Apparent equilibrium constants tables

In this chapter we have seen that acid dissociation constants are needed to calculate the dependence of apparent equilibrium constants on pH. In Chapter 3 we will discuss the calculation of the effects of ionic strength and temperature on acid dissociation constants. The database described later can be used to calculate pKs of reactants at 298.15 K at desired ionic strengths. Because of the importance of pKs of weak acids, Table 1.3 is provided here. More experimental measurements of acid dissociation constants and dissociation constants of complex ions with metal ions are needed because they are essential for the interpretation of experimental equilibrium constants and heats of reactions. A major database of acid dissociation constants and dissociation constants of metal ion complexes is provided by Martell, Smith, and Motekaitis (2001). 

The procedure for calculating standard formation properties of species at zero ionic strength from measurements of apparent equilibrium constants is discussed in the next chapter. The future of the thermodynamics of species in aqueous solutions depends largely on the use of enzyme-catalyzed reactions. The reason that more complicated ions in aqueous solutions were not included in the NBS Tables (1992) is that it is difficult to determine equilibrium constants in systems where a number of reactions occur simultaneously. Since many enzymes catalyze clean-cut reactions, they make it possible to determine apparent equilibrium constants and heats of reaction between very complicated organic reactants that could not have been studied classically. 

The values of AtH ° calculated using this table can be used to calculate apparent equilibrium constants at other temperatures not too far from 298.15 K. Note that standard transformed enthalpies of reactants that consist of a single species are not a function of pH (see equation 4.4-12). The standard transformed enthalpies of reactants are functions of pH when there are more than two species because rt depends on pH. As indicated by the pH dependencies in Table 4.3, these differences are often small. 

Table 4.5 gives the corresponding apparent equilibrium constants for the reactions in glycolysis. 

Table 4.5 Apparent equilibrium constants for glycolysis at 298.15 K and 0.25 M ionic strength (see Problem 4.8)...

The values of ArG"°(TotT) in Table 7.1 and AfG"°(TotD) in Table 7.2 make it possible to calculate the apparent equilibrium constant for the reaction... 

Since tables of standard apparent reduction potentials and standard transformed Gibbs energies of formation contain the same basic information, there is a question as to whether this chapter is really needed. However, the consideration of standard apparent reduction potentials provides a more global view of the driving forces in redox reactions. There are two contributions to the apparent equilibrium constant for a biochemical redox reaction, namely the standard apparent reduction potentials of the two half-reactions. Therefore it is of interest to compare the standard apparent reduction potentials of various half reactions. 

Table 9.6 Apparent Equilibrium Constants K for Nitrogenase Reactions at 298.15 K...

The effects of pH on the standard apparent reduction potentials of the half reactions involved in the nitrogenase reaction are shown in Table 9.5. The effects of pH on the apparent equilibrium constants of the reactions involved in the nitrogenase reaction as shown in Table 9.6. 

Calorimetric measurements yield enthalpy changes directly, and they also yield information on heat capacities, as indicated by equation 10.4-1. Heat capacity calorimeters can be used to determine Cj , directly. It is almost impossible to determine ArCp° from measurements of apparent equilibrium constants of biochemical reactions because the second derivative of In K is required. Data on heat capacities of species in dilute aqueous solutions is quite limited, although the NBS Tables give this information for most of their entries. Goldberg and Tewari (1989) have summarized some of the literature on molar heat capacities of species of biochemical interest in their survey on carbohydrates and their monophosphates. Table 10.1 give some standard molar heat capacities at 298.15 K and their uncertainties. The changes in heat capacities in some chemical reactions are given in Table 10.2. 

These tables have been given to 0.01 kJ mol-1. In general this overemphasizes the accuracy with which these formation properties are known. However for some reactants for which species are in classical tables, this accuracy is warranted. An error of 0.01 kJ mol-1 in the standard transformed Gibbs energy of a reaction at 298 K corresponds with an error of about 1 % in the value of the apparent equilibrium constant. It is important to understand that the large number of digits in these tables is required because the thermodynamic information is in differences between entries. 

