Standard state, choice

As can be seen, the two standard-state choices correspond to the limiting Raoult s law [P° (I)] or Henry s law [P° (II)] dashed lines at x, = 1. Accordingly, for solving problems involving activities, we can always use the equation... 

These are the common choices in geochemical calculations, but of course others are possible. Every value of an equilibrium constant implies that standard state choices have been made. 

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

The adsorbed state often seems to resemble liquid adsorbate, as in the approach of the heat of adsorption to the heat of condensation in the multilayer region. For this reason, a common choice for the standard state of free adsorbate is the pure liquid. We now have... 

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

The confinement term is unique because it alone causes a dependence of the binding free energy on the choice of unit concentration in the standard state the volume available per ligand molecule in the free state, and hence the compression factor, depend on the unit concentration. 

The numerical values of AG and A5 depend upon the choice of standard states in solution kinetics the molar concentration scale is usually used. Notice (Eq. 5-43) that in transition state theory the temperature dependence of the rate constant is accounted for principally by the temperature dependence of an equilibrium constant. 

Activity can be thought of as the quantity that corrects the chemical potential at some pressure and/or composition condition" to a standard or reference state. The concept of a standard state is an important one in thermodynamics. The choice of the pressure and composition conditions for the standard state are completely arbitrary, and unusual choices are sometimes made. The common choices are those of convenience. In the next section, we will describe and summarize the usual choices of standard states. But, first, we want to describe the effect of pressure and temperature on a,. 

In defining the activity through equations (6.83) and (6.84), we have made no restrictions on the choice of a standard state except to note that specification of temperature is not a part of the standard state condition. We are free to choose standard states in whatever manner we desire.p However, choices are usually made that are convenient and simplify calculations involving activities. The usual choices differ for a gas, pure solid or liquid, and solvent or solute in solution. We will now summarize these choices of standard states and indicate the reasons. Before doing so, we note that activities for a substance with different choices of standard states are proportional to one another. This can be seen as follows With a particular choice of standard state... 

Activity is a dimensionless quantity, and / must be expressed in kPa with this choice of standard state. It is inconvenient to carry f° = 100 kPa through calculations involving activity of gases. Choosing the standard state for a gas as we have described above creates a situation where SI units are not convenient. Instead of expressing the standard state as /° = 100 kPa, we often express the pressure and fugacity in bars, since 1 bar = 100 kPa. In this case, /0 — 1 bar, and equation (6.92) becomes4... 

Later, we will make equilibrium calculations that involve activities, and we will see why it is convenient to choose the ideal gas as a part of the standard state condition, even though it is a hypothetical state/ With this choice of standard state, equations (6.94) and (6.95) allow us to use pressures, corrected for non-ideality, for activities as we make equilibrium calculations for real gases.s... 

Standard States for Pure Solids and Pure Liquids For condensed phases, the pure solid or liquid under 1 bar (100 kPa) external pressure is usually chosen as the standard state. With this choice, the standard state fugacity is given by... 

Standard State of a Solvent in a Mixture The usual choice of a standard state for a solvent in a solution is the pure solvent at a pressure of 1 bar, the same convention as for a pure solid or liquid. Thus,u... 

In summary, the usual choice of standard states and the implications of these choices are shown in Table 6.1. 

For electrolytes where dissociation is extensive, but not complete, the classification is somewhat arbitrary, and the electrolyte can be considered to be either strong or weak. Thermodynamics does not prevent us from treating an electrolyte either way, but we must be careful to designate our assignment because the choice of standard state is different for a strong electrolyte and a weak electrolyte. Assuming that an electrolyte is weak requires that we have some nonthermodynamic procedure for distinguishing clearly between the dissociated and undissociated species. For example, Raman spectroscopy... 

With the choice of standard states used in Table 7.2, Hf = H°. Making this substitution and adding and subtracting n2H°2 gives... 

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. 

With these choices of standard states, our examples become (with r/H o = 1) Kw = aH + a0u- —... 

With our choice of standard states and the low pressure involved, we can write... 

With the choice of a pure substance standard state for the solid, and a strong electrolyte standard state for the dissolved AgCl, we get... 

This last example provides a demonstration of the flexibility inherent in the choice of standard states. A strong electrolyte standard state is chosen for NaA(aq) and NaCl(aq) so that... 

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