Standard state types

Electrodes of the second type can formally be regarded as a special case of electrodes of the first type where the standard state (when E = °) corresponds not to flAg+ = 1 but to a value of == 10 mol/L, which is established in a KCl solution of unit activity. In this case, the concentration of the potential-determining cation can be varied by varying the concentration of an anion, which might be called the controlling ion. The oxides and hydroxides of most metals (other than the alkali metals) are poorly soluble in alkaline solutions hence, almost all metal electrodes in alkaline solutions are electrodes of the second type. 

In the reaction shown above, the volume of the reaction products (2 mol CO) is seen to be much greater than that of the reactants (2 mol of solid carbon plus 1 mol of oxygen). The effect of pressure on the free energy of formation of an oxide associated with an increase in the number of gas molecules which is representative of the type of reaction in the present illustration is shown in Figure 4.2 (A). Applying the criterion of volume increase per mole accompanying reaction at standard state to the case of metal oxidation such as... 

UNITS The products/reactants ratios may have units associated with them. For example, a reaction of the type A B + C has a products/reactants ratio that has molar units. What you do when you take the log of a products/reactants ratio with molar units is ignore the units. You ve not really made them disappear, you ve just ignored them. The way physical chemist types make this difficult is that they call ignoring the units an assumption of standard state. It does matter, though. If you assume the units are molar (M), the products/reactants ratio has one... 

Because AG° = -nFE%c and AG° = -RT InK, the signs and magnitudes of i ceii> AG° and K are related as shown in the following table for different types of reactions under standard state conditions. 

In solution thermodynamics the standard or reference states of the components of the solution are important. Although the standard state in principle can be chosen freely, the standard state is in practice not taken by chance, but does in most cases reflect the type of model one wants to fit to experimental data. The choice of... 

The JANAF tables specify a volatilization temperature of a condensed-phase material to be where the standard-state free energy A Gf approaches zero for a given equilibrium reaction, that is, M/fyl), M/)y(g). One can obtain a heat of vaporization for materials such as Li20(l), FeO(l), BeO(l), and MgO(l), which also exist in the gas phase, by the differences in the All" of the condensed and gas phases at this volatilization temperature. This type of thermodynamic calculation attempts to specify a true equilibrium thermodynamic volatilization temperature and enthalpy of volatilization at 1 atm. Values determined in this manner would not correspond to those calculated by the approach described simply because the procedure discussed takes into account the fact that some of the condensed-phase species dissociate upon volatilization. 

From the nature of the definition [Equation (16.1)], it is clear that the activity of a given component may have any numeric value, depending on the state chosen for reference, but a/ must be equal to 1. No reason exists other than convenience for one state to be chosen as the standard in preference to any other. It frequently will be convenient to change standard states as we proceed from one type of problem to another. Nevertheless, certain choices generally have been adopted. Unless a clear statement is made to the contrary, we will assume the following conventional standard states in aU of our discussions. 

This theory has been successfully verified experimentally. Buck and Shepard [51] demonstrated that electrodes of the all-solid-state type have a response that is identical to that of similar electrodes of the second kind for response to halide ions and to a silver electrode for response to silver ions, depending on the degree of saturation with silver. This is achieved by soldering a silver contact to the membrane. If however the internal contact material is more noble than silver (platinum, graphite, mercury), the electrode with response to silver ions may attain a potential between the standard potential of a silver electrode g /Ag and the value... 

Figure 3.9 Conformation of Gibbs free energy curve in various types of binary mixtures. (A) Ideal mixture of components A and B. Standard state adopted is that of pure component at T and P of interest. (B) Regular mixture with complete configurational disorder kJ/mole for 500 < r(K) < 1500. (C) Simple mixture IF = 10 - 0.01 X r(K) (kJ/ mole). (D) Subregular mixture Aq = 10 — 0.01 X T (kJ/mole) = 5 — 0.01 X F (kJ/ mole). Adopting corresponding Margules notation, an equivalent interaction is obtained with IFba = 15 - 0.02 X r(kJ/mole) Bab = 5 (kJ/mole).

The most useful type of standard state is one defined in terms of a small number of molecules per unit area of adsorbent surface. In an attempt to have a definition analogous to that for three-dimensional matter—one atmosphere at any temperature—Kemball and Rideal (12) defined a standard state with an area per molecule of 22.53T A.2 where T is the absolute temperature. This corresponds to the same volume per molecule as the three-dimensional state if the thickness of the surface layer is 6A. In terms of surface pressure it corresponds to 0.0608 dynes/cm. for a perfect two-dimensional gas at all temperatures, and as such the definition may be extended to cover condensed films. 

Another example of this type is the adsorption of acetone on mercury (Kemball, 9) where the heat of adsorption to the same standard state is... 

V°rev = 1.229V is the standard state reversible potential for the water splitting reaction and Vaoc is the anode potential at open circuit conditions. Term Vmeas-Vaoc arises from the fact that Voc represents the contribution of light towards the minimum voltage needed for water splitting potential (1.229V) and that the potential of the anode measured with respect to the reference electrode Vmeas has contributions from the open circuit potential and the bias potential applied by the potentiostat (i.e. Vmeas= Vapp+Vaoc). The term Vmeas-Vaoc makes relation (3.6.16) independent of the electrolyte pH and the type of reference electrode used. Thus the use of V°rev in relation (3.6.16) instead of VV or V°hz as in the case of relation (3.6.15) is justified. 

In the case of adsorbed species, a unique standard state—one that makes the bottom part of the logarithm equal to zero—is not defined because it will depend on the type of isotherm chosen to describe the process, i.e., it will depend on the function /(0) in Eq. (6.184) characteristic of each isotherm. Thus, it would be impossible to compare the adsorption energies (i.e., AG° s) of different adsorbates if they were represented by different adsorption isotherms. However, instead of a unique standard state, it is possible to define convenient standard states common to any isotherm. The way to choose this convenient standard state is explained in the following analysis of the Langmuir isotherm. 

Using accurately measured heats of combustion (AH%.) and sublimation (A//sub), Chia and Simmons388 calculated heats of formation for four tetraazapentalenes (type C) referred to the gaseous form in standard states [Ai/f°(g)l, and the following values were found 255, 142.8 1.3 254b, 132.1 1.5 328, 136.4 1.2 329, 128.2 1.3 (in kcal mol-1). These results were used to calculate resonance energies (Section V,B). 

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

Throughout the discussions in Sections 8.15-8.18, we have emphasized methods for obtaining expressions for the chemical potential of a component when we choose to treat the thermodynamic systems in terms of the species that may be present in solution. A complete presentation of all possible types of systems containing charged or neutral molecular entities is not possible. However, no matter how complicated the system is, the pertinent equations can always be developed by the use of the methods developed here, together with the careful definition of reference states or standard states. We should also recall at this point that it is the quantity (nk — nf) that is determined directly or indirectly from experiment. 

Furthermore, it must be clearly stated, if one deals with a conditional constant, being valid for one type of standard state, or with an infinite dilution constant, another type of standard state (i.e. T=25°C and ionic strength 1=0). The latter might be calculated from the former. Standard temperature conditions can be calculated using the van t Hoff equation (Eq. 3), whereas the following equation (Eq. 4) can be applied to determine the effect of pressure ... 

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