Standard states, use

The next point takes the standard-state idea and makes it more suitable for biological processes by defining a new AG°, called AG°. This new standard state is one with a pH of 7. This is the standard state used most of the time for biochemical reactions and is the one we will use. Not only does it make a big difference in reactions in which is consumed or produced, it also requir es us to be aware of the form in which various species exist at a pH of 7. A reaction that is endergonic at [H" ] = 1 M can easily become exergonic at [H" ] = 10 M (pH = 7) and vice versa. 

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

The translational partition function is a function of both temperature and volume. However, none of the other partition functions have a volume dependence. It is thus convenient to eliminate the volume dependence of 5trans by agreeing to report values that use exclusively some volume that has been agreed upon by convention. The choices of the numerical value of V and its associated units define a standard state (or, more accurately, they contribute to an overall definition that may be considerably more detailed, as described further below). The most typical standard state used in theoretical calculations of entropies of translation is the volume occupied by one mole of ideal gas at 298 K and 1 atm pressure, namely, y° = 24.5 L. 

The standard state used to be defined for 1 atm rather than for 1 bar however, the latter is now the accepted standard. The small change in standard pressure makes a negligible difference to most numerical values, so it is normally safe to use tables of data compiled for 1 atm. 

Just as we can define a standard enthalpy of formation (AH°f) and a standard free energy of formation (AG°f), we can define an analogous standard entropy of formation (AS°f) as being the entropy change for formation of a substance in its standard state from its constituent elements in their standard states. Use the standard molar entropies given in Appendix B to calculate AS°f for the following substances ... 

Because K, depends on concentrations and the product KyKx is concentration independent, Kx must also depend on concentration. This shows that the simple equilibrium calculations usually carried out in first courses in chemistry are approximations. Actually such calculations are often rather poor approximations when applied to solutions of ionic species, where deviations from ideality are quite large. We shall see that calculations using Eq. (47) can present some computational difficulties. Concentrations are needed in order to obtain activity coefficients, but activity coefficients are needed before an equilibrium constant for calculating concentrations can be obtained. Such problems are usually handled by the method of successive approximations, whereby concentrations are initially calculated assuming ideal behavior and these concentrations are used for a first estimate of activity coefficients, which are then used for a better estimate of concentrations, and so forth. A G is calculated with the standard state used to define the activity. If molality-based activity coefficients are used, the relevant equation is... 

With respect to composition, the standard states used in this chapter are states of the pure species. For gases, the physical state is the ideal-gas state and for liquids and solids, the real state at the reference pressure and system temperature. 

In summary, the standard states used in this chapter are ... 

The standard state used for the finite concentration data was usually the pure solvent at the temperature and pressure of the mixture. In most cases, the Poynting correction (pressure effect on the liquid) could be neglected. The end result of this approximation is that saturation pressure appears in the expression for the activity coefficient, but not the system pressure. 

It is particularly unfortunate that many calculated free energies of solvation are published without explicit reference to the chosen standard state. By noting the particular value cited for an experimental free energy of solvation, it is sometimes possible to infer the choice of standard state (if one assumes the workers took care to be consistent), but this is dangerous. We have made every effort to convert all results presented in this chapter to the standard state used in Equation [2] that is, one molar in both gaseous and solution phases. But some caution should be applied in accepting results where such conversion is necessary. 

Earlier, it was stated that absolute enthalpy could not be determined for a substance, and therefore we can deal only with changes or differences in this quantity. To simplify calculations of heat of reaction and to make them consistent, we must therefore arbitrarily define a standard state to which we reference all changes in enthalpy for chemical reactions. The standard state used for most engineering calculations is defined as 25°C (298 K) and 1 atm pressure. 

A standard-state pressure of 1 stairdardatirrosphere (101.325 kPa) was irr use for nrairy years, aird older data tabulatioirs are for this pressure. The stairdard is irow 1 bar (10 Pa), but for purposes of this chapter, the differeirce is of iregligible coirsequeirce. With respect to compositioir, the standard states used hr this chapter are states of the pure species. For gases, the physical state is the ideal-gas state aird for liquids aird solids, the real state at the stairdard-state pressure aird at the system temperature. In summary, the standard states used in this chapterare ... 

How are the chemical elements in their standard states used as references for standard enthalpies of formation (16.4)... 

The reverse rate constants for the elementary reactions used in the present work were caJculated from the forward rate constants and the equilibrium constant by assuming microscopic reversibility. Standard states used in tabulations of thermodynamic data are invariably at 1 atm and the temperature of the system. Since concentration units were required for rate constant calculations, a conversion between Kp and Kc was necessary. Values of Kp were taken from the JANAF Thermochemical tables (1984). Kc was calculated from the expression ... 

If and Aa, A/S, etc.,. re available from thermal measurements, it is possible to derive AHo by utilizing the procedure described in 12k if if is known at any one temperature, it is possible to evaluate the integration constant and the variation of In K (or log K) with temperature can then be expressed in the form of equation (33.30). The accuracy of the resulting expression is limited largely by the thermal data, for these are often not known with great certainty. Care should be taken to ensure that the standard states used in connection with the heat of reaction A// are aL- o those employed for the equilibrium constant. Actually, the standard states chosen in 30b, 31b correspond with those almost invariably employed in both equilibrium studies and heat of reaction measurements. 

