Standard Transformed Gibbs Energies

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... 

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). 

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... 

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. 

Table 6.2 Standard Transformed Gibbs Energies of Formation at 298.15 K, pH 7, and 0.25 M Ionic Strength, Standard Further Transformed Gibbs Energies of Formation at [ATP] = 10 4 M and [ADP] = 10 2 M, and Standard Further Transformed Gibbs Energies of Formation at [ATP] = 10 2 M and [ADP] = 10-2 M...

A number of biochemical reactions involve proteins as reactants, and so it is important to be able to determine the standard transformed Gibbs energies of formation of their reactive sites at specified pH. The standard transformed Gibbs energies of formation of the active sites of ferredoxin, cytochrome c, and thioredoxin are given in tables discussed earlier in Chapter 4. 

In order to calculate the standard transformed Gibbs energies of formation of the four oxygenated forms of hemoglobin, we need the value of AfG° for molecular oxygen in aqueous solution at 21.5°C. The NBS Table (1992) indicates that ArG0(O2(ao)) = 16.1 kJ mol-1 at 21.5°C. The value of ArG 0(T(O2)) is calculated using... 

The values of the standard transformed Gibbs energies of formation of the five forms of hemoglobin at specified T, P, and buffer can be used to calculate the equilibrium constants for other reactions that can be written between these forms, such as T + 402 = T(02)4. But it is also of interest to consider the tetramer of hemoglobin as an entity at a specified pressure of molecular oxygen, just as ATP is considered as an entity at a specified pH. This is discussed in the next section. 

Table 7.1 Standard Transformed Gibbs Energy of Formation AfG ° and Standard Further Transformed Gibbs Energies of Formation AfG ° of Hemoglobin Tetramer at 21.5JC, 1 bar, pH 7.4, [Cl ] = 0.2 M, and 0.2 M Ionic Strength...

Therefore, since the standard transformed Gibbs energy of formation of T is taken as zero, the standard transformed Gibbs energy of formation of D is 30.083 kJ mol - . The equilibrium constants for the dimer are given by... 

The fundamental equations for the dimer are similar to those for the tetramer. Table 7.3 gives AfG"° and AtG"°(TotD) at the same three oxygen concentrations as Table 7.1. The standard transformed Gibbs energies of formation of the three forms of the dimer are based on the convention that AfG °(T) = 0. 

Table 7.5 Standard Transformed Gibbs Energies of Formation for the Catalytic Site of Fumarase in kJ moF1 at 25 C and Ionic Strength 0.01 M...

The values of A, G ° for the catalytic site, succinate, and site-succinate calculated in this way are shown in Table 7.5. Similar calculations have been made for D-tartrate, L-tartrate, and meso-tartrate using data from Table 7.4. Since the ArG° values for these three reactants are not known, the convention has been adopted that they are equal to zero. Table 7.5 shows that standard transformed Gibbs energies of formation at specified pH values can be calculated for an unoccupied binding site and the binding site occupied by a ligand. 

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 9.3 Standard Transformed Gibbs Energies (in kJ moE ) of Reactions and Standard Apparent Reduction Potentials (in volts) at 289.15 K, 1 bar, pH 7, and Ionic Strength 0.25 M for Reactions Involved in the Methane Monooxygenase Reaction...

If these reactions were carried out in two galvanic cells in series, the electromotive force would be 0.773 + 1.166 = 1.939 V for a two electron change, and the standard transformed Gibbs energy of the overall monooxygenase reaction would be — 2 ( 1.939) = — 374.13 kJ mol-1, as expected. 

The change in binding of hydrogen ions in a biochemical reaction can be calculated from the derivative of the standard transformed Gibbs energy of... 

---