Transformed Gibbs energy

The derivation of the fundamental equation for the transformed Gibbs energy G starts with the fundamental equation 2.5-5 for the Gibbs energy written in terms of species ... 

Thus the transformed Gibbs energy is additive in the transformed chemical potentials of pseudoisomer groups just like the Gibbs energy G is additive in the chemical potentials of species (equation 2.5-12). 

When equation 4.2-4 is substituted in equation 4.2-3, the following fundamental equation is obtained for the transformed Gibbs energy ... 

The concentration of the reactant is [B] = [BJ + [B2], where [B,] and [BJ are the concentrations of the species at the given pH. The standard transformed Gibbs energy of the reactant when the acid dissociation is at equilibrium can be calculated using... 

The discussion of the standard transformed properties of a species starts with the definition of the transformed chemical potential /x of the species given by n j = fij — /Vh(/)/x(H +) (equation 4.1-4). This equation can be written in terms of Gibbs energies of formation and transformed Gibbs energies of formation 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 ... 

The standard transformed heat capacity at constant pressure of a reactant is discussed later in Chapter 10 on calorimetry. The calculation of A H ° using equation 4.5-3 looks simple, but note that the standard transformed Gibbs energies of formation of all of the species are involved in the calculation. These equations were applied to the ATP series by Alberty and Goldberg (1992). 

When transformed Gibbs energies of formation are used rather than chemical potentials, equation 4.3-4 can be written... 

Table 4.1 Standard Transformed Gibbs Energies in kJ mol 1 of Hydrolysis of ATP as a Function of Temperature, pH, and Ionic Strength...

CALCULATION OF STANDARD TRANSFORMED GIBBS ENERGIES OF SPECIES FROM EXPERIMENTAL MEASUREMENTS OF APPARENT EQUILIBRIUM CONSTANTS... 

Calculation of Standard Transformed Gibbs Energies of Species... 

Thus the fundamental equation for the transformed Gibbs energy can be written as... 

When the reactant of interest consists of two species with different numbers of hydrogen atoms, the pK of the weak acid is needed to calculate ArC °(/ = 0) of the two species, and the calculation is more complicated. The standard transformed Gibbs energy of formation of a pseudoisomer group containing two species is given by... 

The functions of pH and ionic strength that yield ArGj°, ArH °, and Ar/VH can also be used to plot these properties in terms of pH at a chosen ionic strength and in terms of ionic strength at a chosen pH. Figure 4.2 shows the dependence of the standard transformed Gibbs energy of the hydrolysis of ATP to ADP on pH. 

The Legendre transform that defines the further transformed Gibbs energy G", which provides the criterion for spontaneous change and equilibrium in dilute... 

The amount of the oxygen component in the system is given by nc(O) = LN0(i)ni, where N0(i) is the number of oxygen atoms in reactant i. p 0(H2O) is the standard transformed chemical potential for H,0 at the specified pH and ionic strength. The standard further transformed Gibbs energy of formation of reactant i is given by... 

Further transformed Gibbs energies of formation are especially useful in calculating equilibrium compositions by computer programs that accept conservation matrices and vectors of initial amounts, as discussed in the next section. 

When the concentrations of ATP and ADP are in a steady state, these concentrations can be made natural variables by use of a Legendre transform that defines a further transformed Gibbs energy G" as follows. 

These three biochemical reactions are catalyzed by hexokinase (EC 2.7.1.1), glucose-6-phosphate isomerase (EC 5.3.1.9), and 6-phosphofructokinase (EC 2.7.1.11), respectively. The EC numbers are from Enzyme Nomenclature (Webb, 1992). The first step is to write the conservation matrix for this reaction system at specified pH because that will show how to calculate the further transformed Gibbs energies of formation at specified [ATP] and [ADP]. 

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