Thermodynamics Nernst equation

These considerations show the essentially thermodynamic nature of and it follows that only those metals that form reversible -i-ze = A/systems, and that are immersed in solutions containing their cations, take up potentials that conform to the thermodynamic Nernst equation. It is evident, therefore, that the e.m.f. series of metals has little relevance in relation to the actual potential of a metal in a practical environment, and although metals such as silver, mercury, copper, tin, cadmium, zinc, etc. when immersed in solutions of their cations do form reversible systems, they are unlikely to be in contact with environments containing unit activities of their cations. Furthermore, although silver when immersed in a solution of Ag ions will take up the reversible potential of the Ag /Ag equilibrium, similar considerations do not apply to the NaVNa equilibrium since in this case the sodium will react with the water with the evolution of hydrogen gas, i.e. two exchange processes will occur, resulting in an extreme case of a corrosion reaction. 

In spite of the above justification for the kinetic approach to the estimate of l, this has a number of drawbacks. First of all, there is no point in using a kinetic approach to determine a thermodynamic equilibrium quantity such as l. The justification of the validity ofEqs. (42) and (45) by the resulting equilibrium condition of Eq. (46) is far from rigorous, just as is the justification of the empirical Butler-Volmer equation by the thermodynamic Nernst equation. Moreover, the kinetic expressions of Eq. (41) involve a number of arbitrary assumptions. Thus, considering the adsorption step of Eq. (38a) in quasi-equilibrium under kinetic conditions cannot be taken for granted a heterogeneous chemical step, such as a deformation of the solvation shell of the... 

It should be noted that the simple Nernst equation cannot be used since the standard electrode potential is markedly temperature dependent. By means of irreversible thermodynamics equations have been computed to calculate these potentials and are in good agreement with experimentally determined results. 

A simple calculation based on the solubility product of ferrous hydroxide and assuming an interfacial pH of 9 (due to the alkalisation of the cathodic surface by reaction ) shows that, according to the Nernst equation, at -0-85 V (vs. CU/CUSO4) the ferrous ion concentration then present is sufficient to permit deposition hydroxide ion. It appears that the ferrous hydroxide formed may be protective and that the practical protection potential ( —0-85 V), as opposed to the theoretical protection potential (E, = -0-93 V), is governed by the thermodynamics of precipitation and not those of dissolution. 

Before treating specific faradaic electroanalytical techniques in detail, we shall consider the theory of electrolysis more generally and along two different lines, viz., (a) a pragmatic, quasi-static treatment, based on the establishment of reversible electrode processes, which thermodynamically find expression in the Nernst equation, and (b) a kinetic, more dynamic treatment, starting from passage of a current, so that both reversible and non-reversible processes are taken into account. 

In this scheme, H, G and HG in normal or subscript positions represent the host, guest and complex species respectively subscripts ox and red indicate that the corresponding symbols or parameters refer to molecules in oxidized and reduced states E° is the formal potential of the electron transfer reaction and K is the stability constant. According to thermodynamics, there are four relationships linking the concentrations of the four molecules at the four corners of the square. These are two Nernst equations for the upper (2) and lower (3) electron transfer reactions,... 

Since we have preliminarily stated that any kinetic theory must involve agreement between kinetic and thermodynamic data, it follows that, under equilibrium conditions, kinetic theory must afford relationships that coincide with the Nernst equation. 

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

One approach to accounting for the potential and solution effects is to treat them separately (the additive approach). The thermodynamics due to an electric potential is described by the Nernst equation, which is, to the first order of approximation,... 

Tower, Stephen. All About Electrochemistry. Available online. URL http //www.cheml.com/acad/webtext/elchem/. Accessed May 28, 2009. Part of a virtual chemistry textbook, this excellent resource explains the basics of electrochemistry, which is important in understanding how fuel cells work. Discussions include galvanic cells and electrodes, cell potentials and thermodynamics, the Nernst equation and its applications, batteries and fuel cells, electrochemical corrosion, and electrolytic cells and electrolysis. 

This chapter is not concerned with the thermodynamic stability of ions with respect to their formation. Rather, it is concerned with whether or not a given ion is capable of existing in aqueous solution without reacting with the solvent. Hydrolysis reactions of ions are dealt with in Chapter 3. The only reactions discussed in this section are those in which either water is oxidized to dioxygen or reduced to dihydrogen. The Nernst equation is introduced and used to outline the criteria of ionic stability. The bases of construction and interpretation of Latimer and volt-equivalent (Frost) diagrams are described. 

The ranges of Eh and pH over which a particular chemical species is thermodynamically expected to be dominant in a given aqueous system can be displayed graphically as stability fields in a Pourbaix diagram,10-14 These are constructed with the aid of the Nernst equation, together with the solubility products of any solid phases involved, for certain specified activities of the reactants. For example, the stability field of liquid water under standard conditions (partial pressures of H2 and 02 of 1 bar, at 25 °C) is delineated in Fig. 15.2 by... 

The foregoing considerations are based on the concepts of reversible thermodynamics the electrochemical cells are considered to be operating reversibly, which means in effect that no net current is drawn. Real cell EMFs, however, can differ substantially from the predictions of the Nernst equation because of electrochemical kinetic factors that emerge when a nonnegligible current is drawn. An electrical current represents electrons transferred per unit of time, that is, it is proportional to the extent of electrochemical reaction per unit of time, or reaction rate. The major factors that can influence the cell EMF through the current drawn are... 

