Equilibrium constant electrochemical cells

Measurement of Equilibrium Constants Electrochemical cells can be used to measure equilibrium constants for chemical reactions. For example, consider the cell... 

It is much easier to determine the equilibrium constant electrochemically. All one has to do is measure the emf of the cell E°) and then use Equation (19.3) and (18.14) of the text to calculate K. On the other hand, use of Equation (18.14) of the text alone requires measurements of both A//° and to first determine AG° and then K. This is a much longer and tedious process. Keep in mind, however, that most reactions do not lend themselves to electrochemical measurements. 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

Electrochemical Method.—In this the value of the equilibrium constant K is calculated from the maximum work measured by means of the electromotive force of a voltaic cell (cf. Chap. XVI.). 

Other measurements of AfG involve measuring AG for equilibrium processes, such as the measurement of equilibrium constants, reversible voltages of electrochemical cells, and phase equilibrium measurements. These methods especially come into play in the measurement of Afand AfG for ions in solution, which are processes that we will now consider. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Having introduced matters pertaining to the electrochemical series earlier, it is only relevant that an appraisal is given on some of its applications. The coverage hereunder describes different examples which include aspects of spontaneity of a galvanic cell reaction, feasibility of different species for reaction, criterion of choice of electrodes to form galvanic cells, sacrificial protection, cementation, concentration and tempera lure effects on emf of electrochemical cells, clues on chemical reaction, caution notes on the use of electrochemical series, and finally determination of equilibrium constants and solubility products. 

The foregoing two examples have been taken to convey that the data of Table 6.11 can very well be used to determine the equilibrium constant for any reaction which is the overall reaction for a cell assembled with electrodes contained in the electrochemical series table. 

Figure 1. Solute transfer across an idealised eukaryote epithelium. The solute must move from the bulk solution (e.g. the external environment, or a body fluid) into an unstirred layer comprising water/mucus secretions, prior to binding to membrane-spanning carrier proteins (and the glycocalyx) which enable solute import. Solutes may then move across the cell by diffusion, or via specific cytosolic carriers, prior to export from the cell. Thus the overall process involves 1. Adsorption 2. Import 3. Solute transfer 4. Export. Some electrolytes may move between the cells (paracellular) by diffusion. The driving force for transport is often an energy-requiring pump (primary transport) located on the basolateral or serosal membrane (blood side), such as an ATPase. Outward electrochemical gradients for other solutes (X+) may drive import of the required solute (M+, metal ion) at the mucosal membrane by an antiporter (AP). Alternatively, the movement of X+ down its electrochemical gradient could enable M+ transport in the same direction across the membrane on a symporter (SP). A, diffusive anion such as chloride. Kl-6 refers to the equilibrium constants for each step in the metal transfer process, Kn indicates that there may be more than one intracellular compartment involved in storage. See the text for details...

This reaction has a very small equilibrium constant, but by dipping carbon electrodes in concentrated solutions and withdrawing the gaseous CI2 and purifying the NaOH, two valuable products could be made rather cheaply because of the large AG between anode and cathode in an electrochemical cell. Electrochemical reactors will be discussed in Chapter 9. 

At this stage, two facts may be recalled. First, the potential difference across an electrochemical cell, or system, is measurable. Thus, if the Cu2+/Cu interface is incorporated into an electrochemical along with a second metal/solution interface, the potential difference across the whole cell is measurable (Fig. 7.14). Second, if the second interface is nonpolarizable (i.e., its potential does not depart significantly from the equilibrium value on the passage across it of a small current), it contributes a constant value to the potential difference across the cell. Thus, by choosing a standard hydrogen electrode as the nonpolarizable interface, the following system can be built (Fig. 7.14) ... 

The Gibbs energy change is related to some other important physical quantities, such as the equilibrium constant for a chemical reaction and the electromotive force of an electrochemical cell, by the Nemst and van t Hoff equations ... 

While the redox titration method is potentiometric, the spectroelectrochemistry method is potentiostatic [99]. In this method, the protein solution is introduced into an optically transparent thin layer electrochemical cell. The potential of the transparent electrode is held constant until the ratio of the oxidized to reduced forms of the protein attains equilibrium, according to the Nemst equation. The oxidation-reduction state of the protein is determined by directly measuring the spectra through the tranparent electrode. In this method, as in the redox titration method, the spectral characterization of redox species is required. A series of potentials are sequentially potentiostated so that different oxidized/reduced ratios are obtained. The data is then adjusted to the Nemst equation in order to calculate the standard redox potential of the proteic species. Errors in redox potentials estimated with this method may be in the order of 3 mV. 

The equilibrium situation in an electrochemical cell is obtained, if the electrical current is interrupted, if all local actions (e.g. transport in the electrode) have come to an end and no internal short circuits occur. Then, as mentioned (Figure 3.5.10), the cell voltage is determined by the difference in the lithium potential (chemical potential of lithium) between the left-hand side (Ihs) and right-hand side (rhs) of the electrochemical cell (E - open cell voltage, F - Faraday constant) ... 

Electrochemical equilibrium is established at each interface of the cell when the -> electrochemical potentials of the common components of the two phases (a and f) forming the interface are equal, that is pf = ji , and the electrochemical free energy change (AG) for the process occurring at the interface is zero. For the net cell reaction given above, such considerations lead to an expression for the electrochemical equilibrium constant Ka given by [i]... 

Thus, the numerical value of the electrochemical equilibrium constant for a cell in which a net particular reaction occurs is identical to the chemical equilibrium constant Ka for that reaction (see - redox equilibrium) [i]. Ref. [i] OldhamKB, Myland JC (1994) Fundamentals of electrochemical science, 1st edn. Academic Press, San Diego, pp 71-74... 

