Gibbs energy electrical work

If we were to place a piece of zinc metal into an aqueous copper(II) sulfate solution, we would see a layer of metallic copper begin to deposit on the surface of the zinc (see Fig. K.5). If we could watch the reaction at the atomic level, we would see that, as the reaction takes place, electrons are transferred from the Zn atoms to adjacent Cu2 r ions in the solution. These electrons reduce the Cu2+ ions to Cu atoms, which stick to the surface of the zinc or form a finely divided solid deposit in the beaker. The piece of zinc slowly disappears as its atoms give up electrons and form colorless Zn2+ ions that drift off into the solution. The Gibbs free energy of the system decreases as electrons are transferred and the reaction approaches equilibrium. However, although energy is released as heat, no electrical work is done. 

During ATP synthesis, protons move down these gradients from outside [Hour] into the mitochondrial matrix each proton doing both electrical and osmotic work (due to the concentration difference) so that the Gibbs energy change is... 

The theoretical efficiency of a fuel cell is given by the ratio between the Gibbs free energy (AG) which is the maximum electrical work that can be obtained, and the enthalpy (A//) of the fuel (Equation 6.3). 

This equation links the EMF of a galvanic cell to the Gibbs energy change of the overall current-producing reaction. It is one of the most important equations in the thermodynamics of electrochemical systems. It follows directly from the first law of thermodynamics, since nF% is the maximum value of useful (electrical) work of the system in which the reaction considered takes place. According to the basic laws of thermodynamics, this work is equal to -AG . 

First, electric work wx and w2 is calculated for a single ion species denoted as k. For wx the same procedure as for the quantity w2 in the Born treatment of solvation Gibbs energy (Eq. (1.2.5) will be used giving (e = De0))... 

As depicted in Fig. 5, both the protein molecule and the sorbent surface are electrically charged. In an aqueous environment, they are surrounded by counterions, which, together with the surface charge, form the so-called electrical double layer. The Gibbs energy of an electrical double layer, may be calculated as the isothermal, isobaric reversible work required to invoke the charge distribution in the double layer... 

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... 

One may also look at the effect of the electrodes from the point of view of energy balance. Measurement of voltages always requires at least a small electrical current. This corresponds in the case of galvanic cells to the transfer of electroactive species from one electrode to the other. The corresponding chemical work is the change of the Gibbs energy, AG, which... 

Note that the FMF (or A ) is determined by the nature of the reactants and electrolytes, not by the size of the system or amounts of material in it. The change in Gibbs free energy, AG, is the negative value of maximum electric work. 

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... 

To relate these expressions to Gibbs free energy changes, and thus to ion activities, we recall that AG is equivalent to electrical work under constant-T, P conditions. We therefore integrate dwemf [cf. (3.16), where we used the symbol E for electrical potential O] to obtain... 

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,... 

The electrical work done through this reaction is nFE, where F is the Faraday constant and E is the electrode potential. This electrical work equals the Gibbs free energy release ... 

Considering the first equality, Is measurable. It Is the Isothermal reversible work required to extract ions from phase a for electrons In a metal It represents the electronic work function. For metals, a, can also be obtained from thermo-emission or the photo-electric effect. Sometimes a is called the real (Gibbs) energy of hydration of ion i. The logic behind this last definition stems from the second equality In [3.9.61. The standard molar Gibbs energy of solvation of an Ion [1.5.3.11 equals when Is referred to the gas... 

Helmholtz and Gibbs energies are almost indistinguishable). Upon charging, or rather charge-separation, a potential difference is created. The electrical work of withdrawing protons against this potential is... 

The standard Gibbs free energy of the overall cell reaction AG g is related to the electrical work nFU°,... 

Therefore, the changes in Gibbs free energy is equal to the maximum electrical work (or energy) attainable at the given temperature and pressure. 

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. 

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