Free-energy change equilibrium electrode potential

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

Relationship of change in free energy to equilibrium constants and electrode potentials... 

It is in this sense it is said that in an electrochemical energy converter, the ideal maximum efficiency is 100% for, as in the above idealized situation, if one could carry out reactions in such a way that the electrode potentials were infinitely near the equilibrium values, the electrical energy one could draw2 from the reaction would be nFVe and this is all of the free-energy change AG, which is the maximum amount of useful work one can obtain from a chemical reaction. 

The standard equilibrium cell voltage resulting from a combination of any two electrodes is the difference between the two standard potentials, E°(2) - E°( 1). For instance, the standard cell equilibrium voltage of the combination F2/F with the Li+/Li electrode would be 5,911 V. Correspondingly, the standard free energy change of the underlying chemical reaction, 1/2 F2 + Li —> F + Li+, is AG° = -570 KJ (g-equivalent)-1. 

Factors Involved in Galvanic Corrosion. Emf series and practical nobility of metals and metalloids. The emf. series is a list of half-cell potentials proportional to the free energy changes of the corresponding reversible half-cell reactions for standard state of unit activity with respect to the standard hydrogen electrode (SHE). This is also known as Nernst scale of solution potentials since it allows to classification of the metals in order of nobility according to the value of the equilibrium potential of their reaction of dissolution in the standard state (1 g ion/1). This thermodynamic nobility can differ from practical nobility due to the formation of a passive layer and electrochemical kinetics. 

As the potential is increased, there is a point at which no equilibrium state is reached, but instead, an appreciable steady current flows which will obey Ohm s law over a reasonable range of applied potential. The potential at which this steady current is observed is called the decomposition potential because it is accompanied by chemical reaction (electrolysis) at the electrode surfaces. These electrode reactions are quite generally the oxidation (anode) and reduction (cathode) of ionic or molecular species present in the solution. If the reactions at the electrodes are reversible, then the decomposition potential Ed is related by the Nernst equation to the free energy changes of the electrode reactions... 

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). 

The free energy change for the dissociation of solid silver chloride to yield chlorine gas at the pressure pch is zero, since the system is in equilibrium hence, the free energy change of the second reaction is identical with that for the over-all process. An electrode consisting of chlorine gas at the dissociation pressure peu would thus have the same potential, in a given chloride ion solution, as would the Ag, AgCl(s) electrode. 

In an electrochemical cell a redox reaction occurs in two halves (see Topic B4). Electrons are liberated by the oxidation half reaction at one electrode and pass through an electrical circuit to another electrode where they are used for the reduction. The cell potential E is the potential difference between the two electrodes required to balance the thermodynamic tendency for reaction, so that the cell is in equilibrium and no electrical current flows. E is related to the molar Gibbs free energy change in the overall reaction (see Topic B3) according to... 

The cell potential of a galvanic cell comprising these two electrode reactions would be 0.84, so the free energy change AG° = -320 kj. This large negative value tells us that equilibrium strongly favors the oxidation of iron metal. 

Equilibration results in establishment of an electrical potential difference across the metal-solution interface. This prevents any net transfer of reacting species involved in the electrode process described by Eq. (1), in spite of the fact that a chemical potential difference persists with respect to the exchangeable species. Hence, the particular feature of such an electrochemical equilibrium is that the electrode potential is a direct reflection of the chemical potential difference of the species involved or of the free energy change arising from the transformation of the reactants [left side of Eq. (1)] into the products [right side of Eq. (1)]. 

The minimum cell potential is determined by the thermodynamics of the overall chemical change in the cell, and this can only be reduced by changing an electrode reaction (e.g., replacing H2 evolution by O2 reduction in a chlor-alkali cell). The equilibrium cell potential difference, is related to the Gibbs free energy change for the cell reaction, AGj.gn by... 

Here, n is the number of intercalated Li atoms, and dCeiectrode/ dn is the free energy change of the electrode during Li intercalation, usually defined as the Li chemical potential, pu. Thus, directly determines the voltage of the electrochemical cell in the equilibrium state. The Li chemical potential can be separated into contributions from the enthalpy H and entropy 5 of the electrode, giving... 

Now let us discuss nonequilibirum situations. By varying the potential of the working electrode, we can influence the free energy of its resident electrons, thus making one reaction more favorable. For example, a potential shift E from the equilibrium value moves the O + ne curve up or down by <> = -nili. The dashed line in Figure 1.9 displays such a change for the case of... 

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