Thermodynamics standard free-energy changes

Cell Volta.ge a.ndIts Components. The minimum voltage required for electrolysis to begin for a given set of cell conditions, such as an operational temperature of 95°C, is the sum of the cathodic and anodic reversible potentials and is known as the thermodynamic decomposition voltage, is related to the standard free energy change, AG°C, for the overall chemical reaction,... 

Though LFERs are not a necessary consequence of thermodynamics, their occurrence suggests the presence of a real connection between the correlated quantities, and the nature of this connection can be explored. This treatment follows Leffler and Grunwald. - PP Standard free energy changes AG° will pertain to either... 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

The selective binding of molecules to form productive complexes is of central importance to pharmacology and medicinal chemistry. Although kinetic factors can influence the yields of different molecular complexes in cellular and other non-equilibrium environments,1 the primary factors that one must consider in the analysis of molecular recognition are thermodynamic. In particular, the equilibrium constant for the binding of molecules A and B to form the complex AB depends exponentially on the standard free energy change associated with complexation. 

Biochemical reactions are basically the same as other chemical organic reactions with their thermodynamic and mechanistic characteristics, but they have the enzyme stage. Laws of thermodynamics, standard energy status and standard free energy change, reduction-oxidation (redox) and electrochemical potential equations are applicable to these reactions. Enzymes catalyse reactions and induce them to be much faster . Enzymes are classified by international... 

K is related to the standard free energy change in going from reactants to the transition state, AG" by the usual thermodynamic relationship ... 

Equations (16)-(18) contain two terms the first one is a function of the concentrations of the species involved in Eqs. (3"), (4"), and (11), while the second is a function of the activity coefficients of these species. The measurement of the standard free energy changes for these processes involves the determination of both concentration and activity terms. Whenever both terms can be accurately determined, the corresponding pKs are referred to as thermodynamic, that is, based on the standard state defined in Section III,F. 

Perhaps the most important equation relates the thermodynamic equilibrium constant K° to the standard free energy change AG° of the reaction ... 

Before we go on to define the acidity constant of a given organic acid in water, we need to introduce a thermodynamic convention for scaling such constants. We do this relative to H30+ in that we define the dissociation of H30+ in water to have a standard free-energy change ArG° = 0, which means that the equilibrium constant of this reaction is equal to 1 ... 

The free energy function dominates most discussions of thermodynamics in biochemistry. Not only does the sign of AG determine the direction in which a reaction proceeds, but the magnitude of AG indicates just how far the reaction must proceed before the system comes to equilibrium. This is because the standard free energy change AG° has a simple relationship to the equilibrium constant. We elaborate on... 

Fructose-1,6-bisphosphate is converted to fructose-6-phos-phate by hydrolysis of the phosphoryl ester bond at C-l in a reaction catalyzed by fructose bisphosphate phosphatase. The standard free energy change for this reaction is about —4 keal/mol, corresponding to an equilibrium constant of about 103. Thus, the two conversions (the phosphorylation of fructose-6-phosphate to form fructose 1,6-bisphosphate with ATP as the phosphate donor, and the hydrolysis of fructose-bisphosphate to form fructose-6-phosphate) are both thermodynamically favored under any conditions that are likely to exist in a living cell. These two reactions constitute a pseudocycle and, consistent with the principles enunciated in the previous chapter, the pathways have evolved so the number of ATP-to-ADP conversions is greater in one direction than in the other. 

We have from equilibrium thermodynamics Relation 3.50 between standard free-energy change, AG°, and equilibrium constant, K, and from transition-state... 

The equation AG° = —RT In K is one of the most important relationships in chemical thermodynamics because it allows us to calculate the equilibrium constant for a reaction from the standard free-energy change, or vice versa. This relationship is especially useful when K is difficult to measure. Consider a reaction so slow that it takes more than an experimenter s lifetime to reach equilibrium or a reaction that goes essentially to completion, so that the equilibrium concentrations of the reactants are extremely small and hard to measure. We can t measure K directly in such cases, but we can calculate its value from AG°. 

Equation (16-7) is a remarkable statement. It implies that Qeq, the value of the reaction quotient under equilibrium conditions, depends only on thermodynamic quantities that are constant in the reaction (the temperature, and the standard free-energy change for the reaction at that temperature), and is independent of the actual starting concentrations of reactants or products. For this reason, Qeq is usually denoted the equilibrium constant, K, and (16-7) is rewritten as... 

Figure 2.8. The standard free energy change of a reaction depends on the temperature and the pressure. (See Table 2.5 for illustrative data on the standard free energy change for the ionization of water.) d G° dT)p = —AS° and (dAG°/dP)r = AV° are the thermodynamic relationships governing the influence of temperature and pressure on free energy of a reaction.

Because the concentration (activity) of water is essentially constant in dilute aqueous solutions (a mole fraction of unity), the hydration of the proton can be ignored in defining acid-base equilibria. Because the equilibrium activity of the proton and of H30 are not known separately, the thermodynamic convention sets the standard free energy change AG for reaction 10 equal to zero that is, Kt, = 1. In dealing with dilute solutions we can, because of this convention, represent the aquo hydrogen ion by H (aq), or more conveniently by H" that is. 

This is one of the most important equations in chemical thermodynamics it shows that the equilibrium constant is determined entirely by the standard free energy change. At the same time it provides another experimental method of determining standard free energies. 

---