Electrical work reversible

The potential /(r) at a place r is defined as the reversible electrical work, at constant p and T, to transport a unit charge from infinity to r,... 

For the galvanic cell, the Gibbs free energy change caused by supplying n Faradays of electrons is related to the reversible electrical work by the following Nemst equation. 

A chemical reaction can give out (or take in) energy in three forms heat, pressure-volume work, and electrical work. We now specify that the free-energy change excludes the work (P AV) done by or against a constant external pressure. This means that at constant pressure, the free-energy change is equal to minus the reversible electrical work, which is calculated from the reversible electromotive force. 

It suffices to carry out one such experiment, such as the expansion or compression of a gas, to establish that there are states inaccessible by adiabatic reversible paths, indeed even by any adiabatic irreversible path. For example, if one takes one mole of N2 gas in a volume of 24 litres at a pressure of 1.00 atm (i.e. at 25 °C), there is no combination of adiabatic reversible paths that can bring the system to a final state with the same volume and a different temperature. A higher temperature (on the ideal-gas scale Oj ) can be reached by an adiabatic irreversible path, e.g. by doing electrical work on the system, but a state with the same volume and a lower temperature Oj is inaccessible by any adiabatic path. 

Energetic reversibility is achieved when the same amount of electrical work is supplied from the cell reaction proceeding in one direction as is gained from the reaction proceeding to the same degree in the opposite direction. 

In writing the Etudes de dynamique chimique (1884), van t Hoff drew on Helmholtz s 1882 paper but especially on the work of August Horstmann, a student of Bunsen, Clausius, and H. Landolt.59 As has often been discussed, van t Hoffs was an ambitious and original synthesis of disconnected ideas and theories about opposing forces, equilibrium, active masses, work and affinity, electromotive force, and osmotic pressure. He demonstrated that the heat of reaction is not a direct measure of affinity but that the so-called work of affinity may be calculated from vapor pressures (the affinity of a salt for its water of crystallization), osmotic pressure (affinity of a solute for a solution), or electrical work in a reversible galvanic cell (which he showed to be proportional to the electromotive force). 

An electrical potential difference between the electrodes of an electrochemical cell (called the cell potential) causes a flow of electrons in the circuit that connects those electrodes and therefore produces electrical work. If the cell operates under reversible conditions and at constant composition, the work produced reaches a maximum value and, at constant temperature and pressure, can be identified with the Gibbs energy change of the net chemical process that occurs at the electrodes [180,316]. This is only achieved when the cell potential is balanced by the potential of an external source, so that the net current is zero. The value of this potential is known as the zero-current cell potential or the electromotive force (emf) of the cell, and it is represented by E. The relationship between E and the reaction Gibbs energy is given by... 

The reaction also can be carried out reversibly if additional constraints are placed on the system, as in the cell illustrated by Figure 7.2. The H2 and CI2 electrodes are connected to a potentiometer. If the electromotive force of the cell is opposed by the eleetromotive force of the potentiometer, which is maintained at an infinitesimally lower value than that of the H2-CI2 cell, then the conversion to HCl can be carried out reversibly, although it would take an infinitely long time to obtain one mole of reaction. The change in the Gibbs function is the same for either the reversible or the explosively spontaneous path for carrying out the transformation, because the initial and final states are the same in both cases. However, the amount of useful (electrical) work is different, and, for the reversible path... 

When electrical work is obtained from the reaction under reversible conditions, that is, against a counterpotential only infinitesimally smaller than that of the cell, then... 

The electrical work and osmotic work both performed in a perfectly reversible manner are equal, thus... 

The free energy functions are defined by explicit equations in which the variables are functions of the state of the system. The change of a state function depends only on the initial and final states. It follows that the change of the Gibbs free energy (AG) at fixed temperature and pressure gives the limiting value of the electrical work that could be obtained from chemical transformations. AG is the same for either the reversible or the explosively spontaneous path (e.g. H2 -I- CI2 reaction) however, the amount of (electrical) work is different. Under reversible conditions... 

The fiee-energy change, AG, for a chemical reaction conducted reversibly at constant temperature and pressure equals the maximum possible electrical work that can be done by the reaction on its surroundings ... 

In order to derive the relation between EMF and the chemical potential difference probed at different surfaces of the stressed solid, we formulate the reversible work and its electrical equivalent. If zAF-dnA electric charges are transported across the electrolyte between the two surfaces labeled 1 and 2 in Figure 8-8, the electrical work is... 

The value of AG° expresses the maximum useful work that a system can do on the surroundings. Useful work is that which can be extracted from the cell by electrical means to operate a lamp or some other external device. This excludes any P-Vwork that is simply a consequence of volume change (which could of course conceivably be put to some use ) and which would be performed in any case, even if the reactants were combined directly. This quantity of work - AG° can only be extracted from the system under the limiting conditions of a reversible change, which for an electrochemical cell implies zero current. The more rapidly the cell operates, the less electrical work it can supply. 

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... 

Both of these processes are carried out in electrochemical cells which are forced to operate in the reverse , or non-spontaneous direction, as indicated by the negative for the above cell reaction. The free energy is supplied in the form of electrical work done on the system by the outside world (the surroundings). This is the only fundamental difference between an electrolytic cell and the galvanic cell in which the free energy supplied by the cell reaction is extracted as work done on the surroundings. 

As already mentioned, the EMF of a reversibly operating cell may be ealcu lated from the thermodynamic properties of the system, i. e. from the equivalency between the maximum electric work which can be obtained when the cell is operating at constant temperature and pressure, and the change in free energy accompanying the corresponding chemical reaction. 

The galvanic cell operating at constant temperature either absorbs heat from the surroundings, or evolves it this absorbed or evolved heat is called latent heat. It follows from the thermodynamics laws that the sum total of free energy change AC , converted in a reversible cell quantitatively into the electrical work and of latent heat Qtev ) equals the enthalpy change AH ... 

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