Standard potentials, absolute

A problem that has fascinated surface chemists is whether, through suitable measurements, one can determine absolute half-cell potentials. If some one standard half-cell potential can be determined on an absolute basis, then all others are known through the table of standard potentials. Thus, if we know E for... 

To do this, one particular half-reaction has to be selected as a reference reaction with zero potential. Once a reference half-reaction has been selected, all other half-reactions can then be assigned values relative to this reference value of 0 V. This is necessary because an experiment always measures the difference between two potentials rather than an absolute potential. The standard potential of 1.10 V for the Zn/Cu cell, for example, is the difference between the E ° values of its two half-reactions. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

Here, R is the gas constant, 7k is absolute temperature, and XB is the mole fraction of B in the solution phase. Using this equation, we can calculate the equilibrium point of reactions in ideal systems directly from tabulated values of standard potentials p°. 

Once a DISP mechanism has been recognized, the procedures for determining the rate constant of the follow-up reaction and the standard potential of the A/B couple from peak current and/or peak potential measurements are along the same lines as the procedures described above for the ECE mechanism. A distinction between the ECE and DISP mechanisms cannot be made when the pure kinetic conditions are achieved since the peak height, peak width, and variations of the peak potential with the scan rate and rate constant are the same, and so is its independence vis-a-vis the concentration of substrate. The only difference is then the absolute location of the peak, which cannot be checked, however, unless the standard potential of the A/B couple and the follow-up rate constant are known a priori. 

It is noteworthy that the rate constants and the standard potential of the C/D couple may be derived from the experimental data playing with the concentrations of A and Z. As before, both rate constants can be derived from the absolute value of the plateau current and from its variations with the concentration ratio, Cy/C (Figure 2.24b). Once the ratio k /ki is... 

Fig. 4-12. Electron energy levels in electron transfer from a standard gaseous electron throu an electrol3rte solution into an electrode a,(M/sn)) = real potential of electron in electrode E = electrode potential (absolute electrode potential).

Here cq and cr are the concentrations of the reactant and product, respectively, D is a common diffusion coefficient, Cq is the bulk concentration of the reactant, / is the current, n is the number of electrons, F is the Faraday constant, A is the electrode surface area, E is electrode potential, if is the standard potential, R is the gas constant, T is absolute temperature, x is the distance from the electrode surface and t is the time variable [45]. 

An electron transfer reaction, Equation 6.6, is characterised thermodynamically by the standard potential, °, i.e. the value of the potential at which the activities of the oxidised form (O) and the reduced form (R) of the redox couple are equal. Thus, the second term in the Nernst equation, Equation 6.7, vanishes. Here and throughout this chapter n is the number of electrons (for organic compounds, typically, n = 1), II is the gas constant, T is the absolute temperature and F is the Faraday constant. Parentheses, ( ), are used for activities and brackets, [ ], for concentrations /Q and /R are the activity coefficients of O and R, respectively. However, what may be measured directly is the formal potential E° defined in Equation 6.8, and it follows that the relationship between E° and E° is given by Equation 6.9. Usually, it maybe assumed that the activity coefficients are unity in dilute solution and, therefore, that E° = E°. 

The absolute potential for a half-reaction cannot be determined, but the potential for a half-reaction relative to another half-reaction can be determined the tabulated standard potentials for half-reactions are relative to the H2/H30+ half-reaction, which is arbitrarily assigned a standard potential of zero. 

Table 5.1. Standard chemical potentials pi , standard molar enthalpy h , and standard molar absolute entropy values s of substances in the standard state of 298 K and...

As stated in the previous chapter, to determine the reversible potential of any electrode in an arbitrary state, it is first of all necessary to know its standard potential. The required values of these potentials, stated in terms of the hydrogen scale and valid for a temperature of 25 °C, arc tabulated. Such data do not express the absolute potentials but the electromotive force of the combination of the given half coll and the standard hydrogen electrode. This fact must be remembered, when making calculations based on these potentials. 

Standard potential of an electrode reaction, abbreviated as standard electrode potential, is the value of the standard emf of a cell in which molecular hydrogen is oxidized to solvated protons at the left-hand electrode. For example, the standard potential of the Zn2+/Zn electrode, denoted (Zn2+/Zn), is the emf of the cell in which the reaction Zn2+(aq) + H2 ->2H+(aq) + Zn takes place under standard conditions (see p.61). The concept of an absolute electrode potential is discussed in reference [31]. 

Lf transference number in the electrolyte absolute temperature, K open circuit potential of electrode i (i = p, n), V standard potential of the solvent rednction reaction, V spatial coordinate, m... 

Since kxjk is a constant at definite temperature, this equation is obviously of the same form as the electrode potential equations derived by thermodynamic methods, e.g., equation (85) for an electrode reversible with respect to positive ions. The first term on the right-hand side of equation (30) is clearly the absolute single standard potential of the electrode it is equal to the standard free energy of the conversion of solid metal to solvated ions in solution divided by and its physical significance has been already discussed. 

E = potential under the nonstandard conditions = standard potential R = gas constant, 8.314J/mol-K T = absolute temperature in K... 

Here jj. is a standard potential, f. is an activity coefficient referring to the pure phase, R is the gas constant and T is the absolute temperature. The last term in Equation (9) determines whether the diffusion coefficient is positive, negative or zero according to these three piossibilities ... 

Although the thermodynamic analysis has given results with clear contributions from each of the electrodes, the observed EMF cannot be separated into these contributions by experiment. As was seen in the previous section, the solution to this problem has been to choose the SHE as a reference and to quote the standard potentials of all other half-reactions with respect to this point on the redox potential scale. In order to illustrate the application of this concept using absolute electrode potentials, the following cell is considered ... 

The above analysis is easily extended to other half-cell reactions. Much of the data required to do the necessary calculations has been collected for cells involving aqueous solutions [1] and can also be found in thermodynamic tables published by the National Bureau of Standards in Washington [G3]. In practice, standard potentials are always used on the conventional scale because no extra-thermodynamic assumptions are involved in their calculation. Any of these quantities can be converted to the absolute scale by adding the estimate of the absolute potential of the SHE, that is, 4.43 V, to the conventional value of the standard potential. 

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