Reactants transformed thermodynamic properties

Tables of Standard Transformed Thermodynamic Properties at 298.15 K for Biochemical Reactants at Specified pH and Ionic Strength... 

When the pH is specified, we enter into a whole new world of thermodynamics because there is a complete set of new thermodynamic properties, called transformed properties, new fundamental equations, new Maxwell equations, new Gibbs-Helmholtz equations, and a new Gibbs-Duhem equation. These new equations are similar to those in chemical thermodynamics, which were discussed in the preceding chapter, but they deal with properties of reactants (sums of species) rather than species. The fundamental equations for transformed thermodynamic potentials include additional terms for hydrogen ions, and perhaps metal ions. The transformed thermodynamic properties of reactants in biochemical reactions are connected with the thermodynamic properties of species in chemical reactions by equations given here. 

These tables apply to single sets of values of pH and ionic strength. A more general approach is to use the functions of ionic strength and pH for each reactant that give the values of standard transformed thermodynamic properties at 298.15 K. For reactants for which A,//0 is known for all species, functions of temperature, pH, and ionic strength can be used to calculate standard transformed thermodynamic properties at temperatures in the approximate range 273.15 to 313.15 K, as discussed in Section 4.9. 

Equations for the Standard Transformed Thermodynamic Properties of a Reactant... 

The standard formation properties of species are set by convention at zero for the elements in their reference forms at each temperature. The standard formation properties of in aqueous solution at zero ionic strength are also set at zero at each temperature. For other species the properties are determined by measuring equilibrium constants and heats of reaction. Standard transformed Gibbs energies of formation can be calculated from measurements of K, and so it is really these Maxwell relations that make it possible to calculate five transformed thermodynamic properties of a reactant. 

Now we are in a position to calculate the standard transformed thermodynamic properties of reactants from the standard properties of the species that make them up. In this chapter the transformed thermodynamic properties are calculated only at 298.15 K. Caleulations at other temperatures are presented in the next chapter. The first step is to adjust the properties at zero ionic strength to the desired ionic strength in the range 0-0.35 M. Equations 1.3-5 and 1.3-6 Chapter 1 show how these calculations can be made using the extended Debye-HUckel equation. Substituting equation 1.3-5 in equation 3.5-3 in two places yields... 

R. A. Alberty, Calculation of transformed thermodynamic properties of biochemical reactants at specified dpH and pMg, Biophys. Chem. 43.239-254 (1992). 

As shown by the Maxwell relations in equations 3.4-12 to 3.4-16, all the other thermodynamic properties of a biochemical reactant can be calculated by taking partial derivatives of the function of T, pH, and ionic strength for Af G,- °. This is illustrated by calculating the other standard transformed thermodynamic properties of inorganic phosphate. 

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... 

We have seen that calculating species properties from experimental values of K and A // ° is more complicated than calculating K and Ar ° from species values. Thermodynamic calculations can be made by alternate paths, and so there is more than one way to calculate species properties from experimental properties. This chapter emphasizes the concept of the inverse Legendre transform discussed by Callen (8). Biochemical reaction systems are described by transformed thermodynamic properties, and the inverse transform given in equation 6.2-1 provides the transformation from experimental reactant properties to calculated species properties. In this ehapter we first considered calculations of species properties at 298.15 K from measurements of K and Ar ° at 298.15 K. Then we considered the more difficult problem of calculating Af G°(298.15 K) and Af //°(298.15 K) from Ar G "(313.15 K) and Ar H (313.15 K). The programs developed here make it possible to go from Ar G and Ar H (F.pH,/) to Af G (298.15 K,/=0) and Af H (298.15 K,/=0) in one step. 

This package provides data on the species of 131 reactants at 298.15 K and programs for calculating various transformed thermodynamic properties. Programs are given for the calculation of apparent equilibrium constants and other transformed thermodynamic properties of enzyme-catalyzed reactions by simply typing in the reaction. 

The Appendix contains a copy of the Mathematica notebook BasicBiochemDataS.nb, Tables of Transformed Thermodynamic Properties, the Glossary of Names of Reactants, the Glossary of Symbols for Thermodynamic Properties, a List of Mathematica programs, and Sources of Biochemical Thermodynamic Information on the Web. The Mathematica package BasicBiochemData3.m, which is also available at... 

BasicBiochemData3 contains functions of pH and ionic strength that give standard transformed thermodynamic properties of 199 reactants for which values of Af G are known for all species that have significant concentrations in the pH 5 to pH 9 range. Using ATP as an example, these two functions are as follows ... 

Because the enthalpy is a thermodynamic property, the value of AH depends only on the nature and state of the initial reactants and final products, and not on the reactions that have been used to carry out the transformation. If we must deal with a reaction whose AH is not available, it is sufficient to find a series of reactions for which AH s are available and whose sum is the reaction in question. 

As the Gibbs function is a thermodynamic property, values of AG do not depend on the intermediate chemical reactions that have been used to transform a set of reactants, under specified conditions, to a series of products. Thus, one can add known values of a Gibbs function to obtain values for reactions for which direct data are not available. The most convenient values to use are the functions for the formation of a compound in its standard state from the elements in their standard states, as given in Tables 7.2... 

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