This field owes a tremendous debt to the experimentalists who have measured apparent equilibrium constants and heats of enzyme-catalyzed reactions and to those who have made previous thermodynamic tables that contain information needed in biochemical thermodynamics. 

It must be underlined that, in those cases where the system had reached an apparent equilibrium (constant reading for at least 1 h), such values were considered as an acceptable approximation of the value of the system. Firstly, the water content of the two dry biocatalysts was evaluated and it was found that 11% of the water was stiU present in the mycelia after lyophilization (weight variation after 6h in an oven at 110°C). The two biocatalysts were then equilibrated in toluene for 24 h and the amounts were chosen so as to obtain the same water content in both systems. The results of Table 6.7 indicate that the mycelia led to a lower water activity, hence suggesting that water might partition inside the mycelia. 

Chapters 3-5 have described the calculation of various transformed thermodynamic properties of biochemical reactants and reactions from standard thermodynamic properties of species, but they have not discussed how these species properties were determined. Of course, some species properties came directly out of the National Bureau of Standard Tables (1) and CODATA Tables (2). One way to calculate standard thermodynamic properties of species not in the tables of chemical thermodynamic properties is to express the apparent equilibrium constant K in terms of the equilibrium constant K of a reference chemical reaction, that is a reference reaction written in terms of species, and binding polynomials of reactants, as described in Chapter 2. In order to do this the piiTs of the reactants in the pH range of interest must be known, and if metal ions are bound, the dissociation constants of the metal ion complexes must also be known. For the hydrolysis of adenosine triphosphate to adenosine diphosphate, the apparent equilibrium constant is given by... 

This chapter has been about calculating species properties from apparent equilibrium constants and transformed enthalpies of reaction, but there is a prior question. Where is the experimental data Fortunately, Goldberg, Tewari, and coworkers have searched the literature for these data, have evaluated it, and have published a series of review articles (10-15). These review articles provide thermodynamic data on about 500 enzyme-catalyzed reactions involving about KXX) reactants. In principle all these reactants can be put into thermodynamic tables. Goldberg, Tewari, and Bhat (16) have produced a web site to assist in the acquisition of data from the review articles. 

When the pH is specified, each biochemical half reaction makes an independent contribution to the apparent equilibrium constant K for the reaction written in terms of reactants rather than species. The studies of electochemical cells have played an important role in the development of biochemical thermodynamics, as indicated by the outstanding studies by W. Mansfield Clarke (1). The main source of tables of ° values for biochemical half reactions has been those of Segel (2). Although standard apparent reduction potentials ° can be measured for some half reactions of biochemical interest, their direct determination is usually not feasible because of the lack of reversibility of the electrode reactions. However, standard apparent reduction potentials can be calculated from for oxidoreductase reactions. Goldberg and coworkers (3) have compiled and evaluated the experimental determinations of apparent equilibrium constants and standard transformed enthalpies of oxidoreductase reactions, and their tables have made it possible to calculate ° values for about 60 half reactions as functions of pH and ionic strength at 298.15 K (4-8). 

Any half reaction in the preceding tables can be combined with any other half reaction to produce a biochemical reaction, but that does not mean that there are enzymes for all of these reactions. For some of the reactions for which there are enzymes, the apparent equilibrium constants are so large that they cannot be determined by direct experiment. Table 8.6 provides apparent equilibrium constants at 298.15 K, pH 7, and 0,25 M ionic strength for a number of oxidoreductase reactions. 

The apparent equilibrium constants of the reactions in the preceding section are probably generally of greatest interest at pH 7 and 0.25 M ionic strength. The following table has been prepared to make it easier to compare these reactions. 

Table 8.6 Apparent equilibrium constants of redox reactions at 298.15 K, pH 7, and ionic strength 0.25 M...

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