Nernst equilibrium condition

It must be emphasised that standard electrode potential values relate to an equilibrium condition between the metal electrode and the solution. Potentials determined under, or calculated for, such conditions are often referred to as reversible electrode potentials , and it must be remembered that the Nernst equation is only strictly applicable under such conditions. 

Under equilibrium conditions the Nernst equation holds ... 

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. 

It is important to recognize that the Nernst equation is valid only at the equilibrium condition, determined by specifying i, = 0. Most electrochemical techniques (chronoamperometry, chronocoulometry, voltammetry, etc.) involve nonequilibrium conditions and therefore cannot be expected to exhibit a Nernstian response unless the rates are very fast and equilibrium is quickly reestablished at the surface. 

Using a Kx calculated from AT at p - 61 bar, by using equation (15.12) with j(j)= 1, we predict a value for the formation of NH3 of 2.28 mole percent at 900 K, and 0.093 mole percent at 1600 K. These values are much higher than those obtained experimentally by Nernst. He approached the equilibrium condition from only one direction — by mixing N2 and H2) Kinetics plays an important part in this reaction, and even with catalysts, the reaction is slow unless one goes to high temperatures. It seems probable that Nernst did not achieve equilibrium. 

In potentiometry, a two-electrode setup is used and is given schematically in Fig. 1.3. This setup consists of a working and a reference electrode, and it is the aim of this method to measure equilibrium conditions at the surface of the working electrode. Under equilibrium, the Nernst equation is valid ... 

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... 

The postulates of Nernst are those that are required when we wish to determine equilibrium conditions for chemical reactions from thermal data alone. In order to calculate the equilibrium conditions, we need to know the value of AGe for the change of state involved. We take the standard states of the individual substances to be the pure substances at the chosen temperature and pressure. The value of AH° can be determined from measurements of the heat of reaction. We now have... 

This equation is known as the Nernst equation, and is extensively used in electrochemical measurements. Under equilibrium conditions E = E° and the experimentally obtained values of E° are tabulated in the literature. E° values can be used to determine whether a reaction will occur or not. 

Corrosion — Corrosion current density — Figure. Polarization curves of a metal/metal ion electrode and the H2/H+ electrode including the anodic and cathodic partial current curves, the Nernst equilibrium electrode potentials E(Me/Mez+) and (H2/H+), their exchange current densities / o,M> o,redox and related overpotentials Me) and 77(H), the rest potential r, the polarization n and the corrosion current density ic at open circuit conditions (E = Er) [i]... 

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... 

Potentiometric transducers measure the potential under conditions of constant current. This device can be used to determine the analytical quantity of interest, generally the concentration of a certain analyte. The potential that develops in the electrochemical cell is the result of the free-energy change that would occur if the chemical phenomena were to proceed until the equilibrium condition is satisfied. For electrochemical cells containing an anode and a cathode, the potential difference between the cathode electrode potential and the anode electrode potential is the potential of the electrochemical cell. If the reaction is conducted under standard-state conditions, then this equation allows the calculation of the standard cell potential. When the reaction conditions are not standard state, however, one must use the Nernst equation to determine the cell potential. Physical phenomena that do not involve explicit redox reactions, but whose initial conditions have a non-zero free energy, also will generate a potential. An example of this would be ion-concentration gradients across a semi-permeable membrane this can also be a potentiometric phenomenon and is the basis of measurements that use ion-selective electrodes (ISEs). 

To make this clear to the technical student, we will suppose that (according to Nernst results above tabulated) air is exposed to a temperature of 3,000" C. Then in 100 vols. of this air will lie found 5.3 vols. of NO, and this equilibrium will be established in the fraction of a second. Let now this 100 vols. at 3,000° C. of air be suddenly cooled to say 1,500° C. Then, acconling to the equilibrium conditions tabalatcd by Nernst in the above table, the 5 per cent, of NO in the too vols. of air will gradually decrease, according to the ecpiation, 2NO ( + (L until, after... 

In this equation, and represent the surface concentrations of the oxidized and reduced forms of the electroactive species, respectively k° is the standard rate constant for the heterogeneous electron transfer process at the standard potential (cm/sec) and oc is the symmetry factor, a parameter characterizing the symmetry of the energy barrier that has to be surpassed during charge transfer. In Equation (1.2), E represents the applied potential and E° is the formal electrode potential, usually close to the standard electrode potential. The difference E-E° represents the overvoltage, a measure of the extra energy imparted to the electrode beyond the equilibrium potential for the reaction. Note that the Butler-Volmer equation reduces to the Nernst equation when the current is equal to zero (i.e., under equilibrium conditions) and when the reaction is very fast (i.e., when k° tends to approach oo). The latter is the condition of reversibility (Oldham and Myland, 1994 Rolison, 1995). 

The quantitative capability of the Nernst equation to predict the activity of chemical species is valid only under equilibrium conditions. Most of the redox couples are not in equilibrium, except in highly reduced soils steady-state condition may result in pseudoequilibrium conditions. In soils, redox equilibrium is probably never reached because of the continuous addition of electron donors and acceptors. Biological systems add and remove electrons continuously. Thus, redox potential measurements cannot be used to accurately predict the activity of specific reductant and oxidant of the system. 

