Chemical potential absolute zero

The chemical potential pi plays a vital role in both phase and chemical-reaction equilibria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence pi, is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, pi approaches negative infinity when either P or Xi approaches zero. While these characteristics do not preclude the use of chemical potentials, the application of equilibrium criteria is facilitated by introduction of the fugacity, a quantity that takes the place of p. but which does not exhibit its less desirable characteristics. 

One can define intrinsic binding constants in the same way as before, e.g., Eq. (2.2.25), but now these constants will depend on the ligand concentration C. The relation (D.4) gives an implicit dependence of the absolute activity A = exp(Pp) on the ligand concentration C. However, since the analytical dependence of G on C is not known, one cannot write the explicit function A = A(C). This may be done to first order in C. Note that when C — 0 the integral on the rhs of Eq. (D.4) is zero, and we have the ideal gas limit of the chemical potential. If we expand the integral to first order in C, we obtain the first-order deviation with respect to an ideal gas. 

Virtually all chemical reactions in soils are studied as isothermal, isobaric processes. It is for this reason that the measurement of the chemical potentials of soil components involves the prior designation of a set of Standard States that are characterized by selected values of T and P and specific conditions on the phases of matter. Unlike the situation for T and P, however, there is no strictly Ihermodynamic method for determining absolute values of the chemical potential of a substance. The reason for this is that p represents an intrinsic chemical property that, by its very conception, cannot be identified with a universal scale, such as the Kelvin scale for T, which exists regardless of the chemical nature of a substance having the property. Moreover, p cannot usefully be accorded a reference value of zero in the complete absence of a substance, as is the applied pressure, because there is no thermodynamic method for measuring p by virtue of the creation of matter. 

Let us consider for this purpose a chemical reaction at the absolute zero. The heat of reaction at constant pressure Qj, is equal to the change in the heat content H of the system consequent on the reaction. The affinity A is equal to the change in the thermodynamic potentials f of the reacting substances, i.e. = -h 2 and = - 2 -h TIS. 

Chemical tables never contain absolute values of chemical potentials, although the potential can be assigned an absolute zero value, just as temperature can. The reason is that the corresponding values would be enormous. In order to work with the tiny differences in potentials common in chemical and biological reactions, at least 11 digits would be necessary (the ratio between the potential differences and the absolute values is around one to one billion ). This alone would lead to numbers that are much too unwieldy not to mention that the absolute values are not known accurately enough for this to be feasible. 

At zero pressure and temperature, we also have pt = (dE/dN). In this case N is the number of molecules in the system, and pr is the ordinary chemical potential of thermodynamics. The electronic chemical potential of a single molecule plays somewhat the same role. At equilibrium p must be constant everywhere, and p will be the correct electron density for the ground state. The quantity x is called the absolute electronegativity, for reasons that will become clear. ... 

Chemical potential cannot be expressed as an absolute quantity, and the numerical values of chemical potential are difficult to relate to more easily understood physical quantities. Furthermore, the chemical potential approaches an infinite negative value as pressure approaches zero. For these reasons, the chemical potential is not directly useful for phase equilibria calculations. Instead, fugacity, as defined below, is employed as a surrogate. 

The data are taken from steam tables [14, p. 447]. Traditionally, in the steam tables, the specific quantities are given rather than the molar quantities. Moreover, the entropy is normalized not to absolute zero, but to 0 °C. The full curves are the chemical potentials for the liquid phase at fixed pressure as a function of the temperature. The curves are accessible by measurement only at temperatures below the boiling point. The dashed curves represent the chemical potentials for the gaseous phase at fixed pressure as a function of the temperature. These data are accessible by measurement only at temperatures above the boiling point. Both types of chemical potential are extrapolated in the region that is not accessible to measurement. 

As characteristic for thermodynamic cycles, the working system accesses two reservoirs with a low and a high thermodynamic potential. The thermodynamic potentials, i.e., temperature, chemical potential, hydrostatic pressure, electric potential, etc., show an absolute zero of the lower reservoir, when the efficiency of the cycle r] = 1. 

When a metal, M, is immersed in a solution containing its ions, M, several reactions may occur. The metal atoms may lose electrons (oxidation reaction) to become metaUic ions, or the metal ions in solution may gain electrons (reduction reaction) to become soHd metal atoms. The equihbrium conditions across the metal-solution interface controls which reaction, if any, will take place. When the metal is immersed in the electrolyte, electrons wiU be transferred across the interface until the electrochemical potentials or chemical potentials (Gibbs ffee-energies) on both sides of the interface are balanced, that is, Absolution electrode Until thermodynamic equihbrium is reached. The charge transfer rate at the electrode-electrolyte interface depends on the electric field across the interface and on the chemical potential gradient. At equihbrium, the net current is zero and the rates of the oxidation and reduction reactions become equal. The potential when the electrode is at equilibrium is known as the reversible half-ceU potential or equihbrium potential, Ceq. The net equivalent current that flows across the interface per unit surface area when there is no external current source is known as the exchange current density, f. 

We call the quantity 2b the chemical activity. This is based upon the name chemical potential for the quantity //b, from which it stems. The recommended name absolute activity is unfitting because, depending upon the choice of zero point for the scale of fi, other relative 2b values can result that differ by fixed factors. 

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