Standard-state free-energy change

In any of these forms, this relationship allows the standard-state free energy change for any process to be determined if the equilibrium constant is known. More importantly, it states that the equilibrium established for a reaction in solution is a function of the standard-state free energy change for the process. That is, AG° is another way of writing an equilibrium constant. 

Hexokinase catalyzes the phosphorylation of glucose from ATP, yielding glncose-6-P and ADR Using the values of Table 3.3, calculate the standard-state free energy change and equilibrium constant for the hexokinase reaction. 

Using the well known relation between an equilibrium constant and the standard state free energy change for the reaction, AG° = —RT In K, one can re-write this equation as... 

It appears that there are two temperatures of a universal nature that describe the thermodynamic properties for the dissolution of liquid hydrocarbons into water. The first of these, 7h is the temperature at which the heat of solution is zero and has a value of approximately 20°C for a variety of liquids. The second universal temperature is Ts, where the standard-state entropy change is zero and, as noted, Ts is about 140°C. The standard-state free energy change can be expressed in terms of these two temperatures, requiring knowledge only of the heat capacity change for an individual substance... 

Many biological processes involve hydrogen ions the standard state of an H+ solution is (by definition) a 1 mol L"1 solution, which would have a pH of nearly 0, a condition incompatible with most forms of life. Hence, it is convenient to define the biochemical standard state for solutes, in which all components except H+ are at 1 mol L-1, and H+ is present at 10 7mol L (i.e., pH 7). Biochemical standard-state free energy changes are symbolized by AG0, and the other thermodynamic parameters are indicated analogously (AH0, AS0, etc.). 

When the ion appears as a substrate or product, its standard-state concentration is also taken as 1 M (i.e., pH = 0). However, almost all enzymes are denatured at pH 0 and, consequently, there is no reaction to study. Because of this, biochemists have adopted a modified standard-state in which all substrates and products except H" are considered to be 1 M. The H ion concentration is taken to be some physiological value (e.g., 10 M). The relationship between AG and the modified standard-state free energy change, designated AG, can-be easily calculated. For example, consider a reaction that yields an ion as a product. 

Measuring the equilibrium constant for Tyr binding to the enzyme provided a direct measurement of the standard state free energy change ... 

Standard State Free Energy Change AG = AG + RTln([products]/[reactants])... 

Fig. 4. Standard state free-energy changes for an enzyme-catalysed reaction showing saturation kinetics, (Eqn. 36), with the standard state chosen so that the reaction occurs above saturation.

Fig. 6. Standard state free-energy changes for a reaction with the same transition state in the absence and presence of enzyme. Hypothetical case where the enzyme-substrate (in the ground state) and enzyme-transition state complexes are equally stabilised. There can be no catalysis either above saturation (a) or below saturation (b).

One identifies the stoichiometric-coefficient-weighted sum of pure-component chemical potentials in the reference states, at unit fugacity, with the standard-state free-energy change for chemical reaction, since [pi, pure(/ )l° is equivalent to the molar Gibbs free energy of pure component i in this reference state. Hence,... 

Table 1. Standard state free energy changes and equilibrium...

Fig. 7. Standard state free-energy changes for a series of enzyme-catalysed reactions where the substrate (or enzyme) is modified so that the ground states and transition states are equally stabilised by the modification. There can be no catalysis above saturation (a). There is a limited amount of catalysis (see text) bdow saturation (b).

From the equilibrium constant, the standard-state free energy change... 

The location of the GTS corresponding to this minimum flux can be interpreted as a dynamical bottleneck to the reaction, in that it includes both entropic effects (associated with the ratio of the partition functions for the GTS and the reactants) and zero-point energy effects as well as the energetic effects in Vj ep(s)- In addition, since this minimum corresponds to a maximum in the generalized standard-state free energy change for the formation of the GTS at s from the reactants, AG (T,s) [42,44,47,78,79], the CVT approach can also be applied to reactions in which V, Ep(s) does not exhibit a barrier between the reactants and products. 

The molar standard-state free-energy change of a reaction (AG°) is a function of the equilibrium constant K) and is related to changes in the molar standard-state enthalpy (AH°) and entropy (A5°), as described by the Gibbs-Helmholtz equation ... 

Given(Sandler) Standard state free energy change 685 cal/mol d(gmphite) 2.25 g/cm d(diamond) 3.51 g/cm. Assume both substances to be incompressible. 

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