It is possible to use the Nernst equation, which relates reversible potential to pH and cation concentration, to generate phase stability plots in potential/pH space. Such diagrams are called Pourbaix diagrams, after Marcel Pourbaix who pioneered their development. Pourbaix diagrams are visual representations of the equilibrium conditions in potential/pH space. They are based on thermodynamics, and indicate the stable phase for given conditions, but say nothing about rates of reactions from one phase to another. 

Under equilibrium conditions, the ratio of the concentration of the oxidized and reduced species is given by the Nernst equation ... 

The Nernst equation is valid and can be used only under equilibrium conditions The expressions for jo are as follows ... 

The ohmic loses in Eq. 3.25 is given by Eq. 3.20. The Nernst potential or open circuit voltage (OCV) is the maximum possible potential that can be derived from a cell operating reversibly. Therefore, the Nernst potential is also known as the reversible potential. However, during the operation of the cell the maximum possible potential is always lower than the Nernst potential due to the irreversibilities associated with the fuel cell operation. Further, the Nernst equation can be applied only under equilibrium condition. 

In LSV and CV, a redox system may show a Nernstian, quasireversible or totally irreversible behavior depending on the scan rate employed, since V determine the time available for the electrodesolution interphase to attain the equilibrium condition dictated by the Nernst equation. Such a dependence is usually rationalized by the following dimensionless parameter, comparing the standard heterogeneous rate constant with the scan rate v ... 

Weigh electrodes before and after passage of current to determine mass transferred by a known amount of charge. Nernst equation measurement of voltage under potentiometric equilibrium conditions. 

An important technical application of liquid-liquid equilibria uses Nernst s law of phase distribution of a solute Y between two nonmiscible solvents to make up the two phases in contact, a and The equilibrium condition,... 

Also, if a is the transfer coefficient for the forward process, then (1 - a) is the value of the transfer coefficient for the reverse reaction, since, at equilibrium ic = ia and the equilibrium condition corresponding to Nernst s relation must be independent of any kinetic parameters such as a. Then since... 

The Nernst equation describes the equilibrium condition of an electrode. For example, the equlibrium potential of a copper electrode in contact with a solution of Cu ions at a concentration (activity) of 10" mol 1" is equal to... 

Sodium currents were evoked by voltage pulses from a holding potential of —90 mV to a membrane potential, of —60 to +80 mV for 3 ms (Fig. lOA). All stimulation for sodium currents was followed by a similar pulse protocol in which the pulse amplitude was reduced to 1/4 and the holding potential was brought to —120 mV (P/4 protocol [42]). A plot of the peak current as a function of the membrane potential is shown in Fig. lOB. The peak current was estimated by a cubic fit of each record in a short interval around the peak with a third-order polynomial. The reversal potential, V, i.e., the applied voltage for which the peak current changes sign is estimated around 53 mV, which is very close to the Nernst equilibrium potential for sodium ions in these experimental conditions. 

This reasoning is incorrect. The Nernst equation describes the dependence of OCV on the oxygen concentration only at equilibrium. This equation is not applicable in the situation when the cell generates current. Thus, Eq. (3.12) does not represent any real voltage loss in a cell. A true voltage loss in non-equilibrium conditions can be calculated from the kinetic equations as discussed above, this leads to the transport loss in the form Vconc = In Note that in Eq. (3.12) the factor is BT/ nF), while in the... 

The Nernst equation for the reactant species at equilibrium conditions, or when no current is... 

The net reaction is the oxidation of Ce(III) to Ce(IV) by bromate. In the bistable regime there is a state, where essentially no reaction occurs, which coexists with a state in which a percentage of Ce(III) is oxidized to Ce(IV). In this system we measured [6] at the same time the optical density which gives concentrations of Ce(IV) by Beer s law, and hence also the concentration of Ce(III) by conservation, and the emf of a Pt electrode which at equilibrium follows the Nernst equation (10.1). The experiment consisted of the measurement of the emf of the Ce(III)/Ge(IV) half reaction at a redox (Pt-Ag/AgGl) electrode imder equilibrium and stationary non-equilibrium conditions. The apparatus is shown in Fig. 10.1, but in these experiments the parts 4 7 were not present. From these measurements we determined that there exists a non-Nernstian contribution in a non-equilibrium stationary state as shown in Table 10.2. The concentration of [Ce(III)]ss in the stationary state is obtained... 

The first condition for T > 0 is the Nernst equilibrium at potential 0 the second expresses that the sum of fluxes of R and P is zero the third that there is no flux in C into or out of the electrode and we have the ENC also holding at the electrode (or very close to it in solution). Note that it was necessary here to set the potential if to zero in the bulk region X = L), and to use the potential rather than the potential field E. In fact, one finds from the results that E is level near the outer limit X = L, so that E could have been used in the equation system, setting a zero dE/dX at X = L as a boundary condition. But this was not certain beforehand and could not safely be assumed. 

Name Equilibrium reaction and Nernst equation Conditions Potential (V vs. SHE) T coefficient (mV °C-i)... 

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