Chemical equilibria thermodynamics standard potentials

With the establishment of conventions for the Standard State and for the reference zero value of the chemical potential, it is possible to develop fully the thermodynamic description of chemical reactions. This development relies on the concept of thermodynamic activity, introduced in Section 1.2, and on the condition for chemical equilibrium in a reaction 1,15... 

Clearly, an enormous variety of equilibrium constants may be constructed, depending on what one chooses as a specification for composition variable, what value is selected for qj, and whether one elects to refer to a standard or to a reference chemical potential. This indicates that while the equilibrium constant is a useful quantity for characterizing chemical equilibrium, it is not a fundamental concept in the thermodynamic sense, since it cannot be uniquely specified. To prevent proliferation of so many different quantities, we shall henceforth restrict ourselves to equilibrium parameters such as (3.7.3a) or (3.7.5a) that are related to the chemical potentials of the various species in their standard state this is an almost universally accepted practice. 

The quantity of primary interest in our thermodynamic construction is the partial molar Gihhs free energy or chemical potential of the solute in solution. This chemical potential depends on the solution conditions the temperature, pressure, and solution composition. A standard thermodynamic analysis of equilibrium concludes that the chemical potential in a local region of a system is independent of spatial position. The ideal and excess contributions to the chemical potential determine the driving forces for chemical equilibrium, solute partitioning, and conformational equilibrium. This section introduces results that will be the object of the following portions of the chapter, and gives an initial discussion of those expected results. 

The third largest class of enzymes is the oxidoreductases, which transfer electrons. Oxidoreductase reactions are different from other reactions in that they can be divided into two or more half reactions. Usually there are only two half reactions, but the methane monooxygenase reaction can be divided into three "half reactions." Each chemical half reaction makes an independent contribution to the equilibrium constant E for a chemical redox reaction. For chemical reactions the standard reduction potentials ° can be determined for half reactions by using electrochemical cells, and these measurements have provided most of the information on standard chemical thermodynamic properties of ions. This research has been restricted to rather simple reactions for which electrode reactions are reversible on platinized platinum or other metal electrodes. 

Fully thermalised excited states may be treated as distinct chemical species with their own equilibrium thermodynamic properties, including redox potentials. We may therefore define standard redox potentials U°.. and f/%. for reactions of the excited states D and A ... 

F is the Faraday constant, K is the equilibrium constant of the reaction, R is the gas constant, and T is the thermodynamic temperature. However, E jj is not the standard potential of the electrode reaction (or sometimes called half-cell reaction), which is tabulated in the tables mentioned. It is the standard potential of the reaction in a chemical cell which is equal to the standard potential of an electrode reaction (abbreviated as standard electrode potential), E when the reaction involves the oxidation of molecular hydrogen to solvated protons... 

Standard potential values are usually those of ideal unimolal solutions at a pressure of 1 atm (ignoring the deviations of fugacity and activity from pressure and concentration, respectively). A pressure of 1 bar = 10 Pa was recommended as the standard value to be used in place of 1 atm = 101 325 Pa (the difference corresponds to a 0.34-mV shift of potential). If a component of the gas phase participates in the equilibrium, its partial pressure is taken as the standard value if not, the standard pressure should be that of the inert gas over the solution or melt. In a certain case, a standard potential can be established in a system with nonunity activities, if the combination of the latter substituted in the Nemst equation equals unity. For any sohd component of redox systems, the chemical potential does not change in the course of the reaction, and it remains in its standard state. In contrast to the common thermodynamic definition of the standard state, the temperature is ignored, because the potential of the standard hydrogen (protium) electrode is taken to be zero at any temperature in aqueous and protic media. The zero temperature coefficient of the SHE corresponds to the conventional assumption of... 

In these equations, p T) is the chemical standard potential of the component i, p is a standard pressure, tt is the spreading pressure of the adsoibed solution, and /i is an activity coefficient. The virtual pressure p ( ) (not the vapor pressure) depends on the spreading pressure and is the pressure of the component / which has the same spreading pressure either in the pure state or in the gaseous mixture. The equality q = g in the case of thermodynamic equilibrium leads to Raoult s law of adsorption... 

Thermodynamics makes it possible to take into account the deviation from the ideality of the biological media. In the case of media containing ions, these corrections should be taken into account starting from weak concentrations as mentioned previously, the addition of a salt can significantly alter the chemical equilibrium. In the case of media containing non-electrolytes, corrections of activity become significant when the concentration of a solute increases or when the number of solutes increases even if each one has a weak concentration. Figure 1.5 shows all of the relationships between physical-chemical parameters that can be calculated from the activity coefficient and the standard potential. 

In thermodynamic terms the equilibrium constant is related to the standard chemical potential by the equation... 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

It is apparent that CMC values can be expressed in a variety of different concentration units. The measured value of cCMC and hence of AG c for a particular system depends on the units chosen, so some uniformity must be established. The issue is ultimately a question of defining the standard state to which the superscript on AG C refers. When mole fractions are used for concentrations, AG c directly measures the free energy difference per mole between surfactant molecules in micelles and in water. To see how this comes about, it is instructive to examine Reaction (A) —this focuses attention on the surfactant and ignores bound counterions — from the point of view of a phase equilibrium. The thermodynamic criterion for a phase equilibrium is that the chemical potential of the surfactant (subscript 5) be the same in the micelle (superscript mic) and in water (superscript W) n = n. In general, pt, = + RTIn ah in which... 

The thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

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