Free energy change for

The enthalpy, entropy and free energy changes for an isothennal reaction near 0 K caimot be measured directly because of the impossibility of carrying out the reaction reversibly in a reasonable time. One can, however, by a suitable combination of measured values, calculate them indirectly. In particular, if the value of... 

Let us now consider the reduction of a metal oxide by carbon which is itself oxidised to carbon monoxide. The reaction will become energetically feasible when the free energy change for the combined process is negative (see also Figure i.i). Free energies. 

Since the net free energy change for the cycle is zero, the difference between the computable free energies for transforming L to if, when bound to protein and when dissolved in water, is equal to the difference between the measurable standard free energies of binding L and if to protein, i.e., the difference in affinity... 

The dependence of the mean work performed in the extraction for diflferent extraction times is shown in Fig. 3. One sees that in very rapid extractions a very large amount of work is required to overcome the friction, which decreases as the extraction is done more slowly ultimately, only a small amount of work remains to be done to compensate the free energy change for transferring the hydrophobic ligand into the solvent. In a simple system, the friction... 

The standard free energy changes for the process graphite and... 

At equilibrium, the ratio of concentrations is an equilibrium constant, so we can write the standard free energy change for the process as... 

The free energy change for non-standard-state concentrations is given by... 

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. 

The equilibrium constants determined by Brandts at several temperatures for the denaturation of chymotrypsinogen (see previous Example) can be used to calculate the free energy changes for the denaturation process. For example, the equilibrium constant at 54.5°C is 0.27, so... 

Equation (3.12) shows that the free energy change for a reaction can be very different from the standard-state value if the concentrations of reactants and products differ significantly from unit activity (1 Mfor solutions). The effects can often be dramatic. Consider the hydrolysis of phosphocreatine ... 

We can predict whether pairs of coupled reactions will proceed spontaneously by simply summing the free energy changes for each reaction. For example, consider the reaction from glycolysis (discussed in Chapter 19)... 

Calculate the free energy change for acetyl phosphate hydrolysis in a solution of 2 mM acetate, 2 mM phosphate, and 3 iiM acetyl phosphate. 

If the AG° for this reaction is —30.5 kJ/mol, what is AG° (that is, the free energy change for the same reaction with all components, including H, at a standard state of 1 AT) ... 

The process of glycolysis converts some, but not all, of the metabolic energy of the glucose molecule into ATP. The free energy change for the conversion of glucose to two molecules of lactate (the anaerobic route shown in Figure 19.1) is -183.6 kj/mol ... 

Under cellular conditions, this first reaction of glycolysis is even more favorable than at standard state. As pointed out in Chapter 3, the free energy change for any reaction depends on the concentrations of reactants and products. 

FIGURE 19.28 The conversion of phosphoenolpyrnvate (PEP) to pyrnvate may be viewed as involving two steps phosphoryl transfer followed by an enol-keto tantomeriza-don. The tantomerizadon is spontaneons (AG -35-40 kJ/mol) and acconntsfor mnch of the free energy change for PEP hydrolysis. 

Enolase catalyzes the conversion of 2-phosphoglycerate to phosphoenolpyrnvate + H9O. The standard free energy change, AG°, for this reaction is +1.8 kj/mol. If the concentration of 2-phosphoglycerate is 0.045 mM and the concentration of phosphoenolpyrnvate is 0.034 mM, what is AG, the free energy change for the enolase reaction, under these conditions ... 

We have already noted that the standard free energy change for a reaction, AG°, does not reflect the actual conditions in a ceil, where reactants and products are not at standard-state concentrations (1 M). Equation 3.12 was introduced to permit calculations of actual free energy changes under non-standard-state conditions. Similarly, standard reduction potentials for redox couples must be modified to account for the actual concentrations of the oxidized and reduced species. For any redox couple. 

Calculate the value of A l,/ for the glyceraldehyde-3-phos-phate dehydrogenase reaction, and calculate the free energy change for the reaction under standard-state conditions. 

Remembering that AC = -nEF, it follows that the standard free energy change for the half reaction is AC° = -nE°F. e.g. ... 

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