Equilibrium constant, standard free energy related

There can be many reasons why a reaction does not proceed to equilibrium. The standard free energy, then, does not define the amount of work that will be obtained from a reaction it is the maximum energy available under defined conditions. When the standard free energy is known, it can be used to determine the equilibrium constant of a reaction. This, it must be remembered, measures the extent to which a reaction may proceed, but it does not indicate the speed of a reaction or even that a reaction will occur at all. AF is related indirectly to the relative rates of enzyme-catalyzed reactions by the Haldane relationship (p. 12), but the absolute rate of reaction is determined by the amount of enzyme and substrate in a given system. 

One of the fundamental equations of thermo dynamics concerns systems at equilibrium and relates the equilibrium constant K to the dif ference in standard free energy (A6°) between the products and the reactants... 

The standard free-energy change for a reaction M + X - MX is also related to the equilibrium constant for the corresponding reaction... 

Because the equilibrium constant, Keq, and the standard free-energy change, AG°, both measure whether a reaction is favored, they are mathematical related by the equation... 

As pointed out previously, the value of the standard cell voltage, E°, is a measure of the spontaneity of a cell reaction. In Chapter 17, we showed that the standard free energy change, AG°, is a general criterion for reaction spontaneity. As you might suppose, these two quantities have a simple relation to one another and to the equilibrium constant, K, for the cell reaction. 

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)... 

If two reactions differ in maximum work by a certain amount 8wm (= -SAG ), it follows from the Brpnsted relation [when taking into account the Arrhenius equation and the known relation between the equilibrium constant and the Gibbs standard free energy of reaction, A m = exp(-AGm/J r)] that their activation energies will differ by a fraction of this work, with the opposite sign ... 

In all metallurgical processing, heterogeneous reactions and the approach to equilibrium between two or more phases are of great importance. Much of the information on equilibrium is contained in the equilibrium constant which, as mentioned earlier, is related to the standard free energy change by the equation... 

It is instructive to consider the rationale underlying the various linear free energy correlations and to indicate in qualitative fashion how substituents may influence reaction rates. The relation between an equilibrium constant and the standard free energy change accompanying a reaction is given by... 

The equilibrium constant of a chemical reaction is related with standard free energy change AG° as... 

The Gibbs equation relates the change in a reaction s Gibbs standard free energy (AG°) to its equilibrium constant ... 

The standard free energy change of a reaction can be related to its equilibrium constant. For the reaction. 

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

The equilibrium constant is fixed and characteristic for any given chemical reaction at a specified temperature. It defines the composition of the final equilibrium mixture, regardless of the starting amounts of reactants and products. Conversely, we can calculate the equilibrium constant for a given reaction at a given temperature if the equilibrium concentrations of all its reactants and products are known. As we will show in Chapter 13, the standard free-energy change (A(3°) is directly related to Ke[Pg.61]

The Standard Free-Energy Change Is Directly Related to the Equilibrium Constant... 

For a reaction in solution, AG depends on the standard free energy change (AG°) and on the concentrations of the reactants and products. The standard free energy change is related to the equilibrium constant by the expression AG° = —/ rin Keq. Increasing the concentration of the reactants relative to the concentration of the products makes AG more negative. 

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

Kd is an important property of a receptor-ligand system. A ligand with a small KD is said to have a high affinity for the receptor. Affinity is related to binding energy, and the standard free energy of binding can be determined from the association equilibrium constant, KA, or /KV) (Equation 5.10). 

The equilibrium constant K is related to the Gibbs standard free energy change AGj by... 

The standard Gibbs energy change, AG° (still often called standard free energy, but this term should be avoided), is related to the equilibrium constant by equation (6). 

The standard free energy is also related to the equilibrium constant... 

Linear free energy relationship (LFER) — For various series of similar chemical reactions it has been empirically found that linear relationships hold between the series of free energies (-> Gibbs energy) of activation AG and the series of the standard free energies of reactions AGf, i.e., between the series of log fc (k -rate constants) and log K (Kt - equilibrium constants) (z labels the compounds of a series). Such relations correlate the - kinetics and -> thermodynamics of these reactions, and thus they are of fundamental importance. The LFER s can be formulated with the so-called Leffler-Grunwald operator dR ... 

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