Ionic strength transformed thermodynamic properties

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

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. 

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... 

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. 

Figure 4.3 Plots of transformed thermodynamic properties for the reaction ethanol + nadox = acetaldehyde + nadred as a function of pH at 0.25 M ionic strength and temperatures of 273.15, 298.15, and 313.15 K.

Calculation of Standard Transformed Thermodynamic Properties of Inorganic Phosphate at Specified T, pH, pMg and Ionic Strength by Use of Maxwell Relations... 

These five functions are used to calculate values of the various transformed thermodynamic properties at 298.15 K, pH 7, pMg 3, and ionic strength 0.25 M. Since the specified concentration of magnesium ions is so low, these values are not very different from the values calculated in the preceding chapter for the absence of magnesium ions. 

Since the transformed thermodynamic properties of inorganic phosphate are each functions of four variables and we want to see how five transformed properties are affected, it is difficult to describe these dependencies, but Mathematica provides two ways. The first is to make a table, and the second is to make three-dimensional plots at a specified ionic strength. 

Table 5.1 Transformed thermodynamic properties of inorganic phosphate at temperatures 298.15 K, 313.15 K, pHs 5, 7, and 9, pMgs at 2, 4, and 6, and ionic strengths of zero and 0.25 M. Deeply nested lists like this are by default printed with successive dimensions alternating between rows and columns.

Figure 5.1 Transformed thermodynamic properties of inorganic phosphate at 298.15 K and 0.25 M ionic strength.

In order to calculate standard transformed thermodynamic properties for ATP + H2 O = ADP + Pj at specified T, pH, pMg, and ionic strength, we need to carry out the same process for ATP, ADP, and H2O that we have used for inorganic phosphate. The basic data on species at 298.15 K and zero ionic strength are as follows (4,5,6) ... 

The functions of pH and ionic strength and functions of temperature, pH, and ionic strength that yield standard transformed thermodynamic properties are produced in the package BasicBiochemDataS. These functions are used here to make the following four tables ... 

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 ... 

As we have seen in the preceding chapter, the standard thermodynamic properties of species in aqueous solutions are functions of ionic strength when they have electric charges. Substituting equation 3.6-3 for species j and for H + in equation 4.4-9 yields the standard transformed Gibbs energy of formation of species j as a function of pH and ionic strength at 298.15 K ... 

Note that the standard transformed Gibbs energy of formation of a species depends on the pH, but the standard transformed enthalpy of formation does not. When species have electric charges, their standard thermodynamic properties need to be adjusted for the ionic strength according to the extended Debye-Huckel theory (see Section 1.3) At zero ionic strength,... 

The calculation of Af G° and Af H° of species from experimental data on apparent equilibrium constants and transformed enthalpies of reaction is described in R. A. Alberty, Thermodynamics of Biochemical Reactions, Wiley, Hoboken, NJ (2003) and a number of places in the literature. That is not discussed here because this package is oriented toward the derivation of mathematical functions to calculate thermodynamic properties at specified T, pH, and ionic strength. There are two types of biochemical reactants in the database ... 

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