Relating AG to the Equilibrium Constant

To be precise,/(is defined in terms of activities, which are dimensionless quantities numerically equal to effective concentrations and pressures. 

One of the most important results of chemical thermodynamics is an equation relating the standard free-energy change for a reaction to the equilibrium constant. Before we look at this equation, we must discuss the thermodynamic form of the equilibrium constant that occurs in that equation. 

The thermodynamic equilibrium constant, K, is the equilibrium constant in which the concentrations of gases are expressed in partial pressures in atmospheres, whereas the concentrations of solutes in liquid solutions are expressed in molarities. For a reaction involving only solutes in liquid solution, K is identical to Kp, for reactions involving only gases, K equals Kp.  

Write expressions for the thermodynamic equilibrium constants for each of the following reactions  

SOLUTION a. Note that H2O is a solvent, so it does not appear explicitly in K. The gases appear in K as partial pressures, and the solute appears as a molar concentration. 

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In Section 18.6 we will see an equation relating AG to the equilibrium constant K. 

You can derive the equation relating AG° to the equilibrium constant K from the preceding equation. In the previous section, you saw that as a chemical reaction approaches equilibrium, the free energy decreases and continues to decrease until equilibrium is reached. At equilibrium, the free energy ceases to change then AG = 0. Also, the reaction quotient Q becomes equal to the equilibrimn constant K. If you substitute AG = 0 and Q = K into the preceding equation, you obtain... 

Free Energy and Equilibrium Relating AG to the Equilibrium Constant (K) 845... 

AG=AH— TAS, where AH is the change in enthalpy, T is the temperature in Kelvin (K) and AS is the entropy change A second equation relates AG to the equilibrium constant. 

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)... 

Now we can relate Rew to the equilibrium constant (K) of a redox reaction. In Section 10.3, we saw that the standard free-energy change AG° for a reaction is related to its equilibrium constant as follows (Equation 10.12) ... 

Furthermore, the value of AG is related to the equilibrium constant K for the reaction... 

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. 

The free energy AG can also be related to the equilibrium constant K between the free and the bound state of drug and receptor ... 

Overall energy difference between reactants and products. When AG° is negative, a reaction can occur spontaneously. AG° is related to the equilibrium constant by the equation AG° = -RUnKeq... 

The extension of thermodynamic calculations to low temperatures requires knowledge of how the equilibrium composition of a mixture, which varies at different temperatures, can be derived from the standard relation between AG and the equilibrium constant (Equation 8.12) to give the van t Hoff equation for the variation of the equilibrium constant with temperature ... 

With the definition of the activity function, we could derive a general expression that relates AG of a reaction to the equilibrium constant and hence to eliminate the restrictions imposed on previous relationships. 

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

The change in free energy associated with a reaction is related to the equilibrium constant for that reaction (see the preceding section for more about the equilibrium constant), so you can convert between AG and... 

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. 

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). 

But as we have seen, AG° is also related to the equilibrium constant as shown in Equation (4.10),... 

When it is zero, the reaction is in equilibrium and the standard free enei, AG , is related to the equilibrium constant [2]... 

For non-standard conditions we can find the free energy of a reaction using AG = AG° RT InQ. For the special case of equilibrium, the free energy is zero, so AG° = -RT InK, AG° = -5700 log K (in joules). Thus free energy is related to the equilibrium constant, K. 

The transition state theory gives us a framework to relate the kinetics of a reaction with the thermodynamic properties of the activated complex (Brezonik, 1990). In kinetics, one attempts to interpret the stoichiometric reaction in terms of elementary reaction steps and their free energies, to assess breaking and formation of new bonds, and to evaluate the characteristics of activated complexes. If, in a series of related reactions, we know the rate-determining ele-mentaiy reaction steps, a relationship between the rate constant of the reaction, k (or of the free energies of activation, AG ), and the equilibrium constant of the reaction step, K (or the free energy, AG°), can often be obtained. For two related reactions. 

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