Equilibrium constant Galvanic cells

We saw in Section 9.3 that the standard reaction Gibbs free energy, AGr°, is related to the equilibrium constant of the reaction by AGr° = —RT In K. In this chapter, we have seen that the standard reaction Gibbs free energy is related to the standard emf of a galvanic cell by AGr° = —nFE°, with n a pure number. When we combine the two equations, we get... 

Direct measurements of solute activity are based on studies of the equilibria in which a given substance is involved. The parameters of these equilibria (the distribution coefficients, equilibrium constants, and EMF of galvanic cells) are determined at different concentrations. Then these data are extrapolated to very low concentrations, where the activity coincides with concentration and the activity coefficient becomes unity. 

Another proposed procedure of finding the ionic data is the application of a special salt bridge, which provides practically constant or negligible liquid junction potentials. The water-nitrobenzene system, containing tetraethylammonium picrate (TEAPi) in the partition equilibrium state, has been proposed as a convenient liquid junction bridge for the liquid voltaic and galvanic cells. 

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. 

Although the law of mass action is equally valid for oxidation-reduction processes, and therefore conclusions as to the direction of reactions may be drawn from the knowledge of equilibrium constants, traditionally a different approach is used for such processes. This has both historical and practical reasons. As pointed out in the previous sections, in oxidation-reduction processes electrons are transferred from one species to another. This transfer may occur directly, i.e. one ion collides with another and during this the electron is passed on from one ion to the other. It is possible, however, to pass these electrons through electrodes and leads from one ion to the other. A suitable device in which this can be achieved is a galvanic cell, one of which is shown in Fig. 1.14. A galvanic cell consists of two half-cells, each made up of an electrode and an electrolyte. The two electrolytes are connected with a salt bridge and, if... 

Corresponding to the general equation E(, i/,A, - 0 which may involve pure components, gases, and ionic species, one obtains an equilibrium constant Kq - (S)(ag)l/s (j)(aj)eq- When galvanic cell operations can be carried out that exactly reproduce the particular chemical reaction of interest one has... 

Electroanalytical chemistry has been defined as the application of electrochemistry to analytical chemistry. For the determination of the composition of samples, the three most fundamental measurements in electroanalytical chemistry are those for potential, current, and time. In this chapter several aspects relating to electrode potentials are considered current and time as well as further consideration of potentials are treated in Chapter 14. The electrode potentials involved in the classical galvanic cell are of considerable theoretical and practical significance for the understanding of many aspects not only of electroanalytical chemistry but also of thermodynamics and chemical equilibria, including the measurement of equilibrium constants. 

The only assumption made in the derivation of equation (2) (p. 347), apart from the two laws of thermodynamics, was the validity of the simple laws of solution. The equation is therefore also applicable to reactions which proceed practically to completion, so that the equilibrium cannot be investigated directly. This is the case in the great majority of galvanic cells, especially those which are used in practice, as it is only under these conditions that the equilibrium constant and therefore the e.m.f. can assume considerable values. It is, of course, impossible to predict the value of the e.m.f. in such cases (as K is unknown),... 

We can measure the equilibrium constant for this reaction easily from the voltage of a galvanic cell, and then calculate from it the equilibrium concentrations that will result from arbitrary initial conditions. It is considerably harder to determine the exact pathway by which the reaction goes from reactants to products. This path certainly does not involve the simultaneous collision of five Fe ions and one Mn04 ion with eight ions, because such a collision would be ex-... 

We wish to determine the equilibrium constant K for the overall cell reaction. At equilibrium the reaction fraction for the cell reaction Y is equal to the equilibrium constant for the cell reaction which is why we may be able to use the Nemst equation to determine the value for K. When there is equilibrium in a galvanic cell no transfer of electrons takes place between the two half cell which is why s°ceUe = 0. 

Further we looked at galvanic cells where it was possible to extract electrical energy from chemical reactions. We looked into cell potentials and standard reduction potentials which are both central and necessary for the electrochemical calculations. We also looked at concentration dependence of cell potentials and introduced the Nemst-equation stating the combination of the reaction fraction and cell potentials. The use of the Nemst equation was presented through examples where er also saw how the equation may be used to determine equilibrium constants. 

We mentioned in Sect. 23.2 that galvanic cells can make the energy released by a chemical reaction usable, but they can also be utilized as a measuring instrument for the differences of redox potentials and therefore the electron potentials of various redox pairs. Moreover, because the electron potential itself is determined by the chemical potentials of the substances making up the redox pair, it is also possible to find the fi values as well as the drive A of the underlying total reaction with the help of galvanic cells. Reversible cell voltages measured with zero current can be used to determine these quantities and derived ones such as equilibrium constants. 

Table 2. Measured voltages and equilibrium constants for some galvanic cells using standard electrodes at 25 °C (all ions and soluble species at 1 M and all gases at 1 atm).

If you can build a galvanic cell with the tin as one half-cell and the N2O as the other half-cell, the measurement of the standard cell potential would provide the best means to determine the equilibrium constant. You could also calculate this standard cell potential if the necessary reduction potentials for the relevant half-reactions are available. 

During the operation of a galvanic cell, electrons flow from the anode to the cathode, resulting in product formation and a decrease in reactant concentration. Thus, Q increases, which means that E decreases. Eventually, the cell reaches equilibrium. At equilibrium, there is no net transfer of electrons, so E = 0 and Q = K, where K is the equilibrium constant. 

The decrease in free energy of the system in a spontaneous redox reaction is equal to the electrical work done by the system on the surroundings, or AG = nFE. The equilibrium constant for a redox reaction can be found from the standard electromotive force of a cell. 10. The Nernst equation gives the relationship between the cell emf and the concentrations of the reactants and products under non-standard-state conditions. Batteries, which consist of one or more galvanic cells, are used widely as self-contained power sources. Some of the better-known batteries are the dry cell, such as the Leclanche cell, the mercury battery, and the lead storage battery used in automobiles. Fuel cells produce electrical energy from a continuous supply of reactants. 

A galvanic cell is constructed as follows. One halfcell consists of a platinum wire immersed in a solution containing 1.0 Af Sn and 1.0 Af Sn the other half-cell has a thallium rod immersed in a solution of 1.0 Af TU. (a) Write the half-cell reactions and the overall reaction, (b) What is the equilibrium constant at 25°C (c) What is the cell voltage if the Tl concentration is increased tenfold (fiTi+zTi = —0.34 V.)... 

Thus, if we can determine the standard emf, we can calculate the equilibrium constant. We can determine the fE u of a hypothetical galvanic cell made up of two couples (Sn ISn and Cu ICu ) from the standard reduction potentials in Table 13.1. 

---