Pseudoisomer groups

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). 

This equation has the same form as equation 4.1-5, which applies to a chemical reaction described in terms of species. It shows why the world of biochemical thermodynamics at specified pH looks so much like the world of chemical thermodynamics that is described by equation 4.1-5. An important difference between these equations is that the terms in the summation on the right side of equation 4.1-30 deal with pseudoisomer groups, like ATP, rather than species. 

Equation 4.1-18 can be used to derive the expression for the apparent equilibrium constant K for a biochemical reaction at a specified pH. If a single biochemical reaction is catalyzed, the amounts n of the pseudoisomer groups at each stage of the reaction are given by... 

This confirms that K is written in terms of concentrations of pseudoisomer groups and that there are no terms for hydrogen ions. When dilute aqueous solutions are considered, the convention is that [HzO] is omitted, but the contribution for ju 0(H2O) in equation 4.2-8 is included. 

The standard transformed enthalpy of formation of the pseudoisomer group is a... 

Note that although AfH ° values for species are independent of pH, this is not true for Af/T ° values of reactants consisting of two or more species because the r are functions of pH. The pseudoisomer group has a corresponding standard transformed entropy of formation given by... 

When a system contains a single pseudoisomer group, equation 4.1-18 shows that... 

The summation in equation 4.10-3 can be written in terms of species exclusive of the hydrogen ion because when species in a pseudoisomer group are in equilibrium at a specified pH, these species have the same transformed chemical potential. 

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 product of the apparent conservation matrix A and the column vector of amounts of reactants (pseudoisomer groups) gives the column vector ric of the amounts of the apparent components ... 

It can be shown that when the reactions of ATP and ADP with reactants in the system are at equilibrium, the further transformed chemical potentials of some of the reactants are equal these reactants form a pseudoisomer group with amount it". Thus holding [ATP] and [ADP] constant makes it possible to reconceptualize the system into a smaller set of pseudoisomer groups specifically, the number of... 

The fundamental equation for G" given in equation 6.5-10 leads to several new types of relations between properties. First consider the equation for dG" for a system containing a single pseudoisomer group that is, the summation is replaced with ArG"sodn"0. The Maxwell equation between this term and the term in dpH is... 

The expressions for apparent equilibrium constants K" are written in terms of concentrations of the N" pseudoisomer groups thus [ATP] and [ADP] do not appear explicitly in equilibrium constant expressions for the system. The criterion... 

The standard transformed enthalpy of formation of a pseudoisomer group is given by equation 10.2-3. The standard transformed Gibbs energy of formation is given by... 

In Chapter 4 the effects of temperature on Af G ° and AfH ° and on ArG ° and ArH ° are discussed on the basis of the assumption that A,H° at zero ionic strength is independent of temperature. Therefore the effects of heat capacities of species were not treated. When a biochemical reactant contains two or more species, the standard transformed molar heat capacity of the pseudoisomer group is given by (Alberty, 1983a)... 

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