Chemically equilibrium cell voltage

As a result of the combination of Eqs. (20) and (21), the reaction free energy, AG, and the equilibrium cell voltage, A< 00, under standard conditions are related to the sum of the chemical potentials //,. of the substances involved ... 

The standard equilibrium cell voltage resulting from a combination of any two electrodes is the difference between the two standard potentials, E°(2) - E°( 1). For instance, the standard cell equilibrium voltage of the combination F2/F with the Li+/Li electrode would be 5,911 V. Correspondingly, the standard free energy change of the underlying chemical reaction, 1/2 F2 + Li —> F + Li+, is AG° = -570 KJ (g-equivalent)-1. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Thus measuring the cell voltage at equilibrium vs charge passed between the electrodes is equivalent to measuring the chemical potential as a function of x, the Li content of a compound like Li Mo Seg. Thermodynamics requires that p increase with concentration of guest ions, and so E decreases as ions are added to the positive electrode. 

Considering Equation (4), it is clear that one has to operate a galvanic cell at the maximum possible cell voltage in order to maximize the electric energy yield. As shown previously (Figure 3.1.6), the maximum value of U is the equilibrium electrode potential difference E or E°. Thus, one may formulate the fundamental relationship between chemical and electric energy ... 

The equilibrium situation in an electrochemical cell is obtained, if the electrical current is interrupted, if all local actions (e.g. transport in the electrode) have come to an end and no internal short circuits occur. Then, as mentioned (Figure 3.5.10), the cell voltage is determined by the difference in the lithium potential (chemical potential of lithium) between the left-hand side (Ihs) and right-hand side (rhs) of the electrochemical cell (E - open cell voltage, F - Faraday constant) ... 

Therefore such sensors are called Nernstian sensors. As a reference air with defined humidity is used. In reducing gases that are in chemical equilibrium (e.g., H2, H2Oj CO, C02 water gas) the oxygen partial pressure is determined by the mass law constant Kv and this in turn depends on the temperature. In the case of H2,H20-mixtures the cell voltage is obtained by insertion of a temperature function of log Kp into the Nernst equation... 

The theoretical efficiency in such systems is close to unity, but in practice, the practical efficiency is significantly lower. This is attributable to the different mechanical and thermal losses in the system but also to the direct chemical reactions between the reactants and secondary electrochemical reactions in the cell. The voltage efficiency of the cell, q, is defined as the quotient between the cell voltage, V. at a given cell current, I, and the cell voltage at open circuit, (the maximum value of the cell voltage, equivalent, if the cell is in equilibrium, to the reversible cell potential, Ej) ... 

E is the cell voltage measured and corresponds to flAg = 1. that is, equilibrium Ag/Ag2S [31]. The conclusion is that the strong change of the chemical potential of /iAg is caused by its electronic part ... 

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. 

This may be easily visualized by an electrochemical cell. The electrochemical reactions at both electrodes lead to a potential difference between them, i.e., the voltage U of the electrochemical cell, which will cause a current flow I in the external circuit As a consequence, an electrical work = Ult will be exchanged for a given time t with a related amount of the chemical process. This work has its maximum value if the electrochemical processes at the electrodes occur very slowly with 7 0 requiring a long time f —> >. In this case, the electrode processes stay at equilibrium and the cell voltage keeps its maximum value =AE ). 

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present -O-, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Equilibrium is reestablished by stepwise recombination at the defect levels D within the forbidden gap.

It means that when the chemical driving force (AG) is exactly balanced by the external opposing voltage (-E), the whole system (die cell) is at equilibrium, i.e., electrochemical equilibrium. 

Figure 4.10. Overview of nerve impulse transmission in chemical synapses. The action potential in the presynaptic nerve cell induces release of the nemotransmitter (e.g., acetylcholine) into the synaptic cleft. The transmitter binds to its receptor, e.g. the nicotinic acetylcholine receptor (NAR). The NAR is a hgand-gated channel it will open and become permeable to both and Na. This will move the membrane potential toward the average of the two respective equilibrium potentials however, in the process, the firing level of adjacent voltage-gated sodium charmels will be exceeded, and a full action potential will be triggered (inset).

Since it is impossible to measure the individual electric potential differences at the phase boundaries, we shall hereinafter speak only in terms of the difference in electric potential across the two terminals connected to the electrodes of the battery. When in a battery the current is not flowing or tends to zero, the measurable potential difference across the two terminals is called the open-circuit voltage (OCV), fJc, and it represents the battery s equilibrium potential (or voltage). Since it is related to the free energy of the cell reaction, the OCV is a measure of the tendency of the cell reaction to take place. Indeed, while the conversion of chemical into electric energy is regulated by thermodynamics, the behavior of a battery under current flow (the current is a measure of the electrochemical reaction rate) comes under electrochemical kinetics. 

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