Choice of Standard States

If the molality is a more convenient composition measure than the mole fraction, the activity coefficient of the solute is defined as 

Although we cannot determine its absolute value, the chemical potential of acomponent of a solution has a value that is independent of the choice of concentration scale and standard state. The standard chemical potential, the activity, and the activity coefficient have values that do depend on the choice of concentration scale and standard state. To complete the definitions we have given, we must define the standard states we wish to use. 

Whether p 7, and a, refer to a mole fraction composition scale or to a molality composition scale will be clear from the context in which they are used. We will not attempt to use different S5mbols for each scale. 

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. 

If Equation (16.1) is to be consistent with Equation (10.14), it is clear that, for a real gas 

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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... 

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... 

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... 

Certain choices of standard states have found such widespread use that they have achieved... 

The effect of pressure on AG° and AH0 depends on the choice of standard states employed. When the standard state of each component of the reaction system is taken at 1 atm pressure, whether the species in question is a gas, liquid, or solid, the values of AG° and AH0 refer to a process that starts and ends at 1 atm. For this choice of standard states, the values of AG° and AH0 are independent of the system pressure at which the reaction is actually carried out. It is important to note in this connection that we are calculating the enthalpy change for a hypothetical process, not for the actual process as it occurs in nature. This choice of standard states at 1 atm pressure is the convention that is customarily adopted in the analysis of chemical reaction equilibria. 

It should be emphasized that the choice of standard states implied by equation 2.2.9 is not that which is conventionally used in the analysis of chemically reacting systems. Furthermore,... 

For cases where the standard states of the reactants and products are chosen as 1 atm, the value of AG° is pressure independent. Consequently, equation 2.4.7 indicates that Ka is also pressure independent for this choice of standard states. For the unconventional choice of standard states discussed in Section 2.2, equations 2.4.7 and 2.2.10 may be combined to give the effect of pressure on Ka. 

This illustrates the statement made earlier that the most convenient choice of standard state may depend on the problem. For gas-phase problems involving A, it is convenient to choose the standard state for A as an ideal gas at 1 atm pressure. But, where the vapor of A is in equilibrium with a solution, it is sometimes convenient to choose the standard state as the pure liquid. Since /a is the same for the pure liquid and the vapor in equilibrium... 

One cannot emphasize too often that the numerical values of I a > °A> ar d Ya depend on the choice of standard state. The usual thermodynamic... 

In Equation 50 the chemical potential of non-electrolyte A depends on the usual choice of standard-state conventions described above, and the chemical potentials of both H2(g) and H+(sod are taken to be zero (this defines e.s.s., the electrolyte standard state). By setting the standard-state free energy of the solvated proton equal to zero, this standard-state convention... 

The Gibbs energy of adsorption is a measure of adsorbate-metal interactions. Its values depend, however, on the choice of standard states for the chemical potentials of the components involved in the process. Therefore AG° values determined for different systems can only be compared if they refer to the same standard-state conditions. AG° values of adsorption of thiourea (TU) on several metallic electrodes, calculated for the most often used standard states, are presented in Table 1. 

The form of the equilibrium constant in Equation (10.21) is different from that presented in introductory courses. It has the advantages that 1) it is explicit that Kp is a dimensionless quantity 2) it is explicit that the numerical value of Kp depends on the choice of standard state but not on the units used to describe the standard state pressure the equilibrium constant has the same value whether P° is expressed as 750.062 Torr, 0.98692 atm, 0.1 MPa, or 1 bar. 

Two other conventions exist for the choice of standard states for components of a solution. One convention chooses the pure component at 1 bar of pressure, for conformance with the usual standard state for pure components. This choice has the disadvantage that it requires aterm for the effect of pressure in the relation between the chemical potentials of the pure component and of the component in solution. The other convention chooses the pure component at the vapor pressure of the solution. This choice has the disadvantage of having different standard states for each composition of solution. 

For solutions obeying Henry s law, as for ideal solutions, and for solutions of ideal gases, the chemical potential is a linear function of the logarithm of the composition variable, and the standard chemical potential depends on the choice of composition variable. The chemical potential is, of course, independent of our choice of standard state and composition measure. 

Solvent in Solution. We shall use the pure substance at the same temperature as the solution and at its equilibrium vapor pressure as the reference state for the component of a solution designated as the solvent. This choice of standard state is consistent with the limiting law for the activity of solvent given in Equation (16.2), where the limiting process leads to the solvent at its equilibrium vapor pressure. To relate the standard chemical potential of solvent in solution to the state that we defined for the pure liquid solvent, we need to use the relationship... 

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