Cell potential work done

Recall that free energy is related to the maximum possible amount of work that can he done hy the system. In the case of a galvanic cell, the work done is electrical work, so we can state the relationship between fi-ee energy and the cell potential as... 

Knowledge of the Volta potential of a metal/solution interface is relevant to the interpretation of the absolute electrode potential. According to the modem view, the relative electrode potential (i.e., the emf of a galvanic cell) measures the value of the energy of the electrons at the Fermi level of the given metal electrode relative to the metal of the reference electrode. On the other hand, considered separately, the absolute value of the electrode potential measures the work done in transferring an electron from a metal surrounded by a macroscopic layer of solution to a point in a vacuum outside the solotion. ... 

The first equation simply states the balance in chemical potentials inside and outside of the cell. The expression for the chemical potential inside the protocell separates into a term involving the mole fraction and the chemical potential associated with the pressure difference. The work done by the cell in opposing the pressure change, assuming that the cell remains at constant volume, is given below, where the change in pressure is from p to p + tv. 

Consider a cell with some host as one electrode and Li metal as the other. Denote the chemical potential of Li in the host and in Li metal as p and Po, respectively. If the guest has charge ze in the solution of the cell (z = 1 for Li), one ion is intercalated for every z electrons passed through the external circuit. Since the electrons move through the potential difference E, the work done on the cell per ion intercalated is —zeE. This work must equal the change in free energy of the two electrodes, which is p — po), so... 

Work done with electrochemical cells, with particular reference to the temperature dependence of their potentials, has demonstrated that an accurate value for S (H h, aq) is — 20.9 J K mol-1. Table 2.15 gives the absolute molar entropies for the ions under consideration. The values of the absolute standard molar entropies of the ions in Table 2.15 are derived by using the data from Tables 2.13 and 2.14 in equations (2.51) and (2.57). 

The potential difference between two electrodes is defined as the amount of work done in transporting a charge from one electrode to the other. There is an analogy between the work function in vacuum and the electrochemical potential in the electrochemical cell the work function is the minimum energy required to remove an electron from a solid, i.e., to take out an electron from the Fermi level in solid materials. The work function is often measured experimentally by photoemission spectroscopy. 

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)... 

An electrochemical cell generates a potential difference E. (The symbol E, commonly used in electrochemistry, refers to electromotive force, an archaic term for potential difference.) The electrical work done when n moles of electrons is passed by the cell can be found using Eq. (15-1), w = -nFE. It can be shown that the electrical work done by an electrochemical cell, at constant temperature and pressure, is equal to the change in Gibbs free energy of the cell components,... 

Electrical energy is considered to allow us to discuss batteries and electrochemical cells, as well as motors and resistance heating. If a charge Q is transferred to a system at an electrostatic potential (voltage) < ) with respect to the surroundings, the work done is Q ... 

Electrical work is done when an electric charge q moves through a potential difference AV. The right side of. Eq. 10 refers to the movement of n moles of charge across the cell potential E°, and thus has the dimensions of work. 

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. 

Apart from the ease of precise control in an electrochemical path to synthesis, there is the unique feature of being able to force the electrode reaction to take place against its own AG. This is because the principal rule of chemical equilibria is AG = 0, but in electrochemical equilibria, the equilibrium condition is AG = -nFEKV Thus, if the cell potential is exactly rev, the chemical reaction in the cell is at equilibrium and nothing happens. However (in contrast to what can be done chemically), moving the potential of the working electrode in a more negative direction than its reversible potential stimulates the reaction to take off in a cathodic direction at a fixed rate i.e., it acts to reduce the reactant ... 

What of Lee and Tai s assumption that a charge-free surface involves no potential contribution to the cell In facL work done much later suggests that the missing temperature coefficient is only 0.01, so that the error Lee and Tai introduced by their outmoded assumption is indeed negligible. 

Although we can never actually realize the maximum work from a cell reaction, its value is still useful for evaluating the efficiency of a real process based on the cell reaction. For example, suppose a certain galvanic cell has a maximum potential of 2.50 V. In a particular experiment 1.33 moles of electrons passes through this cell at an average actual potential of 2.10 V. The actual work done is... 

The potential difference A% is positive for a galvanic cell, so meiec is negative in this case and net electrical work is performed by the galvanic cell. In an electrolytic cell, in contrast, A% is negative and rngiec is positive, corresponding to net electrical work done on the system by an external source such as an electric generator. 

The reversible work done per mol of electrons is the change in the Gibbs free energy, AG = tt eiec wS A. The standard cell potential is related to the standard free energy change by AG° = tt eiec = wS A °. 

Equation (4.23) is known as the first law of thermodynamics for a closed system.] Keep in mind that a system may do work, or have work done on it, without some obvious mechanical device such as a pump, shaft, and so on, being present. Often the nature of the work is implied rather than explicity stated. For example, a cylinder filled with gas enclosed by a movable piston implies that the surrounding atmosphere can do work on the piston or the reverse a batch fuel cell does no mechanical work, unless it produces bubbles, but does deliver a current at a potential difference electromagnetic radiation can impinge on or leave a system and so forth. 

The work done and reaction free energy are given by the product of the total charge, - F, and the cell potential, AGr = = -nFE. 

The maximum electrical work done by such a cell is equal to the product of the charge flowing and the potential difference across which it flows. The work done on the cell is... 

Potential difference, electrical work done and AG for the cell reaction... 

The electrostatic potential difference is the electrical work done by the cell per unit charge conveyed between two points, here the terminals of the cell. In physical terms the potential... 

The Daniell cell is an example of a galvanic cell, in this type of electrochemical cell, electrical work is done by the system. The potential difference, between the two half-cells can be measured (in volts, V) on a voltmeter in the circuit (Figure 7.1) and the value of is related to the change in Gibbs energy for the cell reaction. Equation 7.9 gives this relationship under standard conditions, where is°ceu is the standard cell potential. 

This maximum work is obtained if the process is sufficiently slow that there are no irreversibilities, for example, no resistive heating as a result of the current flow. This implies that the rate of reaction is very slow, and that the electrical potential produced is just balanced by an external potential so that the current flow is infinitesimal. This electrical potential produced by the cell (or of the balancing external potential) will.be referred-to as-the zero-current cell potential and designated by E. The work done by... 

How are the units of cell potential related to those of energy available to do work As you ve seen, work is done when charge moves between electrode compartments that differ in electrical potential. The SI unit of electrical potential is the volt (V), and the SI unit of electrical charge is the coulomb (C). By definition, for two electrodes that differ by 1 volt of electrical potential, 1 joule of energy is released (that is, 1 joule of work can be done) for each coulomb of charge that moves between the electrodes. Thus,... 

This electrical work is by definition (Chapter 5) the AG associated with the process, as long as the electrical work is the only non-PAV work done. Therefore for any half-cell or complete cell or indeed any electrostatic process in which nT coulombs are moved through a potential difference ,... 

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