Nernst equation — A fundamental equation in -> electrochemistry derived by - Nernst at the end of the nineteenth century assuming an osmotic equilibrium between the metal and solution phases (- Nernst equilibrium). This equation describes the dependence of the equilibrium electrode - potential on the composition of the contacting phases. The Nernst equation can be derived from the - potential of the cell reaction (Ecen = AG/nF) where AG is the - Gibbs energy change of the - cell reaction, n is the charge number of the electrochemical cell reaction, and F is the - Faraday constant. 

To obtain the equilibrium constant in these systems, one can use electrochemical cells such as those described in Section 3.4.8. For example, measurements that involve... 

The difference in chemical potential of (A) between the source and sink side of the PEVD system causes a gradient of the chemical potential of (A) across the solid electrolyte (E) between (I) and (II). In order to have a constant electrochemical potential of (A+) inside (E) to prevent ionic current under equilibrium, an internal electric field is built up inside solid electrolyte (E). This is justified since electronic conductivity in (E) is negligible. The internal electric field causes an electric potential difference between (I) and (II). The value of the internal electric field is the EME of the cell, and can be calculated from the change in chemical potential of (A) across the solid electrolyte (E) according to Nernsf s equation. It can be measured by a high impedance electrometer in the external electric circuit. According to the Stockholm convention, EME... 

Because the potential of an electrochemical cell depends on the concentrations of the participating ions, the observed potential can be used as a sensitive method for measuring ion concentrations in solution. We have already mentioned the ion-selective electrodes that work by this principle. Another application of the relationship between cell potential and concentration is the determination of equilibrium constants for reactions that are not redox reactions. For example, consider a modified version of the silver concentration cell shown in Fig. 11.11. If the 0.10 M AgN03 solution in the left-hand compartment is replaced by 1.0 M NaCl and an excess of solid AgCl is added to the cell, the observed cell potential can be used to determine the concentration of Ag+ in equilibrium with the AgCl(s). In other words, at 25°C we can write the Nernst equation as... 

Because the measured potential of an electrochemical cell provides a very sensitive method for the experimental determination of equilibrium concentrations, the values of equilibrium constants are often determined from electrochemical measurements. 

The third largest class of enzymes is the oxidoreductases, which transfer electrons. Oxidoreductase reactions are different from other reactions in that they can be divided into two or more half reactions. Usually there are only two half reactions, but the methane monooxygenase reaction can be divided into three "half reactions." Each chemical half reaction makes an independent contribution to the equilibrium constant E for a chemical redox reaction. For chemical reactions the standard reduction potentials ° can be determined for half reactions by using electrochemical cells, and these measurements have provided most of the information on standard chemical thermodynamic properties of ions. This research has been restricted to rather simple reactions for which electrode reactions are reversible on platinized platinum or other metal electrodes. 

It is necessary to distinguish between the concept of a potential and the measurement of a potential. Redox or electrode potentials (quoted in tables in Stability Constants of Metal-Ion Complexes or by Bard et al., 1985) have been derived from equilibrium data, thermal data, and the chemical behavior of a redox couple with respect to known oxidizing and reducing agents, and from direct measurements of electrochemical cells. Hence there is no a priori reason to identify the thermodynamic redox potentials with measurable electrode potentials. 

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 graphing calculator can run a program that calculates the equilibrium constant for an electrochemical cell using an equation called the Nemst equation, given the standard potential and the number of electrons transferred. Given that the standard potential is 2.041 V and that two electrons are transferred, you will calculate the equilibrium constant. The program will be used to make the calculations. 

The foregoing example illustrates how equilibrium constants for overall cell reactions can be determined electrochemically. Although the example dealt with redox equilibrium, related procedures can be used to measure the solubility product constants of sparingly soluble ionic compounds or the ionization constants of weak acids and bases. Suppose that the solubility product constant of AgCl is to be determined by means of an electrochemical cell. One half-cell contains solid AgCl and Ag metal in equilibrium with a known concentration of CP (aq) (established with 0.00100 M NaCl, for example) so that an unknown but definite concentration of Kg aq) is present. A silver electrode is used so that the half-cell reaction involved is either the reduction of Ag (aq) or the oxidation of Ag. This is, in effect, an Ag" Ag half-cell whose potential is to be determined. The second half-cell can be any whose potential is accurately known, and its choice is a matter of convenience. In the following example, the second half-cell is a standard H30" H2 half-cell. 

Apply the Nernst equation to calculate the voltage of a cell in which reactants and products are not in their standard states and to calculate the value of an equilibrium constant from the voltage of an electrochemical cell (Section 17.3, problems 27-38). 

When zero voltage is reached in the cell in Figure 18-2b, the concentrations of Cu(II) and Ag(I) ions will have values that satisfy the equilibrium-constant expression shown in Equation 18-4. At this point, no further net flow of electrons will occur. It is important to recognize that the overall reaction and its position of equilibrium are totally independent of the way the reaction is carried out, whether it is by direct reaction in a solution or by indirect reaction in an electrochemical cell. 

Electrochemical cells can also be used to determine other thermodynamic parameters such as equilibrium constants. For example, the solubility product for the sparingly soluble salt AgCl may be determined by comparing the properties of the silver silver chloride electrode (9.2.23) with those of the silver silver ion electrode (9.2.39). The potentials of these electrodes are equal when they are in a saturated solution of AgCl, that is, when the activities of these ions are those given by equilibrium (9.2.40). Therefore, under these conditions... 

The electrochemical cell provides a very powerful way of determining equilibrium constants and the changes in thermodynamic properties accompanying reactions in solution, f... 

---