Transformed Gibbs energy thermodynamic properties

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 ... 

Statistical mechanics is often thought of as a way to predict the thermodynamic properties of molecules from their microscopic properties, but statistical mechnics is more than that because it provides a complementary way of looking at thermodynamics. The transformed Gibbs energy G for a biochemical reaction system at specified pH is given by... 

These tables have been given to 0.01 kJ mol-1. In general this overemphasizes the accuracy with which these formation properties are known. However for some reactants for which species are in classical tables, this accuracy is warranted. An error of 0.01 kJ mol-1 in the standard transformed Gibbs energy of a reaction at 298 K corresponds with an error of about 1 % in the value of the apparent equilibrium constant. It is important to understand that the large number of digits in these tables is required because the thermodynamic information is in differences between entries. 

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. 

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,... 

Thus measurements of Af G, ° and Af //, ° at a single temperature yield Af 5, ° at that temperature. In the next chapter we will see that if Af //, ° is known, the standard transformed Gibbs energy of formation can be expressed as a function of temperature, and then all the other thermodynamic properties can be calculated by taking partial derivatives of this function. Note that in equations 3.4-5 to 3.4-9, the only Maxwell relation that does not involve a partial derivative with respect to the temperature is the one that yields Fh (0-... 

Chapters 1 and 2 dealt with species properties. But in this chapter we have found that when the pH is specified, it is necessary to use a Legendre transform to define a transformed Gibbs energy G of a system and that this automatically brings in a transformed enthalpy H and transformed entropy S. In fact we have entered a whole new world of thermodynamics where attention is focussed on reactants, which are sums of species, rather than on species. This world of biochemical... 

At specified concentration of molecular oxygen, the five forms of hemoglobin are pseudoisomers, and they have the same further transformed Gibbs energy of formation at equilibrium. The further transformed thermodynamic properties of the tetramer can be calculated from experimental measurements of the fractional saturation, but in order to interpret experimental data, it is necessary to provide for the partial dissociation of tetramer 02 Bz into dimers a/3 (3). Seven apparent equilibrium constants are required to describe experimental data, and it is shown that all seven can be determined using limiting forms (4). 

Chemical reaction systems are discussed in terms of species, and many chemical thermodynamic properties can be calculated from the species properties given in the next section, for example pKs. However, in making calculations on enzyme-catalyzed reactions it is useful to take the pH as an independent variable. When this is done the principal thermodynamic properties of a reactant are the standard transformed Gibbs energy of formation Af G the standard transformed enthalpy of formation A( H the standard transformed entropy of formation Af 5 and the average number of hydrogen atoms in the reactant 77h. These properties are related by the following equations ... 

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