Thermodynamics of galvanic cells

Discharge of the Daniell cell causes zinc metal to ionize at one electrode and copper ions to deposit at the other. The net result of charge flow round the circuit is therefore equivalent to the reaction 

A cell is said to act reversibly if the net cell reaction is reversed when the current through the cell is made to flow in the opposite direction. When no current is being drawn, such a cell is in a true equilibrium state. Note that the absence of net current flow does not necessarily signify that a cell is in equilibrium. If an iron wire is placed in a solution of low pH, the most likely electron transfer reactions at the metal/solution interface are 

At a particular potential, no net current at the interface will be observed. However, a cell containing such an electrode would obviously fail to fulfil the reversibility condition. 

Under these circumstances, current flows and the work done (in joules) by the cell as one mole of reactants are converted to products would be equal to the product of the charge driven through the applied voltage (say nF coulombs) and the value of this potential difference ( -5 volts) 

By definition, n/max = -AG, where AG is the free energy change associated with one mole of reaction and hence 

The free energy change for a process represents the maximum amount of non-PV7 work that can be extracted from it. In the case of an electrochemical cell, this work is due to the flow of electrons through the potential difference between the two electrodes. Note, however, that as the rate of electron flow (i.e., the current) increases, the potential difference must decrease if we short-circuit the cell by connecting the two electrodes with a conductor having negligible resistance, the potential difference is zero and no work will be done. The full amount of work can be realized only if the cell operates at an infinitessimal rate- that is, reversibly. 

The total amount of energy a reaction can supply under standard conditions at constant pressure and temperature is given by AH0. If the reaction takes place by combining the reactants directly (no cell) or in a short-circuited cell, no work is done and the heat released is AH. If the reaction takes place in a cell that performs electrical work, then the heat released is diminished by the amount of electrical work done. In the limit of reversible operation, the heat released becomes 

---

Gottingen (where he was offered a professorship in 1901). He became full professor at Harvard in 1901, being appointed in 1912 to the Erving professorship on the retirement of Prof. Jackson. Besides atomic weights, Richards worked on the compressibility of solid elements (which led him to the idea of compressible atoms ) and on the thermodynamics of galvanic cells (see p. 620). All his work is characterised by great accuracy and originality. ... 

The thermodynamics of galvanic cells will be treated in detail in Chap. 14. 

The EMF values of galvanic cells and the electrode potentials are usually determined isothermally, when all parts of the cell, particularly the two electrode-electrolyte interfaces, are at the same temperature. The EMF values will change when this temperature is varied. According to the well-known thermodynamic Gibbs-Helmholtz equation, which for electrochemical systems can be written as... 

Measurements of the potentials of galvanic cells at open circuit give information about the thermodynamics of cells and cell reactions. For example, the potential of the cell in Figure 1, when the solution concentrations are 1 molar (1 M) at 25°C, is 1.10 V. This is called the standard potential of the cell and is represented by E°. The available energy (the Gibb s free energy AG°) of the cell reaction given in equation (3) is related to E° by... 

This equation in not only of considerable value in electrochemistry proper, when calculating the reversible potential of galvanic cells, but is also of great service in thermodynamics for ascertaining various thermodynamic constants. 

In describing the operation of galvanic cells we introduce a specific example rather than invoking the cumbersome machinery needed for a generalized approach. The example chosen for this purpose will then be generalized, and a thermodynamic analysis of the resulting processes will be furnished. 

Measurements of the emf of galvanic cells can be used to advantage to extract thermodynamic information concerning the characteristics of chemical reactions. As already stated, corresponding to the symbolic chemical reaction one may specify an equilibrium parameter Kx = Oy If cell can... 

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),... 

Further, and more concrete, examples of the use of the thermodynamic functions are contained in the discussion of galvanic cells immediately following. 

From the figures given in Table IV the increase of entropy during the reaction is 8.5 units. As a test of the third law of thermodynamics this value may be compared with a determination of the entropy change of this reaction made by Gerke,21 from the potentials of galvanic cells, in a research already referred to. He measured the potential, E, and the change of the potential with temperature, AE/AT, of cells of the type... 

We now turn our attention to a study of the thermodynamic theory of galvanic cells. Galvanic cells are heterogeneous systems in which current is transmitted between the phases and in which chemical reactions may occur. The terminal phases of a galvanic cell are termed electrodes, and current passes from one electrode through the other phases to the other electrode. 

Equation (13-33) is the fundamental equation for the thermodynamic study of galvanic cells. The chemical potential of component i in phase a is related to the corresponding activity by the equation... 

Equation (13-78) is the fundamental equation for the study of the thermodynamic properties of galvanic cells with liquid junctions. 

Similar phenomena such as diffusion potential and thermal diffusion potential in systems where ion transport is involved are also of considerable interest. Coupling of flow of ions relative to solvent is involved in the development of diffusion potential, while in the case of thermal diffusion potential, coupling of flow of ions and energy flow is involved. In such situations, the effective transference number as compared to Hittorf transference number is affected. Interesting experimental results have been reported in the context of galvanic cells (thermo-cells), in which the two electrodes are not at the same temperature where results have been interpreted in terms of thermodynamics of irreversible processes [3]. 

This chapter explains the fundamental principles and applications of galvanic cells, the thermodynamics of electrochemical reactions, and the cause and prevention of corrosion by electrochemical means. Some simple electrolytic processes and the quantitative aspects of electrolysis are also discussed. 

---