduces the dye. This mediator (the regenerable redox system) must continually produce a consistent reduction potential in the dye liquor, so that no reducing agent has to be added. The prevailing potential is defined by the Nemst Equation (12.2) ... 

The potential developed is determined by the chloride concentration of the inner solution, as defined by the Nemst equation. As can been seen from the above reaction, the potential of the electrode remains constant as long as the chloride concentration remains constant. Potassium chloride is widely used for the inner solution because it does not generally interfere with pH measurements, and the mobility of the potassium and chloride ions is nearly equal. Thus, it minimizes liquid-junction potentials. The saturated potassium chloride is mainly used, but lower concentrations such as 1M potassium chloride can also be used. When the electrode is placed in a saturated potassium chloride solution, it develops a potential of 199 mV vs the standard hydrogen electrode. 

Thus far, all of our calculations have been based on the standard cell potential or standard halfcell potentials—that is, the standard state conditions that were defined previously. However, many times the cell is not at standard conditions—commonly the concentrations are not 1 M. The actual cell potential, E, can be calculated by the use of the Nemst equation ... 

Underpotential deposition is described as less than monolayer metal deposition on a foreign metal substrate, which occurs at more positive potentials than the equilibrium potential of a metal ion deposed on its own metal, expressed by the Nemst equation. Kolb reviewed state-of-the-art Underpotential deposition up to 1978. As Underpotential deposition is a process indicative of less than a monolayer metal on a substrate, it is expected to be quite sensitive to the surface stmcture of the substrate crystal a well-defined single-crystal electrode preparation is a prerequisite to the study of Underpotential deposition. In the case of Au and Ag single-crystal electrodes, Hamelin and co-workers extensively studied the necessary crystal surface structure, as reviewed in Ref. 2. 

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]. 

The ideal performance of a fuel cell is defined by its Nemst potential represented as cell voltage. The overall cell reactions corresponding to the individual electrode reactions listed in Table 2-1 are given in Table 2-2, along with the corresponding form of the Nemst equation. The Nemst... 

So far, we have defined the Nemst equation in terms of activities (a) rather than concentrations (c). This representation is rather false, so we need to remedy the situation. The concept of activity was introduced because the Nemst equation cannot adequately describe the relationship between an electrode potential Eq.r... 

The pH electrode (and its less sophisticated parent, the glass electrode) are the most commonly encountered forms of ion-selective electrodes (ISEs). Such an electrode is best defined as an electrode having a nemstian response to a single ion in solution where, by nemstian , we again mean that the Nemst equation is obeyed. The pH electrode is an ion-selective electrode since it only responds to protons in solution (with the occasional exception of cations of the alkali and alkaline-earth metals, as discussed below). 

The potential of this electrode is defined (Section 5.2) as the voltage of the cell Pt H2(l atm) H (a = 1) M M, where the left-hand electrode, = 0, is the normal hydrogen reference electrode (described in Section 5.6). In Chapter 6, we derive the Nemst equation on the basis of the electrochemical kinetics. Here we use a simplified approach and consider that Eq. (5.9) can be used to determine the potential E of the M/M electrode as a function of the activity of the products and reactants in the equilibrium equation (5.10). Since in reaction (5.10) there are two reactants, and e, and only one product of reaction, M, Eq. (5.9) yields... 

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. 

Reduction-oxidation reactions are mediated by micro-organisms and involve the transfer of electrons between reactants and products. Free electrons do not exist in solution, so an oxidation reaction (loss of electrons) must be balanced by a reduction reaction (gain of electrons). Redox potential is defined by the Nemst equation and is the energy gained in the transfer of 1 mol of electrons from an oxidant to H2. 

The definition of Eh, and thus Pe, is given by the Nemst equation, in which the Eh of a solution is related to concentrations of aqueous redox couples at chemical equilibrium and the voltage of a standard hydrogen electrode ( ). For example, when concentrations of aqueous Fe and Fe " " are at equilibrium. Eh is defined as... 

The diffusion of charged ions is more complicated because of the law of electroneutrality, which states that the sum of the positive charges on each side of the membrane must equal the sum of the negative charges. In addition to the concentration gradient, the electrical potential difference determines the Bnal equilibrium of a substance across the membrane. Therefore at equilibrium, the concentration of an ionic species may be unequal across the membrane and this gradient will balance the electrical difference across the membrane. The driving force for transport in this situation is defined as the electrochemical potential. The Nemst equation describes the equilibrium situation for ions... 

For a 3D Me bulk phase on top of S, the thermodynamic equilibrium is again given by the Nemst equation (1.2). The actual electrode potential, E, determines the direction of reaction (1.1). This statement is valid, however, for 3D Me bulk phases only, while small 3D Me cluster phases have a more negative potential of stability, E < Me/Me + (cf. Section 4.1). Under certain conditions, 2D Me phases are stable at > jye/Me + and A/f < 0 (undersaturation) on a foreign substrate S. Therefore, in this case the potential difference E - defined by convention as [1.22-1.26] ... 

Equations for the open-circuit potential of cells can be simplified further by defining all the activity coefficients and fugacity coefficients equal to 1. This simplification is known as Nemst equation for the open-circuit potential. The Nernst equation for the open-circuit potential of the cell shown in Eq. (5) is given by simplifying Eq. (19) ... 

The indicator electrode must have a stable and reproducible potential for a course of measurement and should be able to respond in a Nernstian manner to varying conditions in the high-temperature aqueous environment. In other words, the activity of the dissolved species, a,-, and the standard open-circuit potential, E°, should be, in principle, definable by measuring the open-circuit potential between the indicator and reference electrodes and applying the Nemst equation (17). 

Redox potential is defined by the half cell reduction potential that is created by redox couples that are primarily due to GSH, NAD+ and nicotinamide dinucleotide phosphate. These couples are in ratios of the oxidized to reduced form of the molecules (NAD /NAD, NADP /NADPH, and GSSG/2GSH). The redox couples can be independent, as well linked to each other to form related couples. The redox environment is a reflection of these couples. These ratios can be measured by the Nemst equation, similar to a voltaic cell. 

The activity of electrons in equilibrium with the standard hydrogen electrode is arbitrarily defined to be unity and — log (a ) is defined as pE in a manner analogous to the definition of pH as — logP ]. Hostettler (1984) discusses the difficulty of associating pE with an electron activity. By substitution, an expression similar to the Nemst equation is obtained for pE. The term pE is — AG/ (2.303z T) ... 

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 ... 

If we know the form of the complex, we could write a new half-reaction involving the acid anion and determine an E value for this reaction, keeping the acid and all other species at unit activity. However, the complexes are frequently of unknown composition. So we define the formal potential and designate this as E°. This is the standard potential of a redox couple with the oxidized and reduced forms at 1 M concentrations and with the solution conditions specified. For example, the formal potential of the Ce +/Ce + couple in 1 M HCl is 1.28 V. The Nemst equation is written as usual, using the formal potential in place of the standard potential. Table C.5 lists some formal potentials. 

Thinking it Through The Nemst equation expresses the dependence of cell potential on concentration of the cell components. The equation itself may be given in the problem, or may be found in a general table of useful equations in other ACS exams. There may also be questions where you are expected to know the relationship, or derive it from changes in free energy. The value of Q is defined in the same manner as an equilibrium constant, but remember that these cell concentrations are not standard state concentrations.. For this problem, Q is evaluated by this expression. 

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