Standard equilibrium

This term is associated with deformation of a bond from its standard equilibrium length. For small displacements from equilibrium, a harmonic function is often used ... 

It follows from equation 1.14 that for any constant ratio of a /a the E vs. pH relationship will be linear with a slope -0-059m/z, and that when = 1 fhe intercept of the curve on the E axis (i.e. pH= 0) will be E, the standard equilibrium potential, which by definition is the potential when the species involved in the equilibrium are at unit activity. 

It must not be assumed that the protection potential is numerically equal to the equilibrium potential for the iron/ferrous-ion electrode (E ). The standard equilibrium potential (E ) for iron/ferrous-ion is -0-440V (vs. the standard hydrogen electrode). If the interfacial ferrous ion concentration when corrosion ceases is approximately 10 g ions/1 then, according to the Nernst equation, the equilibrium potential (E ) is given by ... 

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

These equations show that whereas the kinetic coefficients of an individual reaction can assume any value, the coefficients of its forward and reverse process are always interrelated. The relation between the standard equilibrium potential EP and the rate constants and is analogous to the well-known physicochemical relation between equilibrium constant K and the rate constants of the forward and reverse process. 

This last equation contains the two essential activation terms met in electrocatalysis an exponential function of the electrode potential E and an exponential function of the chemical activation energy AGj (defined as the activation energy at the standard equilibrium potential). By modifying the nature and structure of the electrode material (the catalyst), one may decrease AGq, thus increasing jo, as a result of the catalytic properties of the electrode. This leads to an increase in the reaction rate j. 

In the two bulk phases the potential of mean force is constant, but it may vary near the interface. The difference in the bulk values of the chemical part is the free energy of transfer of the ion, which in our model is —2mu (we assume u < 0). Let us consider the situation in which the ion-transfer reaction is in equilibrium, and the concentration of the transferring ion is the same in both phases the system is then at the standard equilibrium potential 0oo- In Ihis case the potential of mean force is the same in the bulk of both phases the chemical and the electrostatic parts must balance ... 

The generic case is a subsystem with phase function x(T) that can be exchanged with a reservoir that imposes a thermodynamic force Xr. (The circumflex denoting a function of phase space will usually be dropped, since the argument T distinguishes the function from the macrostate label x.) This case includes the standard equilibrium systems as well as nonequilibrium systems in steady flux. The probability of a state T is the exponential of the associated entropy, which is the total entropy. However, as usual it is assumed (it can be shown) [9] that the... 

Standard emf standard equilibrium electrode potential equilibrium electrode rest potential Non-equilibrium electrode potential... 

The phenomenological treatment assumes that the Gibbs energies of activation Gox and Gred depend on the electrode potential , but that the pre-exponential factor A does not. We expand the energy of activation about the standard equilibrium potential >0o of the redox reaction keeping terms up to first order, we obtain for the anodic reaction ... 

Figure 5.1 Potential energy curves for an outer-sphere reaction the upper curve is for the standard equilibrium potential oo the lower curve for

At the standard equilibrium potential eox = ered changing the electrode potential by an overpotential r/ lowers the energy of the oxidized state, where the electron has been transferred to the electrode, by —... 

For simplicity we assume that the intermediate stays at the electrode surface, and does not diffuse to the bulk of the solution. Let (j>l0 and 0oo denote the standard equilibrium potentials of the two individual steps, and cred, Cint, cox the surface concentrations of the three species involved. If the two steps obey the Butler-Volmer equation the current densities j and j2 associated with the two steps are ... 

The standard equilibrium condition that savings equal investment can also be represented by... 

If tbe equation is related to a standard equilibrium, it is possible to write ... 

Explosive boiling is certainly not the normal event to occur when liquids are heated. Thus, the very rapid vaporization process must be explained by theories other than standard equilibrium models. For example, if two liquids are brought into contact, and one is relatively nonvolatile but at a temperature significantly above the boiling point of the second liquid, an explosive rapid-phase transition sometimes results. Various models have been proposed to describe such transitions. None has been... 

TABLE 6-L Die standard equilibrium potentials for redox electrode reactions of h rdrated redox particles at 25 C nhe = relative electrode potential referred to the normal hydrogen electrode. [Handbooks of electrochemistry.]... 

Table 6-1 shows the standard equilibrium potentials of several redox reactions of hydrated redox particles. 

TABLE 6-2. Hie standard equilibrium potentials for transfer reactions of metal ions at metal electrodes at 25 C. [Handbooks of electrocfaemistiy.]... 

It follows from Eqn. 6-22 that the standard chemical potential of hydrated ions determined from the standard equilibrium potential of the ion transfer reaction is a relative value that is to the standard chemical potential of hydrated protons at unit activity, which, by convention in aqueous electrochemistry, is assigned a value of zero on the electrodiemical scale of ion levels. 

Expressing the anodic and the cathodic activation energies in the standard state as 4 4. o) respectively, and the standard equilibrium potential... 

E is the standard equilibrium potential, i. e. the potential corresponding to unit activity and RTF. The dissolution reaction leads to the development of an electrical double layer at the iron-solution interface. The potential difference of the Fe/Fe " half cell cannot be measured directly, but if the iron electrode is coupled with a reference electrode (usually the standard hydrogen electrode, SHE), a relative potential difference, E, can be measured. This potential is termed the single potential of the Fe/Fe electrode on the scale of the standard hydrogen couple H2/H, the standard potential of which is taken as zero. The value of the equilibrium potential of an electrochemical cell depends upon the concentrations of the species involved. 

E° standard equilibrium (or reversible) potential of an electrode reaction, V... 

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