The standard state used here is unit pressure. If unit activity is used for the standard state of O2, the redox potentials for reactions of that species must be adjusted by +0.17 V. ... 

What is the standard state used in the acoj column in Table 11.1 ... 

Using crystal radii from Appendix B-1, calculate the lattice energy for PbS, which crystallizes in the NaCl structure. Compare the results with the Bom-Haber cycle values obtained using the ionization energies and the following data for enthalpies of formation. Remember that enthalpies of formation are calculated beginning with the elements in their standard states. Use these data AHf. S (g), 535 kJ/mol ... 

A little similar but another choice of standard state, used e.g. in gas chemical kinetics, see Sect. 4.9, is the pure ideal gas at given temperature and at fixed standard molar concentration Cs (usually unit one, say c, = 1 mol/m ). Therefore, by (4.433), the standard function (/u, in (4.441)) is defined as iif(T) = 4- RTlnCj and... 

Here/represents an intensive property value for the real mixture, and all three terms in (5.2.1) are at the same temperature T, pressure P, composition x, and phase. The excess properties provide a convenient way for measuring how a real mixture deviates from an ideal solution. In general, an excess property/ may be positive, negative, or zero. An ideal solution will have all excess properties equal to zero. Note that the value for depends on the choice of standard state used to define the ideal solution. Further note that the definition (5.2.1) is not restricted to any phase excess properties may be defined for solids, liquids, and gases, although they are most commonly used for condensed phases. 

Before a reaction-equilibrium calculation can be performed, we must select an appropriate standard state for each species. Moreover, we must clearly distinguish quantities, such as fugacities and activities, that depend on the final equilibrium state (T, P, x ), from those quantities, such as equilibrium constants, that depend only on the equilibrium temperature T, the standard-state pressures P , and the phase. Typically, the standard-state pressure and phase are chosen according to whether the real substance is gas, liquid, or solid at the equilibrium conditions. Those three possibilities are discussed, in turn, here, and each discussion culminates with a particular expression for the activity. Those expressions can be used either in the stoichiometric development, via (10.3.14), or in the nonstoichiometric development, via (10.3.38). We emphasize that when we use the stoichiometric approach, the standard states used for the fugacities must be consistent with those associated with the equilibrium constant. 

If solvent 2 had Ax2 = then the solute would attain the same mole fraction in both phases and Ci would be unity for all compositions. Figure 12.7 shows that as Ax2 is decreased away from Ax3 = 1.9, increases that is, the mole fraction of solute increases in the solvent-2 phase. As a general rule, the larger the disparity in intermo-lecular forces between solute 1 and each solvent, 2 and 3, the easier it is to extract solute from one phase into the other. Note that each curve in the figure obeys the pure-component (12.1.26) and dilute-solution (12.1.27) limits (with the same standard states used for both phases). Also note that at high concentrations (xxP > 0.85) both phases are dominated by solute molecules and no separation occurs. Finally, note that a weak maximum occurs in Ci when Ax2 > 1-... 

The standard state used for all the chemical potentials appearing in Equations 3 and 4 is one of infinite dilution, that is, the one in which all the solute molecules are completely surrounded by and interact only with solvent molecules (3). Under those conditions, for a given species, say A, the difference (S2,T) — x (S),T) is a measure of its differential solvation by S2 and Si. 

In a liquid mixture, when there is a fairly balanced composition in the compounds then the pure compounds can be kept as standard states using the molar ratios to define the ideal activities. Consequently, the activities are expressed as ji. x,. However, the solutions most commonly seen in electrochemistry involve a compound, called a solvent, which is found in much greater quantity than other compounds, called solutes. Here one often distinguishes between these two types of compounds by choosing a different standard state for the solvent and the solutes ... 

We shall disregard the specific standard states used by Frank and Evans. The qualitative argument presented here is independent of the choice of standard states. 

In this chapter, we discuss the various standard states used for the Gibbs energy and the activity. The standard state used for enthalpy, volume and heat capacity is quite different, and is discussed, along with a more detailed look at partial molar properties, in Chapter 10. 

Finally, comparing Equations (8.32) and (8.19) we see that it is quite possible for the activity of i to be numerically identical to the fugacity of i. It just requires that the standard state chosen for i is ideal gas i at T and 1 bar. We will find (Chapter 9) that this is a very common situation when i is a gas or a gaseous component, and in fact it is the standard state used in program supcrt92, as shown in Table 8.1. In this table, note that at each of the three temperatures... 

So the calculated activity of dissolved methane is lO"". With a standard state of ideal 1 molal methane, this means WCH4TCH4 = 10 , and on the reasonable assumption that 7 4 = 1-0, then Wch4 = 10 . So in spite of the fact that two different standard states are used for the same component in the same reaction, we arrive at a useful answer. This is because the standard states used do not... 

In Equation 10.12, it is important that the quantities that go into making up K are measured relative to the standard states used to determine AGJ. For gases that means partial pressures in units of bar, and for solutes it means molarity. In a gas-phase reaction, for example, the K in Equation 10.12 refers to Kp, whereas in a reaction in solution it would be K. The larger the value of K, the more negative AG is. For chemists. Equation 10.12 is one of the most important equations in thermodynamics because it enables us to determine the equilibrium constant of a reaction if we know the change in standard free energy and vice versa. 

---