Equilibrium potential difference

A cell whose equilibrium potential difference is affected by outer potentials is depicted in the scheme... 

Nernst s equation, 857, 1057, 1058, 1060, 1062 1066 1255. 1351 diffusion layer, 1233 electrochemical potential, 1064 equilibrium potential difference. 1061 importance, 1064... 

Equilibrium is reached when the driving force for the diffusion (the concentration gradient) is compensated for by the electric field (the potential gradient). Under these equilibrium conditions, there is an equilibrium net charge on each side of the junction and an equilibrium potential difference d< >e. This process is analogous to the way charge transfer across a nonpolarizable electrode/solution interface results in the establishment of an equilibrium potential difference across the interface. 

What is the quantitative relationship between the steady state, convection-with-diffusion current density and the potential difference across the interface How is the steady-state potential difference at a steady current density related to the zero-current, or equilibrium, potential difference These questions are the relevant ones for steady passage of current in convection-aided situations. 

Experiment shows that when the transport of reactants cannot keep pace with the charge-transfer reaction, the potential d observed at the current density i is not equal to the zero-current, or equilibrium potential difference J< > =0 = J< >e. If an electronation reaction is considered,... 

J< >, corresponding to a current density i, and the equilibrium-potential difference... 

The Equilibrium Potential Difference across an Electrochemical Cell... 

Before treating cells with currents flowing across them, an expression will be developed for the zero current or equilibrium potential difference across a cell." Since there is zero cell current, the cell is not connected to either an external current source or an external current sink (or (load) one says the cell is on open circuit. It is neither a driven cell nor a self-driving system. Each interface therefore must be at equilibrium because the net current is zero across both interfaces. 

With this background, consider the calculation of the equilibrium-potential difference Ve across the cell... 

The actual potential difference across the electrode/electrolyte interface minus the equilibrium potential difference across the interface is known as the electrode overpotential, t, and is, in effect, the driving force for net charge-transfer,... 

Two points may be made at this stage. First, the quantity of charge transferred between phases in order to establish an equilibrium potential difference is normally so small that the actual change in composition of the solution is negligible. For example, one can show that when a 1 cm2 platinum electrode is immersed in a Fe2+/Fe3+ solution, a net reduction of between 10-9 and 10-,° moles of Fe3+ takes place. Second, and as will be stressed later, the kinetics of the charge transfer process are very important, since if rates are slow, it may not be possible for a true equilibrium to be established. 

When a metal is immersed in a solution of an electrolyte, a potential difference is set up at the ra tal—solution interface this is the electrode potential. When a metal dips into a solution of its own ions, some ions may leave the metal and enter the solution, while others will deposit on the metal from solution. Since the ions are charged, an electrical double layer is created at the metal—solution interface. The equilibrium potential difference between metal and solution is the Galvani potential. When ions are transferred from solution to deposit on the metal, the metal consititutes the positive side of the double layer and vice versa. 

Table 13.1 lists the Gibbs free-energy change and the corresponding equilibrium-potential differences for the reactions of the oxidation of some currently used and potential fuels. 

Consider two half-cell reactions, one for an anodic and the other for a cathodic reaction. The exchange current densities for the anodic and the cathodic reactions are lO-6 A/cm2 and 1(T2 A/cm2, respectively, with transfer coefficients of 0.4 and 1, respectively. The equilibrium potential difference between the two reactions is 1.5 V. (a) Calculate the cell potential when the current density of 1CT5 A/cm2 flows through the self-driving cell, neglecting the concentration overpotentials. The solution resistance is 1000 Q cm2, (b) What is the cell potential when the current density is 10-4 A/cm2 (Kim)... 

In order to characterize the equilibrium state of the electrochemical cells, the electronic conductor connecting the electrodes of Figure 3.1.5 is removed. Now, both electrodes may establish their individual charge-transfer equilibrium state. A stable equilibrium potential difference, E, is established between the two electrodes. 

If the electrode reactants and products are not in the standard state, the equilibrium cell voltage will be the difference between the E values (i.e. the corresponding activity terms have to be included). Consider again the cell consisting of the half reactions Ag+/Ag and H+/H2. The equilibrium potential difference between the two electrodes, E - E(2) - E(l), is represented in Equation (20). Considering that czAg - 1 and 0(H+/H2) = 0 V, Equation (20) is identical to Equation (18). 

The electrolysis voltage between two electrodes is the summation of the equilibrium potential difference, anode overpotential, cathode overpotential, and ohmic potential drop of the aqueous solution as shown below (Scott 1995 Chen et al. 2002c) ... 

Fig. 13. Logarithm of the apparent forward rate constant k vs. the equilibrium potential difference A o 0 (Thfel plot) derived from equilibrium impedance measurements for (A) monovalent cation and (B) anion transfer from a solution of 0.05 M LiCl in water to a solution of 0.05 M Bu4NPh4B or (Ph4AsDCC) in nitrobenzene at 293 K. (After [132]).

When the current does not flow through battery the measurable diflerence in electric potential between the terminals of the two electrodes is the result of all the equilibrium potential differences at the interphase between the conducting phases in contact. In the example of the Daniell cell, with both electrodes having copper terminals, there are three interfacial potential differences (apart from the small liquid junction potential difference at the contact between the two electrolyte phases) one potential difference at the contact between the zinc rod and the copper terminal (Zn/Cu) and two potential differences at the metal-solution interphases (Zn/Zn + and Cu/Cu +), which are mainly due to the charge transfer processes. 

K lumped-parameter rate constant for an electrochemical reaction which includes the equilibrium potential difference, see equation (10.7), mA/cm ... 

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