These matters show up in terminology. For the physical electrochemist, there is the state of thermodynamic reversibility, the domain of the Nernst equation, and this state is the bedrock and the base from which he or she starts out. When a reaction departs from equilibrium in the cathodic and anodic direction, it has a degree of irreversibility in the thermodynamic sense. Thus, for overpotentials less than RT/b one refers to the linear region (i a It)I), where departure from reversibility is small enough to be measured in millivolts. If 11)1 > RT/F (about 26 mV at room temperature), the reaction is simply and straightforwardly irreversible the forward reaction has been made to become much faster than the back-reaction. 

We conclude this chapter with a discussion of adsorption at the interface between mercury and a solution (usually aqueous) under the influence of an applied potential. The y value for this interface is easily measured, and potential and electrolyte concentration can be studied as variables. The Nernst equation provides a familiar reminder that potentials can be dealt with by thermodynamics. 

In order to transform eqns. (174) into more explicit expressions, use is made of (i) the Nernst equation, relating E, cQ and cR (ii) the general rule that any isotherm is of the form (3jCj = f(Pj) (iii) the thermodynamic relationship [144, 145]... 

This is the Nernst equation defined from the electrode kinetics considerations. Later, we derive the same relationship on purely thermodynamic grounds. 

It is important to note that the electrode potential is related to activity and not to concentration. This is because the partitioning equilibria are governed by the chemical (or electrochemical) potentials, which must be expressed in activities. The multiplier in front of the logarithmic term is known as the Nernst slope . At 25°C it has a value of 59.16mV/z/. Why did we switch from n to z when deriving the Nernst equation in thermodynamic terms Symbol n is typically used for the number of electrons, that is, for redox reactions, whereas symbol z describes the number of charges per ion. Symbol z is more appropriate when we talk about transfer of any charged species, especially ions across the interface, such as in ion-selective potentiometric sensors. For example, consider the redox reaction Fe3+ + e = Fe2+ at the Pt electrode. Here, the n = 1. However, if the ferric ion is transferred to the ion-selective membrane, z = 3 for the ferrous ion, z = 2. 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

An electron transfer reaction, Equation 6.6, is characterised thermodynamically by the standard potential, °, i.e. the value of the potential at which the activities of the oxidised form (O) and the reduced form (R) of the redox couple are equal. Thus, the second term in the Nernst equation, Equation 6.7, vanishes. Here and throughout this chapter n is the number of electrons (for organic compounds, typically, n = 1), II is the gas constant, T is the absolute temperature and F is the Faraday constant. Parentheses, ( ), are used for activities and brackets, [ ], for concentrations /Q and /R are the activity coefficients of O and R, respectively. However, what may be measured directly is the formal potential E° defined in Equation 6.8, and it follows that the relationship between E° and E° is given by Equation 6.9. Usually, it maybe assumed that the activity coefficients are unity in dilute solution and, therefore, that E° = E°. 

A reversible electron transfer reaction is the limiting case where O and R are in thermodynamic equilibrium at the electrode surface, i.e. the electron transfer reaction responds instantaneously to a change in E. Thus, the ratio between [O]x=o and [R] x o is given by the Nernst equation, Equation 6.7. In principle, the equilibrium condition implies an infinitely... 

An electrolytic cell is essentially composed of a pair of electrodes submerged into an electrolyte for conduction of ions and connected to a direct current (DC) generator via an external conductor to provide for continuity of the circuit. The electrode connected to the positive pole of the DC generator is called anode, while that linked to the negative one, cathode. The current flow in an electrolyte results from the movement of positive and negative ions and is assumed as positive when directed as the positive charges or opposite to the electrons in the external circuit. When the cell is not operating under conditions of standard concentration, the thermodynamic electrode (or cell) potential (ET) can be estimated from the Nernst equation ... 

As electrochemical reactions are, at their heart, chemical reactions, their thermodynamics depend on the concentrations of the species involved, as well as the temperature. The Nernst equation describes this dependence. Derivations of the Nernst equation are available in many standard texts (4-6). For our purposes, it will be simply stated that for a reaction described by... 

The standard reversible potential is that listed in the EMF series of Table 1 and represents a special case of the Nernst equation in which the second term is zero. The influence of the solution composition manifests itself through the logarithmic term. The ratio of activities of the products and reactants influences the potential above which the reaction is thermodynamically favorted toward oxidation (and conversely, below which reduction is favored). By convention, all solids are considered to be at unit activity. Activities of gases are equal to their fugacity (or less strictly, their partial pressure). 

It is the constant that appears in the universal gas equation, however, R is widely used in thermodynamic and electrochemical relationships, e.g., in the - Nernst equation. 

Nernst equilibrium — It was - Nernst who first treated the thermodynamical - equilibrium for an -> electrode [i], and derived the - Nernst equation. Although the model used by Nernst was not appropriate (see below) the Nernst equation - albeit in a modified form and with a different interpretation - is still one of the fundamental equations of electrochemistry. In honor of Nernst when equilibrium is established at an electrode, i.e., between the two contacting phases of the electrode or at least at the interface (interfacial region), it is called Nernst equilibrium. In certain cases (see - reversibility) the Nernst equation can be applied also when current flows. If this situation prevails we speak of reversible or... 

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