Equilibrium constant electrochemical

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

Compare the ease of measuring the equilibrium constant electrochemically with that by chemical means [see Equation (18.10)]. 

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. 

The effect of increasing temperature is twofold an increase in the rate of reaction gives faster response time and a shift in the equilibrium value due to variations in the equilibrium constant. Electrochemical sensors of the gas-permeable membrane type (ammonia and carbon dioxide) lead to an additional effect, since the gas membrane and the features of the diffusion are sensitive to temperature variations. Despite the above considerations, a classical bell-shaped curve is almost always obtained when recording the response of the probe as function of temperature. Room temperature, or 25°C (controlled to + 0.2°C is recommended), is often employed when using an electrochemical probe, although when using a gas permeable membrane control to +0.1°C is required. 

According to Fig. 7-41 a Galvani potential difference results between the sample and the probe, which in the equilibrium (constant electrochemical potentials) is given by... 

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... 

The standard-state electrochemical potential, E°, provides an alternative way of expressing the equilibrium constant for a redox reaction. Since a reaction at equilibrium has a AG of zero, the electrochemical potential, E, also must be zero. Substituting into equation 6.24 and rearranging shows that... 

In a redox reaction, one of the reactants is oxidized while another reactant is reduced. Equilibrium constants are rarely used when characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products. 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

For the non-electrochemical reaction 1.119, the equilibrium constant (K) for the reaction is written as... 

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. 

One of the most useful applications of standard potentials is in the calculation of equilibrium constants from electrochemical data. The techniques that we develop here can be applied to any kind of reaction, including neutralization and precipitation reactions as well as redox reactions, provided that they can be expressed as the difference of two reduction half-reactions. 

HOWTO CALCULATE EQUILIBRIUM CONSTANTS FROM ELECTROCHEMICAL DATA... 

The procedure for calculating an equilibrium constant from electrochemical data is as follows. 

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. 

Comproportionation equilibrium constants for Equation 9.3 between dications and neutral molecules of carotenoids were determined from the SEEPR measurements. It was confirmed that the oxidation of the carotenoids produced n-radical cations (Equations 9.1 and 9.3), dications (Equation 9.2), cations (Equation 9.4), and neutral ir-radicals (Equations 9.5 and 9.6) upon reduction of the cations. It was found that carotenoids with strong electron acceptor substituents like canthaxanthin exhibit large values of Kcom, on the order of 103, while carotenoids with electron donor substituents like (J-carotene exhibit Kcom, on the order of 1. Thus, upon oxidation 96% radical cations are formed for canthaxanthin, while 99.7% dications are formed for P-carotene. This is the reason that strong EPR signals in solution are observed during the electrochemical oxidation of canthaxanthin. 

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...

We start with the case where the initial electron transfer reaction is fast enough not to interfere kinetically in the electrochemical response.1 Under these conditions, the follow-up reaction is the only possible rate-limiting factor other than diffusion. The electrochemical response is a function of two parameters, the first-order (or pseudo-first-order) equilibrium constant, K, and a dimensionless kinetic parameter, 2, that measures the competition between chemical reaction and diffusion. In cyclic voltammetry,... 

This kind of electrochemical measurement enables the oxygenation equilibrium constant K to be calculated by taking advantage of the fact that ... 

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. 

A ring-opening/ring-closure pathway has also been proposed to explain the conversion of 4-phenylfuroxan to the 3-phenyl tautomer under electrochemical oxidation conditions <86IZV1691>. The factors influencing both the equilibrium constants and the equilibration rates have been dis-... 

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