Further transformed Gibbs energy

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]. 

The standard further transformed Gibbs energies of formation of the pseudoisomers can be calculated using equation 6.5-2 and can be written in the form... 

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...

Table 6.3 Standard Further Transformed Gibbs Energies of Formation of C(, and C, at pH 7 Ionic Strength 0.25 M for Different Specified Concentrations of ATP...

Further Transformed Gibbs Energy at Specified Oxygen Concentration... 

FURTHER TRANSFORMED GIBBS ENERGY AT SPECIFIED OXYGEN CONCENTRATION... 

In order to introduce the chemical potential of molecular oxygen as a natural variable, the following Legendre transform is used to define a further transformed Gibbs energy G" (Alberty, 1996b) ... 

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...

The further transformed Gibbs energy G" for a biochemical rection system at specified pH and specified concentrations of certain coenzymes is given by... 

The standard further transformed Gibbs energies of formation in kJ mol 1 are... 

This calculation using equcalcc involves the problem that Af G° H2 O) is used in the calculation of the equilibrium constant K, but the expression for the equilibrium constant does not involve the concentration of H2 O. Thus in effect oxygen atoms are not conserved, because in dilute aqueous solutions they are drawn for th essentially infinite reservoir of the solvent. Therefore, the further transformed Gibbs energy G has to be used. The conservation matrix with C and P as components and GlcP2-, Glc, and HP042"as species is given by... 

Use the equilibrium constants in equations 7.3-2 and 7.3-3 to calculate the further transformed Gibbs energies of formation of the forms of the dimer of hemoglobin and of the pseudoisomer group at [02] = 5 xlO"6, 10"5, and 2 xlO"5M. Make a table with the last three columns and first four rows of Table 7.